Arch Capital (ACGL) 10-K 28 Feb 20 2019 FY Annual report Financial data

Document and Entity Information

Document and Entity Information - USD ($) $ in Billions	12 Months Ended
	Dec. 31, 2019	Feb. 25, 2020	Jun. 30, 2019
Document and Entity Information [Abstract]
Document Type	10-K
Document Annual Report	true
Amendment Flag	false
Document Transition Report	false
Document Period End Date	Dec. 31, 2019
Entity File Number	001-16209
Entity Registrant Name	ARCH CAPITAL GROUP LTD.
Entity Incorporation, State or Country Code	D0
Entity Tax Identification Number	98-0374481
Entity Address, Address Line One	Waterloo House, Ground Floor
Entity Address, Address Line Two	100 Pitts Bay Road,
Entity Address, City or Town	Pembroke
Entity Address, Postal Zip Code	HM 08,
Entity Address, Country	BM
City Area Code	(441)
Local Phone Number	278-9250
Entity Listings [Line Items]
Entity Well-known Seasoned Issuer	Yes
Entity Voluntary Filers	No
Entity Current Reporting Status	Yes
Entity Interactive Data Current	Yes
Entity Filer Category	Large Accelerated Filer
Entity Small Business	false
Entity Emerging Growth Company	false
Entity Shell Company	false
Entity Public Float			$ 14.6
Entity Common Stock, Shares Outstanding		406,658,701
Documents Incorporated by Reference	Portions of Part III and Part IV incorporate by reference our definitive proxy statement for the 2020 annual meeting of shareholders to be filed with the Securities and Exchange Commission pursuant to Regulation 14A before May 1, 2020.
Entity Central Index Key	0000947484
Current Fiscal Year End Date	--12-31
Document Fiscal Year Focus	2019
Document Fiscal Period Focus	FY
Common shares
Entity Listings [Line Items]
Title of 12(b) Security	Common Shares, $0.0011 par value per share
Trading Symbol	ACGL
Security Exchange Name	NASDAQ
Depositary Series E preferred shares
Entity Listings [Line Items]
Title of 12(b) Security	Depositary shares, each representing a 1/1,000th interest in a 5.25% Series E preferred share
Trading Symbol	ACGLP
Security Exchange Name	NASDAQ
Depositary Series F preferred shares
Entity Listings [Line Items]
Title of 12(b) Security	Depositary shares, each representing a 1/1,000th interest in a 5.45% Series F preferred share
Trading Symbol	ACGLO
Security Exchange Name	NASDAQ

Consolidated Balance Sheets

Consolidated Balance Sheets - USD ($) $ in Thousands	Dec. 31, 2019	Dec. 31, 2018
Investments:
Fixed maturities available for sale, at fair value (amortized cost: $16,598,808 and $14,829,902)	$ 16,894,526	$ 14,699,010
Short-term investments available for sale, at fair value (amortized cost: $957,283 and $956,238)	956,546	955,880
Collateral received under securities lending, at fair value (amortized cost: $388,366 and $274,125)	388,376	274,133
Equity securities, at fair value	838,925	338,899
Investments accounted for using the fair value option	3,663,477	3,983,571
Investments accounted for using the equity method	1,660,396	1,493,791
Total investments	24,402,246	21,745,284
Cash	726,230	646,556
Accrued investment income	117,937	114,641
Securities pledged under securities lending, at fair value (amortized cost: $378,738 and $266,786)	379,868	268,395
Premiums receivable	1,778,717	1,299,150
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	4,346,816	2,919,372
Contractholder receivables	2,119,460	2,079,111
Ceded unearned premiums	1,234,683	975,469
Deferred acquisition costs	633,400	569,574
Receivable for securities sold	24,133	36,246
Goodwill and intangible assets	738,083	634,920
Other assets	1,383,788	929,611
Total assets	37,885,361	32,218,329
Liabilities
Reserve for losses and loss adjustment expenses	13,891,842	11,853,297
Unearned premiums	4,339,549	3,753,636
Reinsurance balances payable	667,072	393,107
Contractholder payables	2,119,460	2,079,111
Collateral held for insured obligations	206,698	236,630
Senior notes	1,871,626	1,733,528
Revolving credit agreement borrowings	484,287	455,682
Securities lending payable	388,366	274,125
Payable for securities purchased	87,579	90,034
Other liabilities	1,513,330	911,500
Total liabilities	25,569,809	21,780,650
Commitments and Contingencies
Redeemable noncontrolling interests	55,404	206,292
Shareholders’ Equity
Non-cumulative preferred shares	780,000	780,000
Common shares ($0.0011 par, shares issued: 574,617,195 and 570,737,283)	638	634
Additional paid-in capital	1,889,683	1,793,781
Retained earnings	11,021,006	9,426,299
Accumulated other comprehensive income (loss), net of deferred income tax	212,091	(178,720)
Common shares held in treasury, at cost (shares: 168,997,994 and 168,282,449)	(2,406,047)	(2,382,167)
Total shareholders' equity available to Arch	11,497,371	9,439,827
Non-redeemable noncontrolling interests	762,777	791,560
Total shareholders' equity	12,260,148	10,231,387
Total liabilities, noncontrolling interests and shareholders' equity	$ 37,885,361	$ 32,218,329

Consolidated Balance Sheets (Pa

Consolidated Balance Sheets (Parentheticals) - USD ($) $ in Thousands	Dec. 31, 2019	Dec. 31, 2018
Fixed maturities available for sale, at amortized cost	$ 16,598,808	$ 14,829,902
Short-term investments available for sale, at amortized cost	957,283	956,238
Collateral received under securities lending agreements, at amortized cost	388,366	274,125
Securities pledged under securities lending, at amortized cost	$ 378,738	$ 266,786
Common shares, par value per share	$ 0.0011	$ 0.0011
Common shares issued (shares)	574,617,195	570,737,283
Common shares held in treasury (shares)	168,997,994	168,282,449

Consolidated Statements of Inco

Consolidated Statements of Income - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Revenues
Net premiums written	$ 1,455,453	$ 1,613,457	$ 1,444,898	$ 1,525,259	$ 1,301,754	$ 1,333,553	$ 1,298,896	$ 1,412,544	$ 6,039,067	$ 5,346,747	$ 4,961,373
Change in unearned premiums									(252,569)	(114,772)	(116,841)
Net premiums earned	1,515,882	1,438,023	1,463,727	1,368,866	1,369,435	1,290,878	1,336,763	1,234,899	5,786,498	5,231,975	4,844,532
Net investment income	154,263	161,488	155,038	156,949	157,217	144,024	135,668	126,724	627,738	563,633	470,872
Net realized gains (losses)	41,474	62,518	120,806	141,565	(166,030)	(51,705)	(76,611)	(110,998)	366,363	(405,344)	149,141
Net impairment losses recognized in earnings	(644)	(1,163)	(49)	(1,309)	(1,705)	(492)	(470)	(162)	(3,165)	(2,829)	(7,138)
Other underwriting income									24,861	15,073	30,253
Equity in net income of investments accounted for using the equity method									123,672	45,641	142,286
Other income (loss)									2,233	2,419	(2,571)
Total revenues									6,928,200	5,450,568	5,627,375
Expenses
Losses and loss adjustment expenses									3,133,452	2,890,106	2,967,446
Acquisition expenses									840,945	805,135	775,458
Other operating expenses									800,997	677,809	684,451
Corporate expenses									80,111	78,994	83,752
Amortization of intangible assets									82,104	105,670	125,778
Interest expense									120,872	120,484	117,431
Net foreign exchange losses (gains)									20,609	(69,402)	115,782
Total expenses									5,079,090	4,608,796	4,870,098
Income (loss) before income taxes									1,849,110	841,772	757,277
Current tax expense (benefit)									144,361	85,863	(45,736)
Deferred tax expense (benefit)									11,449	28,088	173,304
Income tax expense									155,810	113,951	127,568
Net income	326,384	392,453	468,954	448,528	136,494	227,408	243,646	150,423	1,693,300	727,821	629,709
Net (income) loss attributable to noncontrolling interests									(56,981)	30,150	(10,431)
Net income available to Arch									1,636,319	757,971	619,278
Preferred dividends	(10,403)	(10,403)	(10,403)	(10,403)	(10,403)	(10,402)	(10,403)	(10,437)	(41,612)	(41,645)	(46,041)
Loss on redemption of preferred shares									0	(2,710)	(6,735)
Net income available to Arch common shareholders	$ 315,981	$ 382,050	$ 458,551	$ 438,125	$ 126,091	$ 217,006	$ 233,243	$ 137,276	$ 1,594,707	$ 713,616	$ 566,502
Net income per common share and common share equivalent
Basic (per share)	$ 0.78	$ 0.95	$ 1.14	$ 1.09	$ 0.31	$ 0.54	$ 0.58	$ 0.34	$ 3.97	$ 1.76	$ 1.40
Diluted (per share)	$ 0.76	$ 0.92	$ 1.12	$ 1.07	$ 0.31	$ 0.53	$ 0.56	$ 0.33	$ 3.87	$ 1.73	$ 1.36
Weighted average common shares and common share equivalents outstanding
Basic (shares)									401,802,815	404,347,621	404,138,364
Diluted (shares)									411,609,478	412,906,478	417,785,025

Consolidated Statements of Comp

Consolidated Statements of Comprehensive Income - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Comprehensive Income
Net income	$ 1,693,300	$ 727,821	$ 629,709
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during year	500,771	(270,057)	252,904
Reclassification of net realized gains, included in net income	(118,941)	144,573	(67,863)
Foreign currency translation adjustments	18,110	(24,830)	47,014
Comprehensive income	2,093,240	577,507	861,764
Net (income) loss attributable to noncontrolling interests	(56,981)	30,150	(10,431)
Other comprehensive (income) loss attributable to noncontrolling interests	(9,130)	3,346	530
Comprehensive income available to Arch	$ 2,027,129	$ 611,003	$ 851,863

Consolidated Statements of Chan

Consolidated Statements of Changes in Shareholders' Equity - USD ($) $ in Thousands	Total	Non-cumulative preferred shares	Common shares	Additional paid-in capital	Retained earnings	Accumulated other comprehensive income (loss)	Unrealized appreciation (decline) in value of available-for-sale investments, net of deferred income tax	Foreign currency translation adjustments, net of deferred income tax	Common shares held in treasury, at cost	Convertible non-voting common equivalent preferred shares
Balance at beginning of year at Dec. 31, 2016		$ 772,555	$ 582	$ 531,687	$ 7,996,701	$ (114,541)	$ (27,641)	$ (86,900)	$ (2,034,570)	$ 1,101,304
Cumulative effect of an accounting change at Dec. 31, 2016					(314)		0
Balance at beginning of year, as adjusted at Dec. 31, 2016					7,996,387		(27,641)
Preferred shares issued		330,000
Preferred shares redeemed		(230,000)
Preferred shares converted to common shares				611,653						(611,677)
Common shares issued, net			29
Other				87,277
Net income	$ 629,709				629,709
Net (income) loss attributable to noncontrolling interests	(10,431)				(10,431)
Preferred dividends	(46,041)				(46,041)
Loss on redemption of preferred shares	(6,735)				(6,735)
Unrealized holding gains (losses) during period, net of reclassification adjustment							185,041
Unrealized holding gains (losses) during period attributable to noncontrolling interests							0
Foreign currency translation adjustments	47,014							47,014
Foreign currency translation adjustments attributable to noncontrolling interests								530
Shares repurchased for treasury	0								(43,171)
Balance at end of year at Dec. 31, 2017	9,196,602	872,555	611	1,230,617	8,562,889	118,044	157,400	(39,356)	(2,077,741)	489,627
Non-redeemable noncontrolling interests	843,411
Total shareholders' equity	10,040,013
Cumulative effect of an accounting change at Dec. 31, 2017	(149,794)				149,794		(149,794)	0
Balance at beginning of year, as adjusted at Dec. 31, 2017					8,712,683		7,606
Preferred shares issued		0
Preferred shares redeemed		(92,555)
Preferred shares converted to common shares				489,608						(489,627)
Common shares issued, net			23
Other				73,556
Net income	727,821				727,821
Net (income) loss attributable to noncontrolling interests	30,150				30,150
Preferred dividends	(41,645)				(41,645)
Loss on redemption of preferred shares	(2,710)				(2,710)
Unrealized holding gains (losses) during period, net of reclassification adjustment							(125,484)
Unrealized holding gains (losses) during period attributable to noncontrolling interests							3,700
Foreign currency translation adjustments	(24,830)							(24,830)
Foreign currency translation adjustments attributable to noncontrolling interests								(356)
Shares repurchased for treasury	(282,762)								(304,426)
Balance at end of year at Dec. 31, 2018	9,439,827	780,000	634	1,793,781	9,426,299	(178,720)	(114,178)	(64,542)	(2,382,167)	0
Non-redeemable noncontrolling interests	791,560
Total shareholders' equity	10,231,387
Cumulative effect of an accounting change at Dec. 31, 2018					0		0
Balance at beginning of year, as adjusted at Dec. 31, 2018					9,426,299		(114,178)
Preferred shares issued		0
Preferred shares redeemed		0
Preferred shares converted to common shares				0						0
Common shares issued, net			4
Other				95,902
Net income	1,693,300				1,693,300
Net (income) loss attributable to noncontrolling interests	(56,981)				(56,981)
Preferred dividends	(41,612)				(41,612)
Loss on redemption of preferred shares	0				0
Unrealized holding gains (losses) during period, net of reclassification adjustment							381,830
Unrealized holding gains (losses) during period attributable to noncontrolling interests							(9,166)
Foreign currency translation adjustments	18,110							18,110
Foreign currency translation adjustments attributable to noncontrolling interests								37
Shares repurchased for treasury	(2,871)								(23,880)
Balance at end of year at Dec. 31, 2019	11,497,371	$ 780,000	$ 638	$ 1,889,683	$ 11,021,006	$ 212,091	$ 258,486	$ (46,395)	$ (2,406,047)	$ 0
Non-redeemable noncontrolling interests	762,777
Total shareholders' equity	$ 12,260,148

Consolidated Statements of Cash

Consolidated Statements of Cash Flows - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Operating Activities
Net income	$ 1,693,300	$ 727,821	$ 629,709
Adjustments to reconcile net income to net cash provided by operating activities:
Net realized (gains) losses	(381,132)	387,550	(174,517)
Net impairment losses recognized in earnings	3,165	2,829	7,138
Equity in net income or loss of investments accounted for using the equity method and other income or loss	(14,013)	36,694	(79,540)
Amortization of intangible assets	82,104	105,670	125,778
Share-based compensation	66,417	55,776	67,798
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	489,981	243,734	614,534
Unearned premiums, net of ceded unearned premiums	252,569	114,772	116,841
Premiums receivable	(237,752)	(211,296)	(31,405)
Deferred acquisition costs, net	(47,260)	(37,847)	(78,378)
Reinsurance balances payable	182,132	73,438	8,529
Other items, net	(41,052)	60,181	(111,609)
Net cash provided by operating activities	2,048,459	1,559,322	1,094,878
Investing Activities
Purchases of fixed maturity investments	(30,053,777)	(33,327,660)	(36,806,913)
Purchases of equity securities	(811,967)	(1,001,149)	(1,021,016)
Purchases of other investments	(1,470,545)	(2,014,622)	(2,020,624)
Proceeds from the sale of fixed maturity investments	28,595,865	31,513,271	35,686,779
Proceeds from sales of equity securities	429,818	1,118,445	1,056,401
Proceeds from sales, redemptions and maturities of other investments	1,209,559	1,561,958	1,528,617
Proceeds from redemptions and maturities of fixed maturity investments	643,265	892,755	907,417
Net settlements of derivative instruments	59,982	44,699	(28,563)
Net (purchases) sales of short-term investments	39,833	485,473	(734,554)
Change in cash collateral related to securities lending	(62,193)	180,883	12,540
Purchases of fixed assets	(37,837)	(29,809)	(22,841)
Other	(348,486)	21,736	90,875
Net cash provided by (used for) investing activities	(1,806,483)	(554,020)	(1,351,882)
Financing Activities
Proceeds from issuance of preferred shares, net	0	0	319,694
Redemption of preferred shares	0	(92,555)	(230,000)
Purchases of common shares under share repurchase program	(2,871)	(282,762)	0
Proceeds from common shares issued, net	6,203	(7,608)	(21,048)
Proceeds from borrowings	200,083	218,259	253,415
Repayments of borrowings	(49,182)	(576,401)	(197,000)
Change in cash collateral related to securities lending	62,193	(180,883)	(12,540)
Change in third party investment in non-redeemable noncontrolling interests	(75,056)	0	0
Change in third party investment in redeemable noncontrolling interests	(161,882)	0	0
Dividends paid to redeemable noncontrolling interests	(12,515)	(17,989)	(17,989)
Other	(6,023)	(7,226)	(51,896)
Preferred dividends paid	(41,612)	(41,645)	(46,041)
Net cash provided by (used for) financing activities	(80,662)	(988,810)	(3,405)
Effects of exchange rate changes on foreign currency cash and restricted cash	17,741	(19,133)	18,124
Increase (decrease) in cash and restricted cash	179,055	(2,641)	(242,285)
Cash and restricted cash, beginning of year	724,643	727,284	969,569
Cash and restricted cash, end of year	903,698	724,643	727,284
Supplemental cash flow information
Income taxes paid (received)	109,463	(980)	51,781
Interest paid	$ 126,945	$ 119,775	$ 117,374

General

General	12 Months Ended
	Dec. 31, 2019
Organization, Consolidation and Presentation of Financial Statements [Abstract]
General	General Arch Capital Group Ltd. (“Arch Capital”) is a Bermuda public limited liability company which provides insurance, reinsurance and mortgage insurance on a worldwide basis through its wholly owned subsidiaries. As used herein, the “Company” means Arch Capital and its subsidiaries. Similarly, “Common Shares” means the common shares of Arch Capital. The Company’s consolidated financial statements include the results of Watford Holdings Ltd., and its wholly owned subsidiaries (“Watford”). See note 11, “Variable Interest Entity and Noncontrolling Interests” .

Business Acquired

Business Acquired	12 Months Ended
	Dec. 31, 2019
Business Combinations [Abstract]
Business Acquired	Business Acquired Barbican Group Holdings Limited On November 29, 2019, the Company closed the acquisition of Barbican Group Holdings Limited and its subsidiaries (“Barbican”), including Barbican Managing Agency Limited (“BMAL”), Lloyd’s Syndicate 1955 (“Barbican Syndicate 1955”), Castel Underwriting Agencies Limited (“Castel”) and other associated entities. The Ardonagh Group On January 1, 2019, the Company’s U.K. insurance operations entered into a transaction with The Ardonagh Group to acquire renewal rights for a U.K. commercial lines book of business, consisting of commercial property, casualty, motor, professional liability, personal accident and travel business. McNeil On December 6, 2018, the Company closed the acquisition of McNeil & Co. (“McNeil”), a nationwide leader in specialized risk management and insurance programs headquartered in Cortland, New York. Arch MI Asia Limited On July 1, 2017, the Company closed the acquisition of AIG United Guaranty Insurance (Asia) Limited (renamed “Arch MI Asia Limited”) following the payment of $40.0 million

Significant Accounting Policies

Significant Accounting Policies	12 Months Ended
	Dec. 31, 2019
Accounting Policies [Abstract]
Significant accounting policies	Significant Accounting Policies (a) Basis of Presentation The consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”) and include the accounts of Arch Capital and its subsidiaries, including Arch Reinsurance Ltd. (“Arch Re Bermuda”), Arch Reinsurance Company (“Arch Re U.S.”), Arch-U.S., Arch Insurance Company, Arch Specialty Insurance Company, Arch Excess & Surplus Insurance Company, Arch Indemnity Insurance Company, Arch Insurance Canada Ltd. (“Arch Insurance Canada”), Arch Reinsurance Europe Underwriting Designated Activity Company (“Arch Re Europe”), Arch Mortgage Insurance Company, Arch Mortgage Guaranty Company, United Guaranty Residential Insurance Company, Arch Insurance (EU) Designated Activity Company (formerly, Arch Mortgage Insurance Designated Activity Company) (“Arch Insurance (EU)”), Arch Insurance (UK) Limited (formerly Arch Insurance Company (Europe) Limited)(“Arch Insurance (U.K.)”), Lloyd’s of London syndicate 2012 and related companies (“Arch Syndicate 2012”), Barbican and Watford. All significant intercompany transactions and balances have been eliminated in consolidation. The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities at the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ materially from those estimates and assumptions. The Company’s principal estimates include: • The reserve for losses and loss adjustment expenses; • Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses, including the provision for uncollectible amounts; • Estimates of written and earned premiums; • The valuation of the investment portfolio and assessment of other-than-temporary impairments (“OTTI”); • The valuation of purchased intangible assets; • The assessment of goodwill and intangible assets for impairment; and • the valuation of deferred tax assets. The Company has reclassified the presentation of certain prior year information to conform to the current presentation. Such reclassifications had no effect on the Company’s net income, shareholders’ equity or cash flows. In 2018, the shareholders approved a three -for-one stock split of the Company's common shares. All historical share and per share amounts reflect the effect of the stock split. (b) Premium Revenues and Related Expenses Insurance. Insurance premiums written are generally recorded at the policy inception and are primarily earned on a pro rata basis over the terms of the policies for all products, usually 12 months . Premiums written include estimates in the Company’s programs, specialty lines, lenders products business and for participation in involuntary pools. Such premium estimates are derived from multiple sources which include the historical experience of the underlying business, similar business and available industry information. Unearned premium reserves represent the portion of premiums written that relates to the unexpired terms of in-force insurance policies. Reinsurance. Reinsurance premiums written include amounts reported by brokers and ceding companies, supplemented by the Company’s own estimates of premiums where reports have not been received. The determination of premium estimates requires a review of the Company’s experience with the ceding companies, familiarity with each market, the timing of the reported information, an analysis and understanding of the characteristics of each line of business, and management’s judgment of the impact of various factors, including premium or loss trends, on the volume of business written and ceded to the Company. On an ongoing basis, the Company’s underwriters review the amounts reported by these third parties for reasonableness based on their experience and knowledge of the subject class of business, taking into account the Company’s historical experience with the brokers or ceding companies. In addition, reinsurance contracts under which the Company assumes business generally contain specific provisions which allow the Company to perform audits of the ceding company to ensure compliance with the terms and conditions of the contract, including accurate and timely reporting of information. Based on a review of all available information, management establishes premium estimates where reports have not been received. Premium estimates are updated when new information is received and differences between such estimates and actual amounts are recorded in the period in which estimates are changed or the actual amounts are determined. Reinsurance premiums written are recorded based on the type of contracts the Company writes. Premiums on the Company’s excess of loss and pro rata reinsurance contracts are estimated when the business is underwritten. For excess of loss contracts, premiums are recorded as written based on the terms of the contract. Estimates of premiums written under pro rata contracts are recorded in the period in which the underlying risks are expected to incept and are based on information provided by the brokers and the ceding companies. For multi-year reinsurance treaties which are payable in annual installments, generally, only the initial annual installment is included as premiums written at policy inception due to the ability of the reinsured to commute or cancel coverage during the term of the policy. The remaining annual installments are included as premiums written at each successive anniversary date within the multi-year term. Reinstatement premiums for the Company’s insurance and reinsurance operations are recognized at the time a loss event occurs, where coverage limits for the remaining life of the contract are reinstated under pre-defined contract terms. Reinstatement premiums, if obligatory, are fully earned when recognized. The accrual of reinstatement premiums is based on an estimate of losses and loss adjustment expenses, which reflects management’s judgment. Premium estimates are reviewed by management at least quarterly. Such review includes a comparison of actual reported premiums to expected ultimate premiums along with a review of the aging and collection of premium estimates. Based on management’s review, the appropriateness of the premium estimates is evaluated, and any adjustment to these estimates is recorded in the period in which it becomes known. Adjustments to premium estimates could be material and such adjustments could directly and significantly impact earnings favorably or unfavorably in the period they are determined because the estimated premium may be fully or substantially earned. A significant portion of amounts included as premiums receivable, which represent estimated premiums written, net of commissions, are not currently due based on the terms of the underlying contracts. Reinsurance premiums written, irrespective of the class of business, are generally earned on a pro rata basis over the terms of the underlying policies or reinsurance contracts. Contracts and policies written on a “losses occurring” basis cover claims that may occur during the term of the contract or policy, which is typically 12 months . Accordingly, the premium is earned evenly over the term. Contracts which are written on a “risks attaching” basis cover claims which attach to the underlying insurance policies written during the terms of such contracts. Premiums earned on such contracts usually extend beyond the original term of the reinsurance contract, typically resulting in recognition of premiums earned over a 24 -month period. Certain of the Company’s reinsurance contracts include provisions that adjust premiums or acquisition expenses based upon the experience under the contracts. Premiums written and earned, as well as related acquisition expenses, are recorded based upon the projected experience under such contracts. The Company also writes certain reinsurance business that is intended to provide insurers with risk management solutions that complement traditional reinsurance. Under these contracts, the Company assumes a measured amount of insurance risk in exchange for an anticipated margin, which is typically lower than on traditional reinsurance contracts. The terms and conditions of these contracts may include additional or return premiums based on loss experience, loss corridors, sublimits and caps. Examples of such business include aggregate stop-loss coverages, financial quota share coverages and multi-year retrospectively rated excess of loss coverages. If these contracts are deemed to transfer risk, they are accounted for as reinsurance. Otherwise, such contracts are accounted for under the deposit method. Mortgage. Mortgage guaranty insurance policies are contracts that are generally non-cancelable by the insurer, are renewable at a fixed price, and provide for payment of premiums on a monthly, annual or single basis. Upon renewal, the Company is not able to re-underwrite or re-price its policies. Consistent with industry accounting practices, premiums written on a monthly basis are earned as coverage is provided. Premiums written on an annual basis are amortized on a monthly pro rata basis over the year of coverage. Primary mortgage insurance premiums written on policies covering more than one year are referred to as single premiums. A portion of the revenue from single premiums is recognized in premiums earned in the current period, and the remaining portion is deferred as unearned premiums and earned over the estimated expiration of risk of the policy. If single premium policies related to insured loans are canceled due to repayment by the borrower and the policy is a non-refundable product, the remaining unearned premium related to each canceled policy is recognized as earned premium upon notification of the cancellation. Unearned premiums represent the portion of premiums written that is applicable to the estimated unexpired risk of insured loans. A portion of premium payments may be refundable if the insured cancels coverage, which generally occurs when the loan is repaid, the loan amortizes to a sufficiently low amount to trigger a lender permitted or legally required cancellation, or the value of the property has increased sufficiently in accordance with the terms of the contract. Premium refunds reduce premiums earned in the consolidated statements of income. Generally, only unearned premiums are refundable. Acquisition Costs. Acquisition costs that are directly related and incremental to the successful acquisition or renewal of business are deferred and amortized based on the type of contract. The Company’s insurance and reinsurance operations capitalize incremental direct external costs that result from acquiring a contract but do not capitalize salaries, benefits and other internal underwriting costs. For the Company’s mortgage insurance operations, which include a substantial direct sales force, both external and certain internal direct costs are deferred and amortized. For property and casualty insurance and reinsurance contracts, deferred acquisition costs are amortized over the period in which the related premiums are earned. Consistent with mortgage insurance industry accounting practice, amortization of acquisition costs related to the mortgage insurance contracts for each underwriting year’s book of business is recorded in proportion to estimated gross profits. Estimated gross profits are comprised of earned premiums and losses and loss adjustment expenses. For each underwriting year, the Company estimates the rate of amortization to reflect actual experience and any changes to persistency or loss development. Deferred acquisition costs are carried at their estimated realizable value and take into account anticipated losses and loss adjustment expenses, based on historical and current experience, and anticipated investment income. A premium deficiency occurs if the sum of anticipated losses and loss adjustment expenses, unamortized acquisition costs and maintenance costs exceed unearned premiums (including expected future premiums) and anticipated investment income. A premium deficiency reserve (“PDR”) is recorded by charging any unamortized acquisition costs to expense to the extent required in order to eliminate the deficiency. If the premium deficiency exceeds unamortized acquisition costs then a liability is accrued for the excess deficiency. To assess the need for a PDR on mortgage exposures, the Company develops loss projections based on modeled loan defaults related to its current policies in force. This projection is based on recent trends in default experience, severity and rates of defaulted loans moving to claim, as well as recent trends in the rate at which loans are prepaid, and incorporates anticipated interest income. Evaluating the expected profitability of the Company’s existing mortgage insurance business and the need for a PDR for its mortgage business involves significant reliance upon assumptions and estimates with regard to the likelihood, magnitude and timing of potential losses and premium revenues. No premium deficiency charges were recorded by the Company during 2019 , 2018 or 2017 . (c) Deposit Accounting Certain assumed reinsurance contracts that are deemed not to transfer insurance risk, are accounted for using the deposit method of accounting. However, it is possible that the Company could incur financial losses on such contracts. Management exercises significant judgment in the assumptions used in determining whether assumed contracts should be accounted for as reinsurance contracts or deposit contracts. For those contracts that contain only significant underwriting risk, the estimated profit margin is deferred and amortized over the contract period and such amount is included in the Company’s underwriting results. When the estimated profit margin is explicit, the margin is reflected as other underwriting income and any adverse financial results on such contracts are reflected as incurred losses. When the estimated profit margin is implicit, the margin is reflected as an offset to paid losses and any adverse financial results on such contracts are reflected as incurred losses. Additional judgments are required when applying the accounting guidance with respect to the revenue recognition criteria for contracts deemed to transfer only significant underwriting risk. For those contracts that contain only significant timing risk, an accretion rate is established at inception of the contract based on actuarial estimates whereby the deposit accounting liability is increased to the estimated amount payable over the contract term. The accretion on the deposit is based on the expected rate of return required to fund the expected future payment obligations. Periodically the Company reassesses the estimated ultimate liability and the related expected rate of return. The accretion of the deposit accounting liability as well as changes to the estimated ultimate liability and the accretion rate would be reflected as part of interest expense in the Company’s results of operations. Any negative accretion in a deposit accounting liability is shown in other underwriting income in the Company’s results of operations. Under some of these contracts, the ceding company retains the related assets on a funds-held basis. Such amounts are included in “Other assets” on the Company’s balance sheet. Interest income produced by those assets are recorded as part of net investment income in the Company's results of operations. (d) Retroactive Reinsurance Retroactive reinsurance reimburses a ceding company for liabilities incurred as a result of past insurable events covered by the underlying policies reinsured. In certain instances, reinsurance contracts cover losses both on a prospective basis and on a retroactive basis and, accordingly, the Company bifurcates the prospective and retrospective elements of these reinsurance contracts and accounts for each element separately where practical. Underwriting income generated in connection with retroactive reinsurance contracts is deferred and amortized into income over the settlement period while losses are charged to income immediately. Subsequent changes in estimated amount or timing of cash flows under such retroactive reinsurance contracts are accounted for by adjusting the previously deferred amount to the balance that would have existed had the revised estimate been available at the inception of the reinsurance transaction, with a corresponding charge or credit to income. (e) Reinsurance Ceded In the normal course of business, the Company purchases reinsurance to increase capacity and to limit the impact of individual losses and events on its underwriting results by reinsuring certain levels of risk with other insurance enterprises or reinsurers. The Company uses pro rata, excess of loss and facultative reinsurance contracts. Reinsurance ceding commissions that represent a recovery of acquisition costs are recognized as a reduction to acquisition costs while the remaining portion is deferred. The accompanying consolidated statement of income reflects premiums and losses and loss adjustment expenses and acquisition costs, net of reinsurance ceded. See note 7, “Reinsurance” for information on the Company's reinsurance usage. Reinsurance premiums ceded and unpaid losses and loss adjustment expenses recoverable are estimated in a manner consistent with that of the original policies issued and the terms of the reinsurance contracts. If the reinsurers are unable to satisfy their obligations under the agreements, the Company’s insurance or reinsurance subsidiaries would be liable for such defaulted amounts. (f) Cash Cash includes cash equivalents, which are investments with original maturities of three months or less which are not part of the investment portfolio. (g) Restricted Cash Restricted cash represents amounts held for the benefit of third parties and is legally or contractually restricted as to withdrawal or usage by the Company. Such amounts are included in “Other assets” on the Company’s balance sheet. (h) Investments The Company currently classifies substantially all of its fixed maturity investments and short-term investments as “available for sale” and, accordingly, they are carried at estimated fair value (also known as fair value) with the changes in fair value recorded as an unrealized gain or loss component of accumulated other comprehensive income in shareholders’ equity. The fair value of fixed maturity securities and equity securities is generally determined from quotations received from nationally recognized pricing services, or when such prices are not available, by reference to broker or underwriter bid indications. Short-term investments comprise securities due to mature within one year of the date of issue. Short-term investments include certain cash equivalents which are part of investment portfolios under the management of external and internal investment managers. The Company enters into securities lending agreements with financial institutions to enhance investment income whereby it loans certain of its securities to third parties, primarily major brokerage firms, for short periods of time through a lending agent. Such securities have been reclassified as “Securities pledged under securities lending, at fair value.” The Company maintains legal control over the securities it lends, retains the earnings and cash flows associated with the loaned securities and receives a fee from the borrower for the temporary use of the securities. Collateral received is required at a rate of 102% or greater of the fair value of the loaned securities including accrued investment income and is monitored and maintained by the lending agent. Such collateral is reflected as “Collateral received under securities lending, at fair value.” The Company’s investment portfolio includes certain funds that, due to their ownership structure, are accounted for by the Company using the equity method. In applying the equity method, these investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the fair value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. Changes in the carrying value of such investments are recorded in net income as “Equity in net income (loss) of investments accounted for using the equity method.” As such, fluctuations in the carrying value of the investments accounted for using the equity method may increase the volatility of the Company’s reported results of operations. The Company’s investment portfolio includes equity securities that are accounted for at fair value. Such holdings primarily include publicly traded common stocks. Dividend income on equities is reflected in net investment income. Changes in fair value on equity securities are included in “Net realized gains (losses)” in the consolidated statement of income. The Company elected to carry certain fixed maturity securities, equity securities and other investments at fair value under the fair value option afforded by accounting guidance regarding the fair value option for financial assets and liabilities. The fair value for certain of the Company’s other investments are determined using net asset values (“NAVs”) as advised by external fund managers. The NAV is based on the fund manager’s valuation of the underlying holdings in accordance with the fund’s governing documents. Changes in fair value of investments accounted for using the fair value option are included in “Net realized gains (losses).” The primary reasons for electing the fair value option were to address simplification and cost-benefit considerations. The Company invests in limited partner interests and shares of limited liability companies. Such amounts are included in investments accounted for using the equity method, other investments available for sale and investments accounted for using the fair value option. These investments can often have characteristics of a variable interest entity (“VIE”). A VIE refers to entities that have characteristics such as (i) insufficient equity at risk to allow the entity to finance its activities without additional financial support or (ii) instances where the equity investors, as a group, do not have the characteristic of a controlling financial interest. If the Company is determined to be the primary beneficiary, it is required to consolidate the VIE. The primary beneficiary is defined as the variable interest holder that is determined to have the controlling financial interest as a result of having both (i) the power to direct the activities of a VIE that most significantly impact the economic performance of the VIE and (ii) the obligation to absorb losses or right to receive benefits from the VIE that could potentially be significant to the VIE. At inception of the VIE as well as on an ongoing basis, the Company determines whether it is the primary beneficiary based on an analysis of the Company’s level of involvement in the VIE, the contractual terms, and the overall structure of the VIE. The Company's maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company's consolidated balance sheet and any unfunded commitment. The Company performs quarterly reviews of its investments to determine whether declines in fair value below the cost basis are considered other-than-temporary in accordance with applicable accounting guidance regarding the recognition and presentation of OTTI. The process of determining whether a security is other-than-temporarily impaired requires judgment and involves analyzing many factors. These factors include (i) an analysis of the liquidity, business prospects and overall financial condition of the issuer, (ii) the time period in which there was a significant decline in value, (iii) the significance of the decline and (iv) the analysis of specific credit events. When there are credit-related losses associated with debt securities for which the Company does not have an intent to sell and it is more likely than not that it will not be required to sell the security before recovery of its cost basis, the amount of the OTTI related to a credit loss is recognized in earnings and the amount of the OTTI related to other factors ( e.g. , interest rates, market conditions, etc.) is recorded as a component of other comprehensive income (loss). The amount of the credit loss of an impaired debt security is the difference between the amortized cost and the greater of (i) the present value of expected future cash flows and (ii) the fair value of the security. In instances where no credit loss exists but it is more likely than not that the Company will have to sell the debt security prior to the anticipated recovery, the decline in fair value below amortized cost is recognized as an OTTI in earnings. In periods after the recognition of an OTTI on debt securities, the Company accounts for such securities as if they had been purchased on the measurement date of the OTTI at an amortized cost basis equal to the previous amortized cost basis less the OTTI recognized in earnings. For debt securities for which OTTI were recognized in earnings, the difference between the new amortized cost basis and the cash flows expected to be collected will be accreted or amortized into net investment income. See note 8, “Investment Information” for additional information. Net investment income includes interest and dividend income together with amortization of market premiums and discounts and is net of investment management and custody fees. Anticipated prepayments and expected maturities are used in applying the interest method for certain investments such as mortgage and other asset-backed securities. When actual prepayments differ significantly from anticipated prepayments, the effective yield is recalculated to reflect actual payments to date and anticipated future payments. The net investment in such securities is adjusted to the amount that would have existed had the new effective yield been applied since the acquisition of the security. Such adjustments, if any, are included in net investment income when determined. Investment gains or losses realized on the sale of investments, except for certain fund investments, are determined on a first-in, first-out basis and are reflected in net income. Investment gains or losses realized on the sale of certain fund investments are determined on an average cost basis. Unrealized appreciation or decline in the value of available for sale securities, which are carried at fair value, is excluded from net income and recorded as a separate component of accumulated other comprehensive income, net of applicable deferred income tax. (i) Derivative Instruments The Company recognizes all derivative instruments, including embedded derivative instruments, at fair value in its consolidated balance sheets. The Company employs the use of derivative instruments within its operations to mitigate risks arising from assets and liabilities held in foreign currencies as well as part of its overall investment strategy. For such instruments, changes in assets and liabilities measured at fair value are recorded as “Net realized gains” in the consolidated statements of income. In addition, the Company’s derivative instruments include amounts related to underwriting activities where an insurance or reinsurance contract meets the accounting definition of a derivative instrument. For such contracts, changes in fair value are reflected in “Other underwriting income” in the consolidated statements of income as the underlying contract originates from the Company’s underwriting operations. For the periods ended 2019 , 2018 , and 2017 , the Company did not designate any derivative instruments as hedges under the relevant accounting guidance. See note 10, “Derivative Instruments” for additional information. (j) Reserves for Losses and Loss Adjustment Expenses Insurance and Reinsurance. The reserve for losses and loss adjustment expenses consists of estimates of unpaid reported losses and loss adjustment expenses and estimates for losses incurred but not reported. The reserve for unpaid reported losses and loss adjustment expenses, established by management based on reports from ceding companies and claims from insureds, excludes estimates of amounts related to losses under high deductible policies, and represents the estimated ultimate cost of events or conditions that have been reported to or specifically identified by the Company. Such reserves are supplemented by management’s estimates of reserves for losses incurred for which reports or claims have not been received. The Company’s reserves are based on a combination of reserving methods, incorporating both Company and industry loss development patterns. The Company selects the initial expected loss and loss adjustment expense ratios based on information derived by its underwriters and actuaries during the initial pricing of the business, supplemented by industry data where appropriate. Such ratios consider, among other things, rate changes and changes in terms and conditions that have been observed in the market. These estimates are reviewed regularly and, as experience develops and new information becomes known, the reserves are adjusted as necessary. Such adjustments, if any, are reflected in income in the period in which they are determined. As actual loss information has been reported, the Company has developed its own loss experience and its reserving methods include other actuarial techniques. Over time, such techniques have been given further weight in its reserving process based on the continuing maturation of the Company’s reserves. Inherent in the estimates of ultimate losses and loss adjustment expenses are expected trends in claims severity and frequency and other factors which may vary significantly as claims are settled. Accordingly, ultimate losses and loss adjustment expenses may differ materially from the amounts recorded in the accompanying consolidated financial statements. Losses and loss adjustment expenses are recorded on an undiscounted basis, except for excess workers’ compensation and employers’ liability business written by the Company’s insurance operations. Mortgage. The reserves for mortgage guaranty insurance losses and loss adjustment expenses are the estimated claim settlement costs on notices of delinquency that have been received by the Company, as well as loan delinquencies that have been incurred but have not been reported by the lenders. Consistent with primary mortgage insurance industry accounting practice, the Company does not establish loss reserves for future claims on insured loans that are not currently delinquent (defined as two consecutive missed payments). The Company establishes loss reserves on a case-by-case basis when insured loans are reported delinquent using estimated claim rates and average claim sizes for each cohort, net of any salvage recoverable. The Company also reserves for delinquencies that have occurred but have not yet been reported to the Company prior to the close of an accounting period. To determine this reserve, the Company estimates the number of delinquencies not yet reported using historical information regarding late reported delinquencies and applies estimated claim rates and claim sizes for the estimated delinquencies not yet reported. The establishment of reserves across the Company’s segments is an inherently uncertain process, are necessarily based on estimates, and the ultimate net cost may vary from such estimates. The methods for making such estimates and for establishing the resulting liability are reviewed and updated using the most current information available. Any resulting adjustments, which may be material, are reflected in current operations. (k) Contractholder Receivables and Payables and Collateral Held for Insured Obligations Certain insurance policies written by the Company’s insurance operations feature large deductibles, primarily in its construction and national accounts lines of business. Under such contracts, the Company is obligated to pay the claimant for the full amount of the claim.

Segment Information

Segment Information	12 Months Ended
	Dec. 31, 2019
Segment Reporting [Abstract]
Segment Information	Segment Information The Company classifies its businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other operating segments — ‘other’ and corporate (non-underwriting). The Company determined its reportable segments using the management approach described in accounting guidance regarding disclosures about segments of an enterprise and related information. The accounting policies of the segments are the same as those used for the preparation of the Company’s consolidated financial statements. Intersegment business is allocated to the segment accountable for the underwriting results. The Company’s insurance, reinsurance and mortgage segments each have managers who are responsible for the overall profitability of their respective segments and who are directly accountable to the Company’s chief operating decision makers, the President and Chief Executive Officer of Arch Capital and the Chief Financial Officer of Arch Capital. The chief operating decision makers do not assess performance, measure return on equity or make resource allocation decisions on a line of business basis. Management measures segment performance for its three underwriting segments based on underwriting income or loss. The Company does not manage its assets by underwriting segment, with the exception of goodwill and intangible assets, and, accordingly, investment income is not allocated to each underwriting segment. The insurance segment consists of the Company’s insurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: • Construction and national accounts: primary and excess casualty coverages to middle and large accounts in the construction industry and a wide range of products for middle and large national accounts, specializing in loss sensitive primary casualty insurance programs (including large deductible, self-insured retention and retrospectively rated programs). • Excess and surplus casualty: primary and excess casualty insurance coverages, including middle market energy business, and contract binding, which primarily provides casualty coverage through a network of appointed agents to small and medium risks. • Lenders products: collateral protection, debt cancellation and service contract reimbursement products to banks, credit unions, automotive dealerships and original equipment manufacturers and other specialty programs that pertain to automotive lending and leasing. • Professional lines: directors’ and officers’ liability, errors and omissions liability, employment practices liability, fiduciary liability, crime, professional indemnity and other financial related coverages for corporate, private equity, venture capital, real estate investment trust, limited partnership, financial institution and not-for-profit clients of all sizes and medical professional and general liability insurance coverages for the healthcare industry. The business is predominately written on a claims-made basis. • Programs: primarily package policies, underwriting workers’ compensation and umbrella liability business in support of desirable package programs, targeting program managers with unique expertise and niche products offering general liability, commercial automobile, inland marine and property business with minimal catastrophe exposure. • Property, energy, marine and aviation: primary and excess general property insurance coverages, including catastrophe-exposed property coverage, for commercial clients. Coverages for marine include hull, war, specie and liability. Aviation and stand-alone terrorism are also offered. • Travel, accident and health: specialty travel and accident and related insurance products for individual, group travelers, travel agents and suppliers, as well as accident and health, which provides accident, disability and medical plan insurance coverages for employer groups, medical plan members, students and other participant groups. • Other: includes alternative market risks (including captive insurance programs), excess workers’ compensation and employer’s liability insurance coverages for qualified self-insured groups, associations and trusts, and contract and commercial surety coverages, including contract bonds (payment and performance bonds) primarily for medium and large contractors and commercial surety bonds for Fortune 1000 companies and smaller transaction business programs. The reinsurance segment consists of the Company’s reinsurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: • Casualty: provides coverage to ceding company clients on third party liability and workers’ compensation exposures from ceding company clients, primarily on a treaty basis. Exposures include, among others, executive assurance, professional liability, workers’ compensation, excess and umbrella liability, excess motor and healthcare business. • Marine and aviation: provides coverage for energy, hull, cargo, specie, liability and transit, and aviation business, including airline and general aviation risks. Business written may also include space business, which includes coverages for satellite assembly, launch and operation for commercial space programs. • Other specialty: provides coverage to ceding company clients for proportional motor and other lines including surety, accident and health, workers’ compensation catastrophe, agriculture, trade credit and political risk. • Property catastrophe: provides protection for most catastrophic losses that are covered in the underlying policies written by reinsureds, including hurricane, earthquake, flood, tornado, hail and fire, and coverage for other perils on a case-by-case basis. Property catastrophe reinsurance provides coverage on an excess of loss basis when aggregate losses and loss adjustment expense from a single occurrence of a covered peril exceed the retention specified in the contract. • Property excluding property catastrophe: provides coverage for both personal lines and commercial property exposures and principally covers buildings, structures, equipment and contents. The primary perils in this business include fire, explosion, collapse, riot, vandalism, wind, tornado, flood and earthquake. Business is assumed on both a proportional and excess of loss basis. In addition, facultative business is written which focuses on commercial property risks on an excess of loss basis. • Other. includes life reinsurance business on both a proportional and non-proportional basis, casualty clash business and, in limited instances, non-traditional business which is intended to provide insurers with risk management solutions that complement traditional reinsurance. The mortgage segment includes the Company’s U.S. and international mortgage insurance and reinsurance operations as well as government sponsored enterprise (“GSE”) credit-risk sharing transactions. AMIC and UGRIC (combined “Arch MI U.S.”) are approved as eligible mortgage insurers by Federal National Mortgage Association (“Fannie Mae”) and Federal Home Loan Mortgage Corporation (“Freddie Mac”), each a government sponsored enterprise, or “GSE.” The corporate (non-underwriting) segment results include net investment income, other income (loss), other expenses incurred by the Company, interest expense, net realized gains or losses, net impairment losses included in earnings, equity in net income or loss of investments accounted for using the equity method, net foreign exchange gains or losses, transaction costs and other, income taxes and items related to the Company’s non-cumulative preferred shares. Such amounts exclude the results of the ‘other’ segment. The ‘other’ segment includes the results of Watford (see note 11, “Variable Interest Entity and Noncontrolling Interests” ). Watford has its own management and board of directors that is responsible for the overall profitability of the ‘other’ segment. For the ‘other’ segment, performance is measured based on net income or loss. The following tables summarize the Company’s underwriting income or loss by segment, together with a reconciliation of underwriting income or loss to net income available to Arch common shareholders, summary information regarding net premiums written and earned by major line of business and net premiums written by location: Year Ended December 31, 2019 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 3,907,993 $ 2,323,223 $ 1,466,265 $ 7,695,645 $ 754,881 $ 8,138,960 Premiums ceded (1,266,267 ) (720,500 ) (204,509 ) (2,189,440 ) (222,019 ) (2,099,893 ) Net premiums written 2,641,726 1,602,723 1,261,756 5,506,205 532,862 6,039,067 Change in unearned premiums (244,646 ) (136,334 ) 104,584 (276,396 ) 23,827 (252,569 ) Net premiums earned 2,397,080 1,466,389 1,366,340 5,229,809 556,689 5,786,498 Other underwriting income (loss) — 6,444 16,005 22,449 2,412 24,861 Losses and loss adjustment expenses (1,615,475 ) (1,011,329 ) (53,513 ) (2,680,317 ) (453,135 ) (3,133,452 ) Acquisition expenses (361,614 ) (239,032 ) (134,319 ) (734,965 ) (105,980 ) (840,945 ) Other operating expenses (454,770 ) (141,484 ) (153,092 ) (749,346 ) (51,651 ) (800,997 ) Underwriting income (loss) $ (34,779 ) $ 80,988 $ 1,041,421 1,087,630 (51,665 ) 1,035,965 Net investment income 491,067 136,671 627,738 Net realized gains (losses) 351,202 15,161 366,363 Net impairment losses recognized in earnings (3,165 ) — (3,165 ) Equity in net income (loss) of investments accounted for using the equity method 123,672 — 123,672 Other income (loss) 2,233 — 2,233 Corporate expenses (65,667 ) — (65,667 ) Transaction costs and other (14,444 ) — (14,444 ) Amortization of intangible assets (82,104 ) — (82,104 ) Interest expense (93,735 ) (27,137 ) (120,872 ) Net foreign exchange gains (losses) (9,252 ) (11,357 ) (20,609 ) Income (loss) before income taxes 1,787,437 61,673 1,849,110 Income tax expense (155,790 ) (20 ) (155,810 ) Net income (loss) 1,631,647 61,653 1,693,300 Dividends attributable to redeemable noncontrolling interests — (16,909 ) (16,909 ) Amounts attributable to nonredeemable noncontrolling interests — (40,072 ) (40,072 ) Net income (loss) available to Arch 1,631,647 4,672 1,636,319 Preferred dividends (41,612 ) — (41,612 ) Loss on redemption of preferred shares — — — Net income (loss) available to Arch common shareholders $ 1,590,035 $ 4,672 $ 1,594,707 Underwriting Ratios Loss ratio 67.4 % 69.0 % 3.9 % 51.3 % 81.4 % 54.2 % Acquisition expense ratio 15.1 % 16.3 % 9.8 % 14.1 % 19.0 % 14.5 % Other operating expense ratio 19.0 % 9.6 % 11.2 % 14.3 % 9.3 % 13.8 % Combined ratio 101.5 % 94.9 % 24.9 % 79.7 % 109.7 % 82.5 % Goodwill and intangible assets $ 289,021 $ 2,516 $ 438,896 $ 730,433 $ 7,650 $ 738,083 Total investable assets $ 22,285,676 $ 2,704,589 $ 24,990,265 Total assets 34,374,468 3,510,893 37,885,361 Total liabilities 22,977,636 2,592,173 25,569,809 (1) Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total. Year Ended December 31, 2018 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 3,262,332 $ 1,912,522 $ 1,360,708 $ 6,534,423 $ 735,015 $ 6,961,004 Premiums ceded (1,050,207 ) (539,950 ) (202,833 ) (1,791,851 ) (130,840 ) (1,614,257 ) Net premiums written 2,212,125 1,372,572 1,157,875 4,742,572 604,175 5,346,747 Change in unearned premiums (6,464 ) (111,356 ) 28,361 (89,459 ) (25,313 ) (114,772 ) Net premiums earned 2,205,661 1,261,216 1,186,236 4,653,113 578,862 5,231,975 Other underwriting income — (682 ) 13,033 12,351 2,722 15,073 Losses and loss adjustment expenses (1,520,680 ) (846,882 ) (81,289 ) (2,448,851 ) (441,255 ) (2,890,106 ) Acquisition expenses, net (349,702 ) (211,280 ) (118,595 ) (679,577 ) (125,558 ) (805,135 ) Other operating expenses (364,138 ) (133,350 ) (142,432 ) (639,920 ) (37,889 ) (677,809 ) Underwriting income (loss) $ (28,859 ) $ 69,022 $ 856,953 897,116 (23,118 ) 873,998 Net investment income 437,958 125,675 563,633 Net realized gains (losses) (284,429 ) (120,915 ) (405,344 ) Net impairment losses recognized in earnings (2,829 ) — (2,829 ) Equity in net income (loss) of investments accounted for using the equity method 45,641 — 45,641 Other income (loss) 2,419 — 2,419 Corporate expenses (58,608 ) — (58,608 ) Transaction costs and other (11,386 ) (9,000 ) (20,386 ) Amortization of intangible assets (105,670 ) — (105,670 ) Interest expense (101,019 ) (19,465 ) (120,484 ) Net foreign exchange gains (losses) 58,711 10,691 69,402 Income (loss) before income taxes 877,904 (36,132 ) 841,772 Income tax (expense) benefit (113,924 ) (27 ) (113,951 ) Net income (loss) 763,980 (36,159 ) 727,821 Dividends attributable to redeemable noncontrolling interests — (18,357 ) (18,357 ) Amounts attributable to nonredeemable noncontrolling interests — 48,507 48,507 Net income (loss) available to Arch 763,980 (6,009 ) 757,971 Preferred dividends (41,645 ) — (41,645 ) Loss on redemption of preferred shares (2,710 ) — (2,710 ) Net income (loss) available to Arch common shareholders $ 719,625 $ (6,009 ) $ 713,616 Underwriting Ratios Loss ratio 68.9 % 67.1 % 6.9 % 52.6 % 76.2 % 55.2 % Acquisition expense ratio 15.9 % 16.8 % 10.0 % 14.6 % 21.7 % 15.4 % Other operating expense ratio 16.5 % 10.6 % 12.0 % 13.8 % 6.5 % 13.0 % Combined ratio 101.3 % 94.5 % 28.9 % 81.0 % 104.4 % 83.6 % Goodwill and intangible assets $ 114,012 $ — $ 513,258 $ 627,270 $ 7,650 $ 634,920 Total investable assets $ 19,566,861 $ 2,757,663 $ 22,324,524 Total assets 28,845,473 3,372,856 32,218,329 Total liabilities 19,518,395 2,262,255 21,780,650 (1) Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total. Year Ended December 31, 2017 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 3,081,086 $ 1,640,399 $ 1,368,138 $ 6,088,254 $ 600,304 $ 6,368,425 Premiums ceded (958,646 ) (465,925 ) (256,796 ) (1,679,998 ) (47,187 ) (1,407,052 ) Net premiums written 2,122,440 1,174,474 1,111,342 4,408,256 553,117 4,961,373 Change in unearned premiums (9,422 ) (31,853 ) (54,176 ) (95,451 ) (21,390 ) (116,841 ) Net premiums earned 2,113,018 1,142,621 1,057,166 4,312,805 531,727 4,844,532 Other underwriting income — 11,336 15,737 27,073 3,180 30,253 Losses and loss adjustment expenses (1,622,444 ) (773,923 ) (134,677 ) (2,531,044 ) (436,402 ) (2,967,446 ) Acquisition expenses, net (323,639 ) (221,250 ) (100,598 ) (645,487 ) (129,971 ) (775,458 ) Other operating expenses (359,524 ) (146,663 ) (146,336 ) (652,523 ) (31,928 ) (684,451 ) Underwriting income (loss) $ (192,589 ) $ 12,121 $ 691,292 510,824 (63,394 ) 447,430 Net investment income 382,072 88,800 470,872 Net realized gains (losses) 148,798 343 149,141 Net impairment losses recognized in earnings (7,138 ) — (7,138 ) Equity in net income (loss) of investments accounted for using the equity method 142,286 — 142,286 Other income (loss) (2,571 ) — (2,571 ) Corporate expenses (61,602 ) — (61,602 ) Transaction costs and other (22,150 ) — (22,150 ) Amortization of intangible assets (125,778 ) — (125,778 ) Interest expense (103,592 ) (13,839 ) (117,431 ) Net foreign exchange gains (losses) (113,345 ) (2,437 ) (115,782 ) Income (loss) before income taxes 747,804 9,473 757,277 Income tax benefit (127,547 ) (21 ) (127,568 ) Net income 620,257 9,452 629,709 Dividends attributable to redeemable noncontrolling interests — (18,344 ) (18,344 ) Amounts attributable to nonredeemable noncontrolling interests — 7,913 7,913 Net income (loss) available to Arch 620,257 (979 ) 619,278 Preferred dividends (46,041 ) — (46,041 ) Loss on redemption of preferred shares (6,735 ) — (6,735 ) Net income (loss) available to Arch common shareholders $ 567,481 $ (979 ) $ 566,502 Underwriting Ratios Loss ratio 76.8 % 67.7 % 12.7 % 58.7 % 82.1 % 61.3 % Acquisition expense ratio 15.3 % 19.4 % 9.5 % 15.0 % 24.4 % 16.0 % Other operating expense ratio 17.0 % 12.8 % 13.8 % 15.1 % 6.0 % 14.1 % Combined ratio 109.1 % 99.9 % 36.0 % 88.8 % 112.5 % 91.4 % Goodwill and intangible assets $ 22,310 $ 211 $ 622,440 $ 644,961 $ 7,650 $ 652,611 Total investable assets $ 19,716,421 $ 2,440,067 $ 22,156,488 Total assets 29,037,004 3,014,654 32,051,658 Total liabilities 19,959,574 1,846,149 21,805,723 (1) Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total. The following tables provide summary information regarding net premiums earned by major line of business and net premiums written by underwriting location: INSURANCE SEGMENT Year Ended December 31, 2019 2018 2017 Net premiums earned (1) Professional lines (2) $ 499,224 $ 458,425 $ 444,137 Programs 414,103 389,186 364,639 Property, energy, marine and aviation 298,966 205,069 173,779 Construction and national accounts 325,687 322,440 324,517 Travel, accident and health 305,085 297,147 257,358 Excess and surplus casualty (3) 200,615 172,424 195,154 Lenders products 66,079 94,248 97,043 Other (4) 287,321 266,722 256,391 Total $ 2,397,080 $ 2,205,661 $ 2,113,018 Net premiums written by underwriting location (1) United States $ 1,983,476 $ 1,736,651 $ 1,715,467 Europe 559,214 401,974 344,836 Other 99,036 73,500 62,137 Total $ 2,641,726 $ 2,212,125 $ 2,122,440 (1) Insurance segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions. (2) Includes professional liability, executive assurance and healthcare business. (3) Includes casualty and contract binding business. (4) Includes alternative markets, excess workers' compensation and surety business. REINSURANCE SEGMENT Year Ended December 31, 2019 2018 2017 Net premiums earned (1) Other specialty (2) $ 478,517 $ 474,568 $ 408,566 Casualty (3) 429,288 347,034 341,122 Property excluding property catastrophe 362,841 287,788 255,453 Property catastrophe 90,934 75,249 73,300 Marine and aviation 48,274 39,238 36,214 Other (4) 56,535 37,339 27,966 Total $ 1,466,389 $ 1,261,216 $ 1,142,621 Net premiums written by underwriting location (1) United States $ 529,943 $ 413,550 $ 399,379 Bermuda 578,618 487,523 350,681 Europe and other 494,162 471,499 424,414 Total $ 1,602,723 $ 1,372,572 $ 1,174,474 (1) Reinsurance segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions. (2) Includes proportional motor, surety, accident and health, workers’ compensation catastrophe, agriculture, trade credit and other. (3) Includes executive assurance, professional liability, workers’ compensation, excess motor, healthcare and other. (4) Includes life, casualty clash and other. MORTGAGE SEGMENT Year Ended December 31, 2019 2018 2017 Net premiums earned by underwriting location United States $ 1,134,849 $ 1,009,765 $ 901,858 Other 231,491 176,471 155,308 Total $ 1,366,340 $ 1,186,236 $ 1,057,166 Net premiums written by underwriting location United States $ 1,032,868 $ 948,323 $ 903,329 Other 228,888 209,552 208,013 Total $ 1,261,756 $ 1,157,875 $ 1,111,342 OTHER SEGMENT Year Ended December 31, 2019 2018 2017 Net premiums earned (1) Casualty (2) $ 246,894 $ 277,589 $ 333,275 Other specialty (3) 185,547 204,485 135,855 Property catastrophe 13,399 10,998 12,690 Property excluding property catastrophe 3,503 2,802 1,392 Other (4) 107,346 82,988 48,515 Total $ 556,689 $ 578,862 $ 531,727 Net premiums written by underwriting location (1) United States $ 127,176 $ 49,800 $ 11,750 Europe 52,065 91,635 91,463 Bermuda 353,621 462,740 449,904 Total $ 532,862 $ 604,175 $ 553,117 (1) Other segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions. (2) Includes professional liability, excess motor, programs and other. (3) Includes proportional motor and other. (4) Includes mortgage and other.

Reserve for Losses and Loss Adj

Reserve for Losses and Loss Adjustment Expenses	12 Months Ended
	Dec. 31, 2019
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]
Reserve for losses and loss adjustment expenses	Reserve for Losses and Loss Adjustment Expenses The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses: Year Ended December 31, 2019 2018 2017 Reserve for losses and loss adjustment expenses at beginning of year $ 11,853,297 $ 11,383,792 $ 10,200,960 Unpaid losses and loss adjustment expenses recoverable 2,814,291 2,464,910 2,083,575 Net reserve for losses and loss adjustment expenses at beginning of year 9,039,006 8,918,882 8,117,385 Net incurred losses and loss adjustment expenses relating to losses occurring in: Current year 3,297,037 3,162,818 3,205,428 Prior years (163,585 ) (272,712 ) (237,982 ) Total net incurred losses and loss adjustment expenses 3,133,452 2,890,106 2,967,446 Net losses and loss adjustment expense reserves of acquired business (1) 209,486 — — Retroactive reinsurance transactions (2) (225,500 ) (420,404 ) — Foreign exchange (gains) losses 36,003 (143,414 ) 186,963 Net paid losses and loss adjustment expenses relating to losses occurring in: Current year (621,202 ) (524,048 ) (505,424 ) Prior years (1,762,053 ) (1,682,116 ) (1,847,488 ) Total net paid losses and loss adjustment expenses (2,383,255 ) (2,206,164 ) (2,352,912 ) Net reserve for losses and loss adjustment expenses at end of year 9,809,192 9,039,006 8,918,882 Unpaid losses and loss adjustment expenses recoverable 4,082,650 2,814,291 2,464,910 Reserve for losses and loss adjustment expenses at end of year $ 13,891,842 $ 11,853,297 $ 11,383,792 (1) The 2019 amount primarily related to the acquisition of Barbican. (2) During the 2019 first quarter and 2018 second quarter, a subsidiary of the Company entered into two separate retroactive reinsurance transactions with third party reinsurers to reinsure run-off liabilities associated with certain U.S. insurance exposures. 2019 Prior Year Reserve Development During 2019, the Company recorded estimated net favorable development on prior year loss reserves of $163.6 million , which consisted of net favorable development of $15.8 million from the insurance segment, $46.4 million from the reinsurance segment and $125.2 million from the mortgage segment, partially offset by $23.8 million of net adverse development from the ‘other’ segment. The insurance segment’s net favorable development of $15.8 million , or 7.0 points of net earned premium, consisted of $54.9 million of net favorable development from short-tailed lines and $39.1 million of net adverse development from medium-tailed and long-tailed lines. Net favorable development in short-tailed lines primarily resulted from lenders products and property (including special risk other than marine) reserves across all accident years, (i.e., the year in which a loss occurred) partially offset by net adverse development in travel business, primarily from the 2018 accident year. Net adverse development in medium-tailed and long-tailed lines of $39.1 million was primarily due to net adverse development of $33.6 million in contract binding business, primarily from the 2013 to 2017 accident years, and $30.1 million in programs, primarily from the 2014 and 2018 accident years. Such amounts were partially offset by net favorable development of $19.3 million in professional liability business, primarily from the 2013 to 2016 accident years, and $15.8 million in surety business, primarily from the 2014 to 2016 accident years. The reinsurance segment’s net favorable development of $46.4 million , or 3.2 points of net earned premium, consisted of $70.5 million of net favorable development from short-tailed lines and $16.0 million of net favorable development from medium-tailed lines, partially offset by $40.1 million of net adverse development from long-tailed lines. Favorable development in short-tailed lines included $33.7 million from property catastrophe and property other than property catastrophe reserves, primarily from the 2017 and 2018 underwriting years (i.e., losses attributable to contracts having an inception or renewal date within the given twelve-month period) and $40.8 million in other specialty, primarily from 2016 to 2018 underwriting years.The net reduction of loss estimates for the reinsurance segment’s short-tailed lines primarily resulted from varying levels of reported and paid claims activity than previously anticipated which led to decreases in certain loss ratio selections during 2019. Net favorable development of $16.0 million in medium-tailed lines included reductions in marine and aviation reserves, primarily from the 2011 to 2017 underwriting years. Net adverse development in long-tailed lines of $40.1 million was primarily due to net adverse development of $44.5 million in casualty business, primarily from the 2013 to 2018 underwriting years. The mortgage segment’s net favorable development of $125.2 million , or 9.2 points of net earned premium, included $117.1 million of favorable development on U.S. primary mortgage business. Such development was primarily driven by continued lower than expected claim rates on first lien business and subrogation recoveries on second lien business. 2018 Prior Year Reserve Development During 2018, the Company recorded estimated net favorable development on prior year loss reserves of $272.7 million , which consisted of $24.4 million from the insurance segment, $138.5 million from the reinsurance segment, $107.6 million from the mortgage segment and $2.2 million from the ‘other’ segment. The insurance segment’s net favorable development of $24.4 million , or 1.1 points of net earned premium, consisted of $48.4 million of net favorable development from short-tailed lines and $26.3 million of net favorable development from long-tailed lines, partially offset by $50.3 million of net adverse development from medium-tailed lines. Favorable development in short-tailed lines predominantly consisted of $50.1 million of net favorable development in property lines, primarily from the 2010 to 2017 accident years, partially offset by $5.0 million of adverse development on travel, accident and health business from the 2013 to 2017 accident years. Net favorable development in long-tailed lines of $26.3 million included $19.7 million of net favorable development on executive assurance business, primarily from the 2015 accident year, and $1.4 million of net favorable development in casualty business, primarily from the 2009 to 2015 accident years. Net adverse development in medium tailed lines of $50.3 million was primarily due to net adverse development in contract binding business for accident years 2013 to 2017. The reinsurance segment’s net favorable development of $138.5 million , or 11.0 points of net earned premium, consisted of $110.4 million from short-tailed lines and $28.1 million from medium-tailed and long-tailed lines. Favorable development in short-tailed lines included $80.8 million from property catastrophe and property other than property catastrophe reserves, primarily from the 2008 to 2017 underwriting years. The net reduction of loss estimates for the reinsurance segment’s short-tailed lines primarily resulted from varying levels of reported and paid claims activity than previously anticipated which led to decreases in certain loss ratio selections during 2018. Net favorable development of $28.1 million in medium-tailed and long-tailed lines included reductions in casualty reserves of $12.5 million , primarily from the 2002 to 2010 underwriting years, and in marine and aviation reserves of $15.6 million , spread across most underwriting years. The mortgage segment’s net favorable development of $107.6 million , or 9.1 points of net earned premium, included $103.4 million of favorable development on U.S. primary mortgage business. Such development was primarily driven by continued lower than expected claim rates on first lien business and subrogation recoveries on second lien business. 2017 Prior Year Reserve Development During 2017, the Company recorded estimated net favorable development on prior year loss reserves of $238.0 million , which consisted of $8.6 million from the insurance segment, $165.4 million from the reinsurance segment, and $95.0 million from the mortgage segment, less adverse development of $31.0 million from the ‘other’ segment. The insurance segment’s net favorable development of $8.6 million , or 4.0 points of net earned premium, consisted of $14.9 million of net favorable development from short-tailed lines and $11.8 million of net favorable development from long-tailed lines, partially offset by $18.1 million of net adverse development from medium-tailed lines. Favorable development in short-tailed lines predominantly consisted of $22.8 million of net favorable development in property lines, primarily from the 2011 to 2016 accident years, partially offset by $11.8 million of adverse development on travel, accident and health business from the 2014 to 2016 accident years. Net favorable development in long-tailed lines of $11.8 million included $10.0 million of net favorable development on executive assurance business, primarily from the 2013 accident year, and $8.3 million of net favorable development in casualty business, primarily from the 2007 to 2013 accident years. Net adverse development in medium-tailed lines of $18.1 million included $56.3 million of net adverse development in program business, primarily from the 2013 to 2015 accident years and primarily driven by a few inactive programs that were non-renewed in 2015 and early in 2016, partially offset by $36.2 million of net favorable development in professional liability business, primarily from the 2010 to 2016 accident years. The reinsurance segment’s net favorable development of $165.4 million , or 14.5 points of net earned premium, consisted of $101.0 million from short-tailed lines and $64.4 million from medium-tailed and long-tailed lines. Favorable development in short-tailed lines included $82.6 million from property catastrophe and property other than property catastrophe reserves, primarily from the 2009 to 2016 underwriting years. The net reduction of loss estimates for the reinsurance segment’s short-tailed lines primarily resulted from varying levels of reported and paid claims activity than previously anticipated which led to decreases in certain loss ratio selections during 2017. Net favorable development of $64.4 million in medium-tailed and long-tailed lines included reductions in casualty reserves of $43.7 million , primarily from the 2002 to 2013 underwriting years, and in marine and aviation reserves of $19.6 million , spread across most underwriting years. The mortgage segment’s net favorable development of $95.0 million , or 9.0 points of net earned premium, for 2017, included $89.3 million of favorable development on U.S. primary mortgage business. Such development was primarily driven by continued lower than expected claim rates on first lien business and subrogation recoveries on second lien business.

Short Duration Contracts

Short Duration Contracts	12 Months Ended
	Dec. 31, 2019
Short Duration Contracts Disclosure [Abstract]
Short duration contracts	Short Duration Contracts The Company’s reserves for losses and loss adjustment expenses primarily relate to short-duration contracts with various characteristics ( e.g. , type of coverage, geography, claims duration). The Company considered such information in determining the level of disaggregation for disclosures related to its short-duration contracts, as detailed in the table below: Reportable segment Level of disaggregation Included lines of business Insurance Property energy, marine and aviation Property energy, marine and aviation Third party occurrence business Excess and surplus casualty (excluding contract binding); construction and national accounts; and other (including alternative market risks, excess workers’ compensation and employer’s liability insurance coverages) Third party claims-made business Professional lines Multi-line and other specialty Programs; contract binding (part of excess and surplus casualty); travel, accident and health; lenders products; and other (c ontract and commercial surety coverages) Reinsurance Casualty Casualty Property catastrophe Property catastrophe Property excluding property catastrophe Property excluding property catastrophe Marine and aviation Marine and aviation Other specialty Other specialty Mortgage Direct mortgage insurance in the U.S. Mortgage insurance on U.S. primary exposures The Company determined the following to be insignificant for disclosure purposes: (i) amounts included in the ‘other’ segment ( i.e. , Watford ) as described in note 11, “Variable Interest Entity and Noncontrolling Interests” ; (ii) certain mortgage business, including non-U.S. primary business, second lien and student loan exposures, global mortgage reinsurance and participation in various GSE credit risk-sharing products; (iii) certain reinsurance business, including casualty clash and non-traditional lines, and (iv) amounts associated with the Barbican acquisition. Such amounts are included as reconciling items. The Company is required to establish reserves for losses and loss adjustment expenses (“Loss Reserves”) that arise from the business the Company underwrites. Loss Reserves for the insurance, reinsurance and mortgage segments represent estimates of future amounts required to pay losses and loss adjustment expenses for insured or reinsured events which have occurred at or before the balance sheet date. Loss Reserves do not reflect contingency reserve allowances to account for future loss occurrences. Losses arising from future events will be estimated and recognized at the time the losses are incurred and could be substantial. Insurance Segment Loss Reserves for the insurance segment are comprised of estimated amounts for (1) reported losses (“case reserves”) and (2) incurred but not reported losses (“IBNR reserves”). Generally, claims personnel determine whether to establish a case reserve for the estimated amount of the ultimate settlement of individual claims. The estimate reflects the judgment of claims personnel based on general corporate reserving practices, the experience and knowledge of such personnel regarding the nature and value of the specific type of claim and, where appropriate, advice of counsel. The Company also contracts with a number of outside third party administrators in the claims process who, in certain cases, have limited authority to establish case reserves. The work of such administrators is reviewed and monitored by our claims personnel. Loss Reserves are also established to provide for loss adjustment expenses and represent the estimated expense of settling claims, including legal and other fees and the general expenses of administering the claims adjustment process. Periodically, adjustments to the case reserves may be made as additional information is reported or payments are made. IBNR reserves are established to provide for incurred claims which have not yet been reported at the balance sheet date as well as to adjust for any projected variance in case reserving. Actuaries estimate ultimate losses and loss adjustment expenses using various generally accepted actuarial methods applied to known losses and other relevant information. Like case reserves, IBNR reserves are adjusted as additional information becomes known or payments are made. The process of estimating reserves involves a considerable degree of judgment by management and, as of any given date, is inherently uncertain. Ultimate losses and loss adjustment expenses are generally determined by extrapolation of claim emergence and settlement patterns observed in the past that can reasonably be expected to persist into the future. In forecasting ultimate losses and loss adjustment expenses with respect to any line of business, past experience with respect to that line of business is the primary resource, developed through both industry and company experience, but cannot be relied upon in isolation. Uncertainties in estimating ultimate losses and loss adjustment expenses are magnified by the length of the time lag between when a claim actually occurs and when it is reported and settled. This time lag is sometimes referred to as the “claim-tail.” During this period additional facts regarding coverages written in prior accident years, as well as about actual claims and trends, may become known and, as a result, may lead to adjustments of the related Loss Reserves. If the Company determines that an adjustment is appropriate, the adjustment is recorded in the accounting period in which such determination is made. Accordingly, should Loss Reserves need to be increased or decreased in the future from amounts currently established, future results of operations would be negatively or positively impacted respectively. The Company authorizes managing general agents, general agents and other producers to write program business on the Company’s behalf within prescribed underwriting authorities. This delegated authority process introduces additional complexity to the actuarial determination of unpaid future losses and loss adjustment expenses. In order to monitor adherence to the underwriting guidelines given to such parties, the Company periodically performs underwriting and claims due diligence reviews. In determining ultimate losses and loss adjustment expenses, the cost to indemnify claimants, provide needed legal defense and other services for insureds and administer the investigation and adjustment of claims are considered. These claim costs are influenced by many factors that change over time, such as expanded coverage definitions as a result of new court decisions, inflation in costs to repair or replace damaged property, inflation in the cost of medical services and legislated changes in statutory benefits, as well as by the particular, unique facts that pertain to each claim. As a result, the rate at which claims arose in the past and the costs to settle them may not always be representative of what will occur in the future. The factors influencing changes in claim costs are often difficult to isolate or quantify and developments in paid and incurred losses from historical trends are frequently subject to multiple and conflicting interpretations. Changes in coverage terms or claims handling practices may also cause future experience and/or development patterns to vary from the past. A key objective of actuaries in developing estimates of ultimate losses and loss adjustment expenses, and resulting IBNR reserves, is to identify aberrations and systemic changes occurring within historical experience and adjust for them so that the future can be projected more reliably. Because of the factors previously discussed, this process requires the substantial use of informed judgment and is inherently uncertain. Although Loss Reserves are initially determined based on underwriting and pricing analyses, the Company’s insurance segment applies several generally accepted actuarial methods, as discussed below, on a quarterly basis to evaluate the Loss Reserves, in addition to the expected loss method, in particular for Loss Reserves from more mature accident years (the year in which a loss occurred). Each quarter, as part of the reserving process, the segments’ actuaries reaffirm that the assumptions used in the reserving process continue to form a sound basis for the projection of liabilities. If actual loss activity differs substantially from expectations based on historical information, an adjustment to Loss Reserves may be supported. The Company places more or less reliance on a particular actuarial method based on the facts and circumstances at the time the estimates of Loss Reserves are made. These methods generally fall into one of the following categories or are hybrids of one or more of the following categories: • Expected loss methods - these methods are based on the assumption that ultimate losses vary proportionately with premiums. Expected loss and loss adjustment expense ratios are typically developed based upon the information derived by underwriters and actuaries during the initial pricing of the business, supplemented by industry data available from organizations, such as statistical bureaus and consulting firms, where appropriate. These ratios consider, among other things, rate increases and changes in terms and conditions that have been observed in the market. Expected loss methods are useful for estimating ultimate losses and loss adjustment expenses in the early years of long-tailed lines of business, when little or no paid or incurred loss information is available, and is commonly applied when limited loss experience exists for a company. • Historical incurred loss development methods - these methods assume that the ratio of losses in one period to losses in an earlier period will remain constant in the future. These methods use incurred losses ( i.e. , the sum of cumulative historical loss payments plus outstanding case reserves) over discrete periods of time to estimate future losses. Historical incurred loss development methods may be preferable to historical paid loss development methods because they explicitly take into account open cases and the claims adjusters’ evaluations of the cost to settle all known claims. However, historical incurred loss development methods necessarily assume that case reserving practices are consistently applied over time. Therefore, when there have been significant changes in how case reserves are established, using incurred loss data to project ultimate losses may be less reliable than other methods. • Historical paid loss development methods - these methods, like historical incurred loss development methods, assume that the ratio of losses in one period to losses in an earlier period will remain constant. These methods use historical loss payments over discrete periods of time to estimate future losses and necessarily assume that factors that have affected paid losses in the past, such as inflation or the effects of litigation, will remain constant in the future. Because historical paid loss development methods do not use incurred losses to estimate ultimate losses, they may be more reliable than the other methods that use incurred losses in situations where there are significant changes in how incurred losses are established by a company’s claims adjusters. However, historical paid loss development methods are more leveraged (meaning that small changes in payments have a larger impact on estimates of ultimate losses) than actuarial methods that use incurred losses because cumulative loss payments take much longer to equal the expected ultimate losses than cumulative incurred amounts. In addition, and for similar reasons, historical paid loss development methods are often slow to react to situations when new or different factors arise than those that have affected paid losses in the past. • Adjusted historical paid and incurred loss development methods - these methods take traditional historical paid and incurred loss development methods and adjust them for the estimated impact of changes from the past in factors such as inflation, the speed of claim payments or the adequacy of case reserves. Adjusted historical paid and incurred loss development methods are often more reliable methods of predicting ultimate losses in periods of significant change, provided the actuaries can develop methods to reasonably quantify the impact of changes. As such, these methods utilize more judgment than historical paid and incurred loss development methods. • Bornhuetter-Ferguson (“B-F”) paid and incurred loss methods - these methods utilize actual paid and incurred losses and expected patterns of paid and incurred losses, taking the initial expected ultimate losses into account to determine an estimate of expected ultimate losses. The B-F paid and incurred loss methods are useful when there are few reported claims and a relatively less stable pattern of reported losses. • Frequency-Severity methods - These methods utilize actual paid and incurred claim experience, but break the data down into its component pieces: claim counts, often expressed as a ratio to exposure or premium (frequency), and average claim size (severity). The component pieces are projected to an ultimate level and multiplied together to result in an estimate of ultimate loss. These methods are especially useful when the severity of claims can be confined to a relatively stable range of estimated ultimate average claim value. • Additional analyses - other methodologies are often used in the reserving process for specific types of claims or events, such as catastrophic or other specific major events. These include vendor catastrophe models, which are typically used in the estimation of Loss Reserves at the early stage of known catastrophic events before information has been reported to an insurer or reinsurer. In the initial reserving process for short-tail insurance lines (consisting of property, energy, marine and aviation and other exposures including travel, accident and health and lenders products), the Company relies on a combination of the reserving methods discussed above. For catastrophe-exposed business, the reserving process also includes the usage of catastrophe models for known events and a heavy reliance on analysis of individual catastrophic events and management judgment. The development of losses on short-tail business can be unstable, especially for policies characterized by high severity, low frequency losses. As time passes, for a given accident year, additional weight is given to the paid and incurred B-F loss development methods and eventually to the historical paid and incurred loss development methods in the reserving process. The Company makes a number of key assumptions in their reserving process, including that historical paid and reported development patterns are stable, catastrophe models provide useful information about our exposure to catastrophic events that have occurred and underwriters’ judgment as to potential loss exposures can be relied on. The expected loss ratios used in the initial reserving process for short-tail business have varied over time due to changes in pricing, reinsurance structure, estimates of catastrophe losses, policy changes (such as attachment points, class and limits) and geographical distribution. As losses in short-tail lines are reported relatively quickly, expected loss ratios are selected for the current accident year based upon actual attritional loss ratios for earlier accident years, adjusted for rate changes, inflation, changes in reinsurance programs and expected attritional losses based on modeling. Furthermore, ultimate losses for short-tail business are known in a reasonably short period of time. In the initial reserving process for medium-tail and long-tail insurance lines ( consisting of third party occurrence business, third party claims made business, and other exposures including surety, programs and contract binding exposures), the Company primarily relies on the expected loss method. The development of the Company’s medium-tail and long-tail business may be unstable, especially if there are high severity major events, as a portion of the Company’s casualty business is in high excess layers. As time passes, for a given accident year, additional weight is given to the paid and incurred B-F loss development methods and historical paid and incurred loss development methods in the reserving process. The Company makes a number of key assumptions in reserving for medium-tail and long-tail lines, including that the pricing loss ratio is the best estimate of the ultimate loss ratio at the time the policy is entered into, that the loss development patterns, which are based on a combination of company and industry loss development patterns and adjusted to reflect differences in the insurance segment’s mix of business, are reasonable and that claims personnel and underwriters analyses of our exposure to major events are assumed to be the best estimate of exposure to the known claims on those events. The expected loss ratios used in the initial reserving process for medium-tail and long-tail business for recent accident years have varied over time, in some cases significantly, from earlier accident years. As the credibility of historical experience for earlier accident years increases, the experience from these accident years will be given a greater weighting in the actuarial analysis to determine future accident year expected loss ratios, adjusted for changes in pricing, loss trends, terms and conditions and reinsurance structure. In 2019 and 2018, the Company entered into two separate loss portfolio transfers and adverse development cover reinsurance agreements accounted for as retroactive reinsurance. These agreements transfer Loss Reserves and future favorable or adverse development on certain runoff programs and other exposures within multi-line and other specialty business, and certain third party occurrence business (the “Covered Lines”). As incurred losses and allocated loss adjustment expenses for the Covered Lines are ceded to the reinsurer, the Company is not exposed to changes in the amount, timing and uncertainty of cash flows arising from the Covered Lines. To avoid distortion, the incurred losses and allocated loss adjustment expenses and cumulative paid losses and loss adjustment expenses for the Covered Lines are excluded entirely from the tables below. Reinsurance recoverables at December 31, 2019 included $319.3 million related to these reinsurance agreements. The following tables present information on the insurance segment’s short-duration insurance contracts: Property, energy, marine and aviation ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2019 Total of IBNR liabilities plus expected development on reported claims Cumulative number of reported claims Year ended December 31, Accident year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2010 $ 197,399 $ 187,305 $ 151,937 $ 139,757 $ 128,475 $ 128,799 $ 127,530 $ 124,974 $ 120,813 $ 118,570 $ 1,310 3,676 2011 266,725 269,790 229,244 217,753 208,494 205,344 198,763 198,956 198,370 868 4,219 2012 230,399 229,820 203,408 197,187 194,746 190,930 188,649 178,394 2,487 4,266 2013 156,936 154,313 146,777 140,967 132,839 132,211 128,247 752 4,279 2014 146,391 143,825 145,065 134,055 133,482 129,973 6,769 3,930 2015 110,867 108,260 102,535 102,221 97,361 5,669 4,613 2016 102,910 99,899 104,246 100,542 560 6,388 2017 278,549 247,072 235,152 14,830 6,744 2018 185,486 179,262 29,117 5,333 2019 161,850 59,863 5,688 Total $ 1,527,721 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2010 $ 28,433 $ 65,846 $ 87,476 $ 105,887 $ 110,892 $ 117,737 $ 119,953 $ 118,437 $ 119,276 $ 116,822 2011 34,002 98,616 140,555 165,950 198,128 199,943 195,613 196,272 196,056 2012 20,301 92,034 137,179 159,862 165,488 177,945 179,138 173,058 2013 31,874 83,689 109,088 118,131 120,385 123,392 123,696 2014 25,620 53,060 76,774 83,080 86,518 99,041 2015 23,271 63,990 75,340 84,964 88,433 2016 24,442 82,357 97,147 97,674 2017 29,915 138,525 196,290 2018 29,641 102,798 2019 26,014 Total 1,219,882 All outstanding liabilities before 2010, net of reinsurance 32,875 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 340,714 Third party occurrence business ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2019 Total of IBNR liabilities plus expected development on reported claims Cumulative number of reported claims Year ended December 31, Accident year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2010 $ 217,431 $ 235,241 $ 230,710 $ 230,859 $ 233,204 $ 229,534 $ 223,618 $ 215,332 $ 218,374 $ 211,046 $ 33,176 62,757 2011 233,958 240,406 253,691 258,348 252,227 253,598 246,721 239,395 233,563 44,601 71,101 2012 240,917 262,373 267,980 270,603 257,059 252,497 242,648 242,454 60,258 65,806 2013 282,629 296,492 306,358 301,403 281,437 275,101 271,116 74,749 66,990 2014 329,448 335,281 338,194 342,455 340,408 341,595 98,049 75,526 2015 358,478 391,198 398,185 394,268 388,744 146,656 77,727 2016 389,333 393,991 406,785 397,914 193,182 77,100 2017 416,856 419,456 421,414 254,057 82,458 2018 434,854 450,950 315,814 74,221 2019 454,723 390,054 62,988 Total $ 3,413,519 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2010 $ 6,753 $ 25,511 $ 45,550 $ 72,696 $ 102,391 $ 117,250 $ 132,818 $ 142,380 $ 148,140 $ 158,370 2011 7,006 25,142 43,309 73,268 113,283 134,342 152,472 160,326 171,744 2012 6,962 30,799 58,387 83,193 108,087 129,369 142,932 153,263 2013 6,842 29,214 71,328 101,148 122,043 148,951 162,910 2014 9,204 40,232 71,397 112,434 161,780 188,871 2015 11,112 44,522 88,383 139,283 179,435 2016 11,684 41,893 87,424 135,617 2017 13,392 52,283 99,225 2018 16,994 62,762 2019 18,202 Total 1,330,399 All outstanding liabilities before 2010, net of reinsurance 181,719 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 2,264,839 Third party claims-made business ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2019 Total of IBNR liabilities plus expected development on reported claims Cumulative number of reported claims Year ended December 31, Accident year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2010 $ 286,202 $ 311,709 $ 332,779 $ 338,238 $ 331,006 $ 314,388 $ 298,444 $ 280,497 $ 283,530 $ 284,427 $ 8,775 12,335 2011 281,448 323,369 314,961 309,684 315,118 294,367 281,487 284,242 279,909 14,003 11,762 2012 309,654 312,143 310,359 305,362 283,903 268,765 271,663 272,826 17,820 14,759 2013 295,759 313,601 317,165 313,738 288,506 286,280 271,290 29,604 14,542 2014 260,698 275,172 293,467 273,876 278,182 287,424 42,805 13,935 2015 254,540 272,413 271,343 257,902 246,366 43,026 13,815 2016 270,537 286,677 306,837 304,266 81,707 15,716 2017 266,526 284,875 300,710 131,795 15,904 2018 272,655 301,247 177,552 14,934 2019 271,824 224,119 9,698 Total $ 2,820,289 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2010 $ 13,811 $ 70,583 $ 127,531 $ 162,490 $ 197,142 $ 213,530 $ 229,824 $ 233,085 $ 241,887 $ 252,119 2011 13,510 71,038 128,011 171,354 204,215 223,458 235,181 248,524 259,416 2012 17,307 67,314 117,891 160,480 185,656 204,240 221,391 240,281 2013 18,557 85,442 134,509 175,328 193,704 212,488 230,377 2014 13,572 62,308 127,683 170,331 204,330 223,907 2015 8,845 51,064 98,371 124,381 168,664 2016 10,371 67,446 125,740 156,030 2017 9,180 66,582 111,532 2018 12,123 67,567 2019 11,443 Total 1,721,336 All outstanding liabilities before 2010, net of reinsurance 126,168 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 1,225,121 Multi-line and other specialty ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2019 Total of IBNR liabilities plus expected development on reported claims Cumulative number of reported claims Year ended December 31, Accident year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2010 $ 173,984 $ 176,796 $ 169,307 $ 166,892 $ 158,092 $ 154,716 $ 153,526 $ 153,598 $ 151,951 $ 150,342 $ 2,508 37,891 2011 182,372 187,924 182,213 175,794 171,923 171,691 168,243 169,851 169,467 3,097 44,881 2012 252,699 263,326 257,420 255,055 254,155 246,077 246,482 243,042 4,255 55,403 2013 263,349 271,603 262,837 263,097 251,187 252,713 247,659 7,096 71,701 2014 300,962 324,736 317,210 317,161 316,047 312,400 11,578 109,295 2015 333,519 356,543 355,484 363,627 355,095 17,097 147,950 2016 406,309 428,530 425,281 413,668 25,881 173,735 2017 479,694 498,860 488,276 46,435 217,360 2018 573,827 621,724 123,652 243,725 2019 604,356 299,028 169,915 Total $ 3,606,029 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2010 $ 49,906 $ 91,265 $ 111,143 $ 125,897 $ 135,981 $ 140,372 $ 143,459 $ 146,357 $ 146,482 $ 146,413 2011 51,145 102,910 117,372 136,078 147,466 151,126 156,619 158,902 161,887 2012 78,178 165,305 189,330 208,372 222,024 230,929 232,064 235,461 2013 86,403 150,432 179,785 212,713 224,665 233,572 235,784 2014 107,529 196,081 232,950 265,927 279,950 290,702 2015 137,561 235,193 276,608 304,464 319,788 2016 174,366 302,470 339,125 360,602 2017 179,777 339,753 378,500 2018 213,065 399,443 2019 213,559 Total 2,742,139 All outstanding liabilities before 2010, net of reinsurance 23,337 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 887,227 The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2019 : Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Property, energy, marine and aviation 19.1 % 39.1 % 19.2 % 9.1 % 5.3 % 5.1 % 0.1 % (1.5 )% 0.3 % (2.1 )% Third party occurrence business 3.1 % 8.8 % 10.9 % 12.0 % 12.3 % 8.5 % 6.5 % 4.1 % 3.8 % 4.8 % Third party claims-made business 4.6 % 19.3 % 19.1 % 13.4 % 11.6 % 6.6 % 5.7 % 4.3 % 3.5 % 3.6 % Multi-line and other specialty 35.2 % 29.9 % 10.5 % 9.4 % 5.4 % 3.2 % 1.7 % 1.6 % 0.9 % — % Reinsurance Segment Loss Reserves for the Company’s reinsurance segment are comprised of (1) case reserves, (2) additional case reserves (“ACRs”) and (3) IBNR reserves. The Company receives reports of claims notices from ceding companies and records case reserves based upon the amount of reserves recommended by the ceding company. Case reserves may be supplemented by ACRs, which may be estimated by the Company’s claims personnel ahead of official notification from the ceding company, or when judgment regarding the size or severity of the known event differs from the ceding company. In certain instances, the Company establishes ACRs even when the ceding company does not report any liability on a known event. In addition, specific claim information reported by ceding companies or obtained through claim audits can alert the Company to emerging trends such as changing legal interpretations of coverage and liability, claims from unexpected sources or classes of business, and significant changes in the frequency or severity of individual claims. Such information is often used in the process of estimating IBNR reserves. IBNR reserves are established to provide for incurred claims which have not yet been reported at the balance sheet date as well as to adjust for any projected variance in case reserving. Actuaries estimate ultimate losses and loss adjustment expenses using various generally accepted actuarial methods applied to known losses and other relevant information. Like case reserves, IBNR reserves are adjusted as additional information becomes known or payments are made. The process of estimating Loss Reserves involves a considerable degree of judgment by management and, as of any given date, is inherently uncertain. The estimation of Loss Reserves for the reinsurance segment is subject to the same risk factors as the estimation of Loss Reserves for the insurance segment. In addition, the inherent uncertainties of estimating such reserves are even greater for reinsurers, due primarily to the following factors: (1) the claim-tail for reinsurers is generally longer because claims are first reported to the ceding company and then to the reinsurer through one or more intermediaries, (2) the reliance on premium estimates, where reports have not been received from the ceding company, in the reserving process, (3) the potential for writing a number of reinsurance contracts with different ceding companies with the same exposure to a single loss event, (4) the diversity of loss development patterns among different types of reinsurance contracts, (5) the necessary reliance on the ceding companies for information regarding reported claims and (6) the differing reserving practices among ceding companies. Ultimate losses and loss adjustment expenses are generally determined by extrapolation of claim emergence and settlement patterns observed in the past that can reasonably be expected to persist into the future.As with the insurance segment, the process of estimating Loss Reserves for the reinsurance segment involves a considerable degree of judgment by management and, as of any given date, is inherently uncertain. As discussed above, such uncertainty is greater for reinsurers compared to insurers. As a result, our reinsurance operations obtain information from numerous sources to assist in the process. Pricing actuaries from the reinsurance segment devote considerable effort to understanding and analyzing a ceding company’s operations and loss history during the underwriting of the business, using a combination of ceding company and industry statistics. Such statistics normally include historical premium and loss data by class of business, individual claim information for larger claims, distributions of insurance limits provided, loss reporting and payment patterns, and rate change history. This analysis is used to project expected loss ratios for each treaty during the upcoming contract period. As mentioned above, there can be a considerable time lag from the time a claim is reported to a ceding company to the time it is reported to the reinsurer. The lag can be several years in some cases and may be attributed to a number of reasons, including the time it takes to investigate a claim, delays associated with the litigation process, the deterioration in a claimant’s physical condition many years after an accident occurs, the case reserving approach of the ceding company, etc. In the reserving process, the Company assumes that such lags are predictable, on average, over time and therefore the lags are contemplated in the loss reporting patterns used in their actuarial methods. This means that the reinsurance segment must rely on estimates for a longer period of time than does an insurance company. Backlogs in the recording of assumed reinsurance can also complicate the accuracy of loss reserve estimation. As of December 31, 2019 there were no significant backlogs related to the processing of assumed reinsurance information at our reinsurance operations. The reinsurance segment relies heavily on information reported by ceding companies, as discussed above. In order to determine the accuracy and completeness of such information, underwriters, actuaries, and claims personnel often perform audits of ceding companies and regularly review information received from ceding companies for unusual or unexpected results. Material findings are usually discussed with the ceding companies. The Company sometimes encounters situations where they determine that a claim presentation from a ceding company is not in accordance with contract terms. In these situations, the Company attempts to resolve the dispute with the ceding company. Most situations are resolved amicably and without the need for litigation or arbitration. However, in the infrequent situations where a resolution is not possible, the Company will vigorously defend its position in such disputes. Although Loss Reserves are initially determined based on underwriting and pricing analysis, the Company applies several generally accepted actuarial methods, as discussed above, on a quarterly basis to evaluate its Loss Reserves in addition to the expected loss method, in particular for reserves from more mature underwriting years (th

Reinsurance

Reinsurance	12 Months Ended
	Dec. 31, 2019
Reinsurance Disclosures [Abstract]
Reinsurance	Reinsurance In the normal course of business, the Company’s insurance subsidiaries cede a portion of their premium through pro rata and excess of loss reinsurance agreements on a treaty or facultative basis. The Company’s reinsurance subsidiaries participate in “common account” retrocessional arrangements for certain pro rata treaties. Such arrangements reduce the effect of individual or aggregate losses to all companies participating on such treaties, including the reinsurers, such as the Company’s reinsurance subsidiaries, and the ceding company. In addition, the Company’s reinsurance subsidiaries may purchase retrocessional coverage as part of their risk management program. The Company’s mortgage subsidiaries cede a portion of their premium through quota share arrangements and enter into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies. Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. If the reinsurers are unable to satisfy their obligations under the agreements, the Company’s insurance or reinsurance subsidiaries would be liable for such defaulted amounts. The effects of reinsurance on the Company’s written and earned premiums and losses and loss adjustment expenses with unaffiliated reinsurers were as follows: Year Ended December 31, 2019 2018 2017 Premiums Written Direct $ 5,681,523 $ 4,838,902 $ 4,447,457 Assumed 2,457,437 2,122,102 1,920,968 Ceded (2,099,893 ) (1,614,257 ) (1,407,052 ) Net $ 6,039,067 $ 5,346,747 $ 4,961,373 Premiums Earned Direct $ 5,447,829 $ 4,799,842 $ 4,379,131 Assumed 2,337,950 1,988,038 1,856,573 Ceded (1,999,281 ) (1,555,905 ) (1,391,172 ) Net $ 5,786,498 $ 5,231,975 $ 4,844,532 Losses and Loss Adjustment Expenses Direct $ 2,953,072 $ 2,472,133 $ 2,568,327 Assumed 1,602,528 1,307,317 1,442,077 Ceded (1,422,148 ) (889,344 ) (1,042,958 ) Net $ 3,133,452 $ 2,890,106 $ 2,967,446 Reinsurance Recoverables The Company monitors the financial condition of its reinsurers and attempts to place coverages only with substantial, financially sound carriers. Although the Company has not experienced any material credit losses to date, an inability of its reinsurers or retrocessionaires to meet their obligations to it over the relevant exposure periods for any reason could have a material adverse effect on its financial condition and results of operations. The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums) at December 31, 2019 and 2018 : December 31, 2019 2018 Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses $ 4,346,816 $ 2,919,372 % due from carriers with A.M. Best rating of “A-” or better 61.2 % 63.0 % % due from unrated fully collateralized reinsurers (1) 13.5 % 12.9 % % due from all other carriers with no A.M. Best rating (2) 25.3 % 24.1 % Largest balance due from any one carrier as % of total shareholders’ equity 1.7 % 2.7 % (1) Such amount is fully collateralized through reinsurance trusts. (2) Over 90% of such amount is collateralized through reinsurance trusts or letters of credit. Bellemeade Re The Company has entered into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the “Bellemeade Agreements”). For the respective coverage periods, the Company will retain the first layer of the respective aggregate losses and the special purpose reinsurance companies will provide second layer coverage up to the outstanding coverage amount. The Company will then retain losses in excess of the outstanding coverage limit. The aggregate excess of loss reinsurance coverage decreases over a ten-year period as the underlying covered mortgages amortize. The following table summarizes the respective coverages and retentions at December 31, 2019 : Initial Coverage at Issuance Coverage at Dec. 31, 2019 First Layer Retention Bellemeade 2017-1 Ltd. (1) 368,114 216,429 165,652 Bellemeade 2018-1 Ltd. (2) 374,460 328,482 168,510 Bellemeade 2018-2 Ltd. (3) 653,278 437,009 352,258 Bellemeade 2018-3 Ltd. (4) 506,110 426,806 179,331 Bellemeade 2019-1 Ltd. (5) 341,790 257,358 208,046 Bellemeade 2019-2 Ltd. (6) 621,022 525,959 221,794 Bellemeade 2019-3 Ltd. (7) 700,920 656,523 232,093 Bellemeade 2019-4 Ltd. (8) 577,267 577,267 162,357 Total $ 4,142,961 $ 3,425,833 $ 1,690,041 (1) Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017. (2) Issued in April 2018, covering in-force policies issued between July 1, 2017 and December 31, 2017. (3) Issued in August 2018, covering in-force policies issued between April 1, 2013 and December 31, 2015. (4) Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018. (5) Issued in March 2019, covering in-force policies primarily issued between 2005 to 2008 under United Guaranty Residential Insurance Company (“UGRIC”); as well as policies issued through 2015 under both UGRIC and Arch Mortgage Insurance Company. (6) Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018. (7) Issued in July 2019, covering in-force policies issued in 2016. (8) Issued in October 2019, covering in-force policies issued between January 1, 2019 and June 30, 2019. See Note 11, “Variable Interest Entity and Noncontrolling Interests.”

Investment Information

Investment Information	12 Months Ended
	Dec. 31, 2019
Disclosure Investment Information [Abstract]
Investment Information	Investment Information At December 31, 2019 , total investable assets of $24.99 billion included $22.29 billion held by the Company and $2.70 billion attributable to Watford. Available For Sale Investments The following table summarizes the fair value and cost or amortized cost of the Company’s securities classified as available for sale: Estimated Fair Value Gross Unrealized Gains Gross Unrealized Losses Cost or Amortized Cost OTTI Unrealized Losses (2) December 31, 2019 Fixed maturities (1): Corporate bonds $ 6,406,591 $ 191,889 $ (12,793 ) $ 6,227,495 $ — Mortgage backed securities 562,309 9,669 (931 ) 553,571 (6 ) Municipal bonds 881,926 24,628 (2,213 ) 859,511 — Commercial mortgage backed securities 733,108 14,951 (2,330 ) 720,487 — U.S. government and government agencies 4,916,592 36,600 (10,134 ) 4,890,126 — Non-U.S. government securities 2,078,757 48,549 (20,330 ) 2,050,538 — Asset backed securities 1,683,753 24,017 (4,724 ) 1,664,460 — Total 17,263,036 350,303 (53,455 ) 16,966,188 (6 ) Short-term investments 956,546 811 (1,548 ) 957,283 — Total $ 18,219,582 $ 351,114 $ (55,003 ) $ 17,923,471 $ (6 ) December 31, 2018 Fixed maturities (1): Corporate bonds $ 5,537,548 $ 14,476 $ (105,428 ) $ 5,628,500 $ (69 ) Mortgage backed securities 541,193 3,991 (3,216 ) 540,418 (6 ) Municipal bonds 1,013,395 5,380 (11,891 ) 1,019,906 — Commercial mortgage backed securities 729,442 2,650 (10,751 ) 737,543 — U.S. government and government agencies 3,758,698 27,189 (8,474 ) 3,739,983 — Non-U.S. government securities 1,771,338 14,477 (50,948 ) 1,807,809 — Asset backed securities 1,600,896 8,060 (14,798 ) 1,607,634 — Total 14,952,510 76,223 (205,506 ) 15,081,793 (75 ) Short-term investments 955,880 36 (394 ) 956,238 — Total $ 15,908,390 $ 76,259 $ (205,900 ) $ 16,038,031 $ (75 ) (1) In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.” (2) Represents the total OTTI recognized in accumulated other comprehensive income (“AOCI”). It does not include the change in fair value subsequent to the impairment measurement date. At December 31, 2019 and 2018, the net unrealized gain related to securities for which a non-credit OTTI was recognized in AOCI was nil . The following table summarizes, for all available for sale securities in an unrealized loss position, the fair value and gross unrealized loss by length of time the security has been in a continual unrealized loss position: Less than 12 Months 12 Months or More Total Estimated Fair Value Gross Unrealized Losses Estimated Fair Value Gross Unrealized Losses Estimated Fair Value Gross Unrealized Losses December 31, 2019 Fixed maturities (1): Corporate bonds $ 675,131 $ (12,350 ) $ 37,671 $ (443 ) $ 712,802 $ (12,793 ) Mortgage backed securities 102,887 (927 ) 203 (4 ) 103,090 (931 ) Municipal bonds 220,296 (2,213 ) — — 220,296 (2,213 ) Commercial mortgage backed securities 147,290 (2,302 ) 2,683 (28 ) 149,973 (2,330 ) U.S. government and government agencies 1,373,127 (10,089 ) 32,058 (45 ) 1,405,185 (10,134 ) Non-U.S. government securities 1,224,243 (20,163 ) 37,610 (167 ) 1,261,853 (20,330 ) Asset backed securities 441,522 (3,334 ) 48,313 (1,390 ) 489,835 (4,724 ) Total 4,184,496 (51,378 ) 158,538 (2,077 ) 4,343,034 (53,455 ) Short-term investments 95,777 (1,548 ) — — 95,777 (1,548 ) Total $ 4,280,273 $ (52,926 ) $ 158,538 $ (2,077 ) $ 4,438,811 $ (55,003 ) December 31, 2018 Fixed maturities (1): Corporate bonds $ 2,983,195 $ (68,910 ) $ 1,234,865 $ (36,518 ) $ 4,218,060 $ (105,428 ) Mortgage backed securities 84,296 (695 ) 109,009 (2,521 ) 193,305 (3,216 ) Municipal bonds 233,081 (2,074 ) 408,155 (9,817 ) 641,236 (11,891 ) Commercial mortgage backed securities 223,341 (2,831 ) 193,956 (7,920 ) 417,297 (10,751 ) U.S. government and government agencies 635,049 (1,354 ) 391,102 (7,120 ) 1,026,151 (8,474 ) Non-U.S. government securities 1,028,340 (35,524 ) 389,671 (15,424 ) 1,418,011 (50,948 ) Asset backed securities 533,592 (8,832 ) 368,095 (5,966 ) 901,687 (14,798 ) Total 5,720,894 (120,220 ) 3,094,853 (85,286 ) 8,815,747 (205,506 ) Short-term investments 122,878 (394 ) — — 122,878 (394 ) Total $ 5,843,772 $ (120,614 ) $ 3,094,853 $ (85,286 ) $ 8,938,625 $ (205,900 ) (1) In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received and reinvested and included the fixed maturities pledged. See “—Securities Lending Agreements.” At December 31, 2019 , on a lot level basis, approximately 2,230 security lots out of a total of approximately 9,590 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $0.9 million . The Company believes that such securities were temporarily impaired at December 31, 2019 . At December 31, 2018 , on a lot level basis, approximately 5,870 security lots out of a total of approximately 8,450 security lots were in an unrealized loss position and the largest single unrealized loss from a single lot in the Company’s fixed maturity portfolio was $2.6 million . The contractual maturities of the Company’s fixed maturities and fixed maturities pledged under securities lending agreements are shown in the following table. Expected maturities, which are management’s best estimates, will differ from contractual maturities because borrowers may have the right to call or prepay obligations with or without call or prepayment penalties. December 31, 2019 December 31, 2018 Maturity Estimated Fair Value Amortized Cost Estimated Fair Value Amortized Cost Due in one year or less $ 428,659 $ 423,617 $ 276,682 $ 279,135 Due after one year through five years 10,126,403 9,996,206 8,666,297 8,738,944 Due after five years through 10 years 3,317,535 3,219,567 2,919,232 2,951,582 Due after 10 years 411,269 388,280 218,768 226,537 14,283,866 14,027,670 12,080,979 12,196,198 Mortgage backed securities 562,309 553,571 541,193 540,418 Commercial mortgage backed securities 733,108 720,487 729,442 737,543 Asset backed securities 1,683,753 1,664,460 1,600,896 1,607,634 Total (1) $ 17,263,036 $ 16,966,188 $ 14,952,510 $ 15,081,793 (1) In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received and reinvested and included the fixed maturities pledged. See “—Securities Lending Agreements.” Securities Lending Agreements The Company enters into securities lending agreements with financial institutions to enhance investment income whereby it loans certain of its securities to third parties, primarily major brokerage firms, for short periods of time through a lending agent. The Company maintains legal control over the securities it lends, retains the earnings and cash flows associated with the loaned securities and receives a fee from the borrower for the temporary use of the securities. An indemnification agreement with the lending agent protects the Company in the event a borrower becomes insolvent or fails to return any of the securities on loan to the Company. The Company receives collateral in the form of cash or securities. Cash collateral primarily consists of short-term investments. At December 31, 2019 , the fair value of the cash collateral received on securities lending was $81.2 million and the fair value of security collateral received was $307.2 million . At December 31, 2018 , the fair value of the cash collateral received on securities lending was $19.0 million and the fair value of security collateral received was $255.1 million . The Company’s securities lending transactions were accounted for as secured borrowings with significant investment categories as follows: Remaining Contractual Maturity of the Agreements Overnight and Continuous Less than 30 Days 30-90 Days 90 Days or More Total December 31, 2019 U.S. government and government agencies $ 240,332 $ — $ 115,973 $ — $ 356,305 Corporate bonds 2,570 — — — 2,570 Equity securities 29,491 — — — 29,491 Total $ 272,393 $ — $ 115,973 $ — $ 388,366 Gross amount of recognized liabilities for securities lending in offsetting disclosure in Note 10 — Amounts related to securities lending not included in offsetting disclosure in Note 10 $ 388,366 December 31, 2018 U.S. government and government agencies $ 219,276 $ — $ 32,583 $ — $ 251,859 Corporate bonds 7,129 — — — 7,129 Equity securities 15,137 — — — 15,137 Total $ 241,542 $ — $ 32,583 $ — $ 274,125 Gross amount of recognized liabilities for securities lending in offsetting disclosure in Note 10 — Amounts related to securities lending not included in offsetting disclosure in Note 10 $ 274,125 Equity Securities, at Fair Value At December 31, 2019 , the Company held $838.9 million of equity securities, at fair value, compared to $338.9 million at December 31, 2018 . Pursuant to applicable accounting guidance, changes in fair value on equity securities are recorded through net income effective January 1, 2018. Other Investments The following table summarizes the Company’s other investments, which are included in investments accounted for using the fair value option, by strategy: December 31, 2019 2018 Term loan investments 1,326,018 1,282,287 Lending 602,841 524,112 Credit related funds 123,020 202,123 Energy 97,402 117,509 Investment grade fixed income 151,594 101,902 Infrastructure 61,786 45,371 Private equity 49,376 24,383 Real estate 17,279 14,252 Total $ 2,429,316 $ 2,311,939 Investments Accounted For Using the Equity Method The following table summarizes the Company’s investments accounted for using the equity method, by strategy: December 31, 2019 2018 Credit related funds $ 428,437 $ 429,402 Equities 293,686 375,273 Real estate 246,851 232,647 Lending 202,690 125,041 Private equity 144,983 114,019 Infrastructure 235,033 113,748 Energy 108,716 103,661 Total $ 1,660,396 $ 1,493,791 In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the fair value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. A summary of financial information for the Company’s investment funds accounted for using the equity method is as follows: December 31, 2019 2018 Invested assets $ 26,383,370 $ 28,299,386 Total assets 28,039,181 29,833,681 Total liabilities 3,595,695 3,406,612 Net assets $ 24,443,486 $ 26,427,069 Year Ended December 31, 2019 2018 2017 Total revenues $ 164,669 $ 4,565,354 $ 3,867,874 Total expenses 528,762 1,135,602 782,773 Net income (loss) $ (364,093 ) $ 3,429,752 $ 3,085,101 Certain of the Company’s other investments and investments accounted for using the equity method are in investment funds for which the Company has the option to redeem at agreed upon values as described in each investment fund’s subscription agreement. Depending on the terms of the various subscription agreements, investments in investment funds may be redeemed daily, monthly, quarterly or on other terms. Two common redemption restrictions which may impact the Company’s ability to redeem these investment funds are gates and lockups. A gate is a suspension of redemptions which may be implemented by the general partner or investment manager of the fund in order to defer, in whole or in part, the redemption request in the event the aggregate amount of redemption requests exceeds a predetermined percentage of the investment fund's net assets which may otherwise hinder the general partner or investment manager's ability to liquidate holdings in an orderly fashion in order to generate the cash necessary to fund extraordinarily large redemption payouts. A lockup period is the initial amount of time an investor is contractually required to hold the security before having the ability to redeem. If the investment funds are eligible to be redeemed, the time to redeem such fund can take weeks or months following the notification. Fair Value Option The following table summarizes the Company’s assets which are accounted for using the fair value option: December 31, 2019 2018 Fixed maturities $ 754,452 $ 1,245,562 Other investments 2,429,316 2,311,939 Short-term investments 377,014 322,177 Equity securities 102,695 103,893 Investments accounted for using the fair value option $ 3,663,477 $ 3,983,571 Limited Partnership Interests In the normal course of its activities, the Company invests in limited partnerships as part of its overall investment strategy. Such amounts are included in ‘investments accounted for using the equity method’ and ‘investments accounted for using the fair value option.’ The Company determined that these limited partnership interests represented variable interests in the funds because the general partner did not have a significant interest in the funds. The Company’s maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company’s consolidated balance sheet and any unfunded commitment. The following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet item: December 31, 2019 2018 Investments accounted for using the equity method (1) $ 1,660,396 $ 1,493,791 Investments accounted for using the fair value option (2) 188,283 162,398 Total $ 1,848,679 $ 1,656,189 (1) Aggregate unfunded commitments were $1.36 billion at December 31, 2019 , compared to $1.22 billion at December 31, 2018 . (2) Aggregate unfunded commitments were $41.7 million at December 31, 2019 , compared to $117.5 million at December 31, 2018 . Net Investment Income The components of net investment income were derived from the following sources: Year Ended December 31, 2019 2018 2017 Fixed maturities $ 505,399 $ 470,912 $ 385,919 Term loans 98,949 87,926 86,017 Equity securities 15,857 13,154 11,752 Short-term investments 15,820 18,793 10,964 Other (1) 80,618 64,942 68,249 Gross investment income 716,643 655,727 562,901 Investment expenses (88,905 ) (92,094 ) (92,029 ) Net investment income $ 627,738 $ 563,633 $ 470,872 (1) Includes income distributions from investment funds and other items. Net Realized Gains (Losses) Net realized gains (losses) were as follows, excluding the other-than-temporary impairment provisions: Year Ended December 31, 2019 2018 2017 Available for sale securities: Gross gains on investment sales $ 235,655 $ 69,299 $ 286,415 Gross losses on investment sales (104,612 ) (223,123 ) (203,873 ) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities 41,910 (90,898 ) 29,451 Other investments (35,734 ) (90,778 ) 51,124 Equity securities 15,869 (5,984 ) 18,707 Short-term investments 3,801 (461 ) 272 Equity securities, at fair value (1): Net realized gains (losses) on securities sold 11,313 (40,117 ) — Net unrealized gains (losses) on equity securities still held at reporting date 97,768 (22,828 ) — Derivative instruments (2) 119,741 15,636 (7,356 ) Other (3) (19,348 ) (16,090 ) (25,599 ) Net realized gains (losses) $ 366,363 $ (405,344 ) $ 149,141 (1) Effective January 1, 2018, changes in fair value on equity securities are recorded through net income. (2) See Note 10 for information on the Company’s derivative instruments. (3) Includes the re-measurement of contingent consideration liability amounts. Equity in Net Income (Loss) of Investments Accounted For Using the Equity Method The Company recorded equity in net income related to investments accounted for using the equity method of $123.7 million for 2019 , compared to $45.6 million for 2018 and $142.3 million for 2017 . Other-Than-Temporary Impairments The Company performs quarterly reviews of its available for sale investments in order to determine whether declines in fair value below the amortized cost basis were considered other-than-temporary in accordance with applicable guidance. The following table details the net impairment losses recognized in earnings by asset class: Year Ended December 31, 2019 2018 2017 Fixed maturities: Mortgage backed securities $ (915 ) $ (437 ) $ (1,488 ) Corporate bonds (1,256 ) (1,232 ) (2,884 ) Non-U.S. government securities — (290 ) (376 ) Asset backed securities (994 ) (811 ) — U.S. government and government agencies — — (426 ) Municipal bonds — — (375 ) Total (3,165 ) (2,770 ) (5,549 ) Short-term investments — (59 ) — Equity securities — — (1,422 ) Other investments — — (167 ) Net impairment losses recognized in earnings $ (3,165 ) $ (2,829 ) $ (7,138 ) A description of the methodology and significant inputs used to measure the amount of net impairment losses recognized in earnings in 2019 is as follows: • Corporate bonds – the Company reviewed the business prospects, credit ratings, estimated loss given default factors, foreign currency impacts and information received from asset managers and rating agencies for certain corporate bonds. Impairment losses were primarily from foreign currency impacts; • Mortgage backed and asset backed securities – the Company utilized underlying data provided by asset managers, cash flow projections and additional information from credit agencies in order to determine an expected recovery value for each security. The Company believes that the OTTI included in accumulated other comprehensive income at December 31, 2019 on the securities which were considered by the Company to be impaired was due to market and sector-related factors ( i.e. , not credit losses). At December 31, 2019 , the Company did not intend to sell these securities, or any other securities which were in an unrealized loss position, and determined that it is more likely than not that the Company will not be required to sell such securities before recovery of their cost basis. The following table provides a roll forward of the amount related to credit losses recognized in earnings for which a portion of an OTTI was recognized in accumulated other comprehensive income: Year Ended December 31, 2019 2018 2017 Balance at start of year $ 637 $ 767 $ 13,138 Credit loss impairments recognized on securities not previously impaired — — 31 Credit loss impairments recognized on securities previously impaired — — 210 Reductions for increases in cash flows expected to be collected that are recognized over the remaining life of the security — — — Reductions for securities sold during the period (291 ) (130 ) (12,612 ) Balance at end of year $ 346 $ 637 $ 767 Restricted Assets The Company is required to maintain assets on deposit, which primarily consist of fixed maturities, with various regulatory authorities to support its underwriting operations. The Company’s subsidiaries maintain assets in trust accounts as collateral for transactions with affiliated companies and also have investments in segregated portfolios primarily to provide collateral or guarantees for letters of credit to third parties The following table details the value of the Company’s restricted assets: December 31, 2019 2018 Assets used for collateral or guarantees: Affiliated transactions $ 4,526,761 $ 4,623,483 Third party agreements 2,278,248 2,181,682 Deposits with U.S. regulatory authorities 797,371 689,114 Deposits with non-U.S. regulatory authorities 119,238 59,624 Total restricted assets $ 7,721,618 $ 7,553,903 In addition, Watford maintains a secured credit facility to provide borrowing capacity for investment purposes and a total return swap agreement and maintains assets pledged as collateral for such purposes. The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from reinsurance transactions. As of December 31, 2019 and December 31, 2018 , Watford held $1.0 billion and $1.3 billion , respectively, in pledged assets to collateralize the credit facility mentioned above. Reconciliation of Cash and Restricted Cash The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets: December 31, 2019 2018 2017 Cash $ 726,230 $ 646,556 $ 606,199 Restricted cash (included in ‘other assets’) 177,468 78,087 121,085 Cash and restricted cash $ 903,698 $ 724,643 $ 727,284

Fair Value

Fair Value	12 Months Ended
	Dec. 31, 2019
Fair Value Disclosures [Abstract]
Fair Value	Fair Value Accounting guidance regarding fair value measurements addresses how companies should measure fair value when they are required to use a fair value measure for recognition or disclosure purposes under GAAP and provides a common definition of fair value to be used throughout GAAP. It defines fair value as the price that would be received to sell an asset or paid to transfer a liability in an orderly fashion between market participants at the measurement date. In addition, it establishes a three-level valuation hierarchy for the disclosure of fair value measurements. The valuation hierarchy is based upon the transparency of inputs to the valuation of an asset or liability as of the measurement date. The level in the hierarchy within which a given fair value measurement falls is determined based on the lowest level input that is significant to the measurement (Level 1 being the highest priority and Level 3 being the lowest priority). The levels in the hierarchy are defined as follows: Level 1: Inputs to the valuation methodology are observable inputs that reflect quoted prices (unadjusted) for identical assets or liabilities in active markets Level 2: Inputs to the valuation methodology include quoted prices for similar assets and liabilities in active markets, and inputs that are observable for the asset or liability, either directly or indirectly, for substantially the full term of the financial instrument Level 3: Inputs to the valuation methodology are unobservable and significant to the fair value measurement Following is a description of the valuation methodologies used for securities measured at fair value, as well as the general classification of such securities pursuant to the valuation hierarchy. The Company reviews its securities measured at fair value and discusses the proper classification of such investments with investment advisers and others. The Company determines the existence of an active market based on its judgment as to whether transactions for the financial instrument occur in such market with sufficient frequency and volume to provide reliable pricing information. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. The Company uses quoted values and other data provided by nationally recognized independent pricing sources as inputs into its process for determining fair values of its fixed maturity investments. To validate the techniques or models used by pricing sources, the Company's review process includes, but is not limited to: (i) quantitative analysis (e.g., comparing the quarterly return for each managed portfolio to its target benchmark, with significant differences identified and investigated); (ii) a review of the prices obtained in the pricing process and the range of resulting fair values; (iii) initial and ongoing evaluation of methodologies used by outside parties to calculate fair value; (iv) a comparison of the fair value estimates to the Company’s knowledge of the current market; (v) a comparison of the pricing services' fair values to other pricing services' fair values for the same investments; and (vi) periodic back-testing, which includes randomly selecting purchased or sold securities and comparing the executed prices to the fair value estimates from the pricing service. A price source hierarchy was maintained in order to determine which price source would be used ( i.e. , a price obtained from a pricing service with more seniority in the hierarchy will be used over a less senior one in all cases). The hierarchy prioritizes pricing services based on availability and reliability and assigns the highest priority to index providers. Based on the above review, the Company will challenge any prices for a security or portfolio which are considered not to be representative of fair value. In certain circumstances, when fair values are unavailable from these independent pricing sources, quotes are obtained directly from broker-dealers who are active in the corresponding markets. Such quotes are subject to the validation procedures noted above. Of the $22.9 billion of financial assets and liabilities measured at fair value at December 31, 2019 , approximately $179.6 million , or 0.8% , were priced using non-binding broker-dealer quotes. Of the $20.4 billion of financial assets and liabilities measured at fair value at December 31, 2018 , approximately $217.9 million , or 1.1% , were priced using non-binding broker-dealer quotes. Fixed maturities The Company uses the market approach valuation technique to estimate the fair value of its fixed maturity securities, when possible. The market approach includes obtaining prices from independent pricing services, such as index providers and pricing vendors, as well as to a lesser extent quotes from broker-dealers. The independent pricing sources obtain market quotations and actual transaction prices for securities that have quoted prices in active markets. Each source has its own proprietary method for determining the fair value of securities that are not actively traded. In general, these methods involve the use of “matrix pricing” in which the independent pricing source uses observable market inputs including, but not limited to, investment yields, credit risks and spreads, benchmarking of like securities, broker-dealer quotes, reported trades and sector groupings to determine a reasonable fair value. The following describes the significant inputs generally used to determine the fair value of the Company’s fixed maturity securities by asset class: • U.S. government and government agencies — valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The Company determined that all U.S. Treasuries would be classified as Level 1 securities due to observed levels of trading activity, the high number of strongly correlated pricing quotes received on U.S. Treasuries and other factors. The fair values of U.S. government agency securities are generally determined using the spread above the risk-free yield curve. As the yields for the risk-free yield curve and the spreads for these securities are observable market inputs, the fair values of U.S. government agency securities are classified within Level 2. • Corporate bonds — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined using the spread above the risk-free yield curve. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for corporate bonds are observable market inputs, the fair value of these securities are classified within Level 2. During 2019, the Company transferred $25.8 million of corporate bonds from Level 2 to Level 3 based on a review of the pricing of such securities, as described above. • Mortgage-backed securities — valuations provided by independent pricing services, substantially all through pricing vendors and index providers with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the expected average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. The pricing services also review prepayment speeds and other indicators, when applicable. As the significant inputs used in the pricing process for mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2. • Municipal bonds — valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities are generally determined using spreads obtained from broker-dealers who trade in the relevant security market, trade prices and the new issue market. As the significant inputs used in the pricing process for municipal bonds are observable market inputs, the fair value of these securities are classified within Level 2. • Commercial mortgage-backed securities — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for commercial mortgage-backed securities are observable market inputs, the fair value of these securities are classified within Level 2. • Non-U.S. government securities — valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities are generally based on international indices or valuation models which include daily observed yield curves, cross-currency basis index spreads and country credit spreads. As the significant inputs used in the pricing process for non-U.S. government securities are observable market inputs, the fair value of these securities are classified within Level 2. • Asset-backed securities — valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models (including Option Adjusted Spread) which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. As the significant inputs used in the pricing process for asset-backed securities are observable market inputs, the fair value of these securities are classified within Level 2. A small number of securities are included in Level 3 due to a low level of transparency on the inputs used in the pricing process. Equity securities The Company determined that exchange-traded equity securities would be included in Level 1 as their fair values are based on quoted market prices in active markets. Other equity securities are included in Level 2 of the valuation hierarchy. A small number of securities are included in Level 3 due to the lack of an available independent price source for such securities. As the significant inputs used to price these securities are unobservable, the fair value of such securities are classified as Level 3. During the 2019 second quarter, the Company transferred $107.4 million of equity securities from Level 2 to Level 3 based on a review of the pricing of such securities, as described above. Other investments The Company determined that exchange-traded investments would be included in Level 1 as their fair values are based on quoted market prices in active markets. Other investments also include term loan investments for which fair values are estimated by using quoted prices of term loan investments with similar characteristics, pricing models or matrix pricing. Such investments are generally classified within Level 2. A small number of securities are included in Level 3 due to the lack of an available independent price source for such securities. During 2019, the Company transferred $31.6 million of other investments from Level 2 to Level 3 based on a review of the pricing of such securities, as described above. Derivative instruments The Company’s futures contracts, foreign currency forward contracts, interest rate swaps and other derivatives trade in the over-the-counter derivative market. The Company uses the market approach valuation technique to estimate the fair value for these derivatives based on significant observable market inputs from third party pricing vendors, non-binding broker-dealer quotes and/or recent trading activity. As the significant inputs used in the pricing process for these derivative instruments are observable market inputs, the fair value of these securities are classified within Level 2. Short-term investments The Company determined that certain of its short-term investments held in highly liquid money market-type funds, Treasury bills and commercial paper would be included in Level 1 as their fair values are based on quoted market prices in active markets. The fair values of other short-term investments are generally determined using the spread above the risk-free yield curve and are classified within Level 2. Contingent consideration liabilities Contingent consideration liabilities (included in ‘other liabilities’ in the consolidated balance sheets) include amounts related to the Company’s 2014 acquisition of CMG Mortgage Insurance Company and its affiliated mortgage insurance companies (the “CMG Entities”) and other acquisitions. Such amounts are remeasured at fair value at each balance sheet date with changes in fair value recognized in ‘net realized gains (losses).’ To determine the fair value of contingent consideration liabilities, the Company estimates future payments using an income approach based on modeled inputs which include a weighted average cost of capital. The Company determined that contingent consideration liabilities would be included within Level 3. The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2019 : Fair Value Measurement Using: Estimated Fair Value Quoted Prices in Active Markets for Identical Assets (Level 1) Significant Other Observable Inputs (Level 2) Significant Unobservable Inputs (Level 3) Assets measured at fair value (1): Available for sale securities: Fixed maturities: Corporate bonds $ 6,406,591 $ — $ 6,397,740 $ 8,851 Mortgage backed securities 562,309 — 562,055 254 Municipal bonds 881,926 — 881,926 — Commercial mortgage backed securities 733,108 — 733,108 — U.S. government and government agencies 4,916,592 4,805,581 111,011 — Non-U.S. government securities 2,078,757 — 2,078,757 — Asset backed securities 1,683,753 — 1,678,791 4,962 Total 17,263,036 4,805,581 12,443,388 14,067 Short-term investments 956,546 904,804 51,742 — Equity securities, at fair value 850,283 789,596 4,798 55,889 Derivative instruments (4) 48,946 — 48,946 — Fair value option: Corporate bonds 488,402 — 487,470 932 Non-U.S. government bonds 50,465 — 50,465 — Mortgage backed securities 11,947 — 11,947 — Municipal bonds 377 — 377 — Commercial mortgage backed securities 1,134 — 1,134 — Asset backed securities 200,163 — 200,163 — U.S. government and government agencies 1,962 1,852 110 — Short-term investments 377,014 333,320 43,694 — Equity securities 102,697 43,962 641 58,094 Other investments 1,418,273 53,287 1,296,169 68,817 Other investments measured at net asset value (2) 1,011,043 Total 3,663,477 432,421 2,092,170 127,843 Total assets measured at fair value $ 22,782,288 $ 6,932,402 $ 14,641,044 $ 197,799 Liabilities measured at fair value: Contingent consideration liabilities $ (7,998 ) $ — $ — $ (7,998 ) Securities sold but not yet purchased (3) (66,257 ) — (66,257 ) — Derivative instruments (4) (39,750 ) — (39,750 ) — Total liabilities measured at fair value $ (114,005 ) $ — $ (106,007 ) $ (7,998 ) (1) In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See Note 8 . (2) In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets. (3) Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets. (4) See Note 10 . The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2018 : Fair Value Measurement Using: Estimated Fair Value Quoted Prices in Active Markets for Identical Assets (Level 1) Significant Other Observable Inputs (Level 2) Significant Unobservable Inputs (Level 3) Assets measured at fair value (1): Available for sale securities: Fixed maturities: Corporate bonds $ 5,537,548 $ — $ 5,529,407 $ 8,141 Mortgage backed securities 541,193 — 540,884 309 Municipal bonds 1,013,395 — 1,013,395 — Commercial mortgage backed securities 729,442 — 729,438 4 U.S. government and government agencies 3,758,698 3,657,181 101,517 — Non-U.S. government securities 1,771,338 — 1,771,338 — Asset backed securities 1,600,896 — 1,600,896 — Total 14,952,510 3,657,181 11,286,875 8,454 Equity securities 353,794 321,927 31,867 — Short-term investments 955,880 875,881 79,999 — Derivative instruments (4) 73,893 — 73,893 — Fair value option: Corporate bonds 852,585 — 846,827 5,758 Non-U.S. government bonds 79,066 — 79,066 — Mortgage backed securities 16,731 — 16,731 — Municipal bonds 7,144 — 7,144 — Commercial mortgage backed securities — — — — Asset backed securities 178,790 — 178,790 — U.S. government and government agencies 111,246 111,138 108 — Short-term investments 322,177 278,579 43,598 — Equity securities 103,893 48,827 55,066 — Other investments 1,254,220 39,107 1,152,408 62,705 Other investments measured at net asset value (2) 1,057,719 Total 3,983,571 477,651 2,379,738 68,463 Total assets measured at fair value $ 20,319,648 $ 5,332,640 $ 13,852,372 $ 76,917 Liabilities measured at fair value: Contingent consideration liabilities $ (66,665 ) $ — $ — $ (66,665 ) Securities sold but not yet purchased (3) (7,790 ) — (7,790 ) — Derivative instruments (4) (20,664 ) — (20,664 ) — Total liabilities measured at fair value $ (95,119 ) $ — $ (28,454 ) $ (66,665 ) (1) In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See Note 8 . (2) In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets. (3) Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets. (4) See Note 10 . The following table presents a reconciliation of the beginning and ending balances for all financial assets and liabilities measured at fair value on a recurring basis using Level 3 inputs for 2019 and 2018 : Assets Liabilities Available For Sale Fair Value Option Fair Value Structured Securities (1) Corporate Bonds Corporate Bonds Other Investments Equity Securities Equity Securities Contingent Consideration Liabilities Year Ended December 31, 2019 Balance at beginning of year $ 313 $ 8,141 $ 5,758 $ 62,705 $ — $ — $ (66,665 ) Total gains or (losses) (realized/unrealized) Included in earnings (2) 1,760 2 (162 ) (8,119 ) 1,949 (3,418 ) (1,478 ) Included in other comprehensive income 3 (267 ) — — — — — Purchases, issuances, sales and settlements Purchases — 881 — 3,746 — 36,077 — Issuances — — — — — — (548 ) Sales (1,757 ) — (28,583 ) (20,495 ) — (27,982 ) — Settlements (552 ) (1,766 ) — (600 ) — — 60,693 Transfers in and/or out of Level 3 5,449 1,860 23,919 31,580 56,145 51,212 — Balance at end of year $ 5,216 $ 8,851 $ 932 $ 68,817 $ 58,094 $ 55,889 $ (7,998 ) Year Ended December 31, 2018 Balance at beginning of year $ 5,927 $ 9,460 $ 12,217 $ 59,167 $ — $ — $ (60,996 ) Total gains or (losses) (realized/unrealized) Included in earnings (2) 4 (1 ) (334 ) (1,416 ) — — (5,669 ) Included in other comprehensive income (11 ) (296 ) — — — — — Purchases, issuances, sales and settlements Purchases — 802 — 6,250 — — — Issuances — — — — — — — Sales (5,003 ) — — (296 ) — — — Settlements (604 ) (1,824 ) (6,125 ) (1,000 ) — — — Transfers in and/or out of Level 3 — — — — — — — Balance at end of year $ 313 $ 8,141 $ 5,758 $ 62,705 $ — $ — $ (66,665 ) (1) Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities. (2) Gains or losses were included in net realized gains (losses). Financial Instruments Disclosed, But Not Carried, At Fair Value The Company uses various financial instruments in the normal course of its business. The carrying values of cash, accrued investment income, receivable for securities sold, certain other assets, payable for securities purchased and certain other liabilities approximated their fair values at December 31, 2019 , due to their respective short maturities. As these financial instruments are not actively traded, their respective fair values are classified within Level 2. At December 31, 2019 , the Company’s senior notes were carried at their cost, net of debt issuance costs, of $1.87 billion and had a fair value of $2.34 billion . At December 31, 2018 , the Company’s senior notes were carried at their cost, net of debt issuance costs, of $1.73 billion and had a fair value of $1.88 billion . The fair values of the senior notes were obtained from a third party pricing service and are based on observable market inputs. As such, the fair value of the senior notes is classified within Level 2. Fair Value Measurements on a Non-Recurring Basis The Company measures the fair value of certain assets on a non-recurring basis, generally quarterly, annually, or when events or changes in circumstances indicate that the carrying amount of the assets may not be recoverable. These assets include investments accounted for using the equity method, certain other investments, goodwill and intangible assets, and long-lived assets. The Company uses a variety of techniques to measure the fair value of these assets when appropriate, as described below: Investments accounted for using the equity method. When the Company determines that the carrying value of these assets may not be recoverable, the Company records the assets at fair value with the loss recognized in income. In such cases, the Company measures the fair value of these assets using the techniques discussed above in “—Fair Value Measurements on a Recurring Basis.” Goodwill and Intangible Assets . The Company tests goodwill and intangible assets for impairment whenever events or changes in circumstances indicate the carrying amount may not be recoverable. When the Company determines goodwill and intangible assets may be impaired, the Company uses techniques including discounted expected future cash flows, to measure fair value. Long-Lived Assets

Derivative Instruments

Derivative Instruments	12 Months Ended
	Dec. 31, 2019
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Derivative Instruments	Derivative Instruments The Company’s investment strategy allows for the use of derivative instruments. The Company’s derivative instruments are recorded on its consolidated balance sheets at fair value. The Company utilizes exchange traded U.S. Treasury note, Eurodollar and other futures contracts and commodity futures to manage portfolio duration or replicate investment positions in its portfolios and the Company routinely utilizes foreign currency forward contracts, currency options, index futures contracts and other derivatives as part of its total return objective. In addition, certain of the Company’s investments are managed in portfolios which incorporate the use of foreign currency forward contracts which are intended to provide an economic hedge against foreign currency movements. In addition, the Company purchases to-be-announced mortgage backed securities (“TBAs”) as part of its investment strategy. TBAs represent commitments to purchase a future issuance of agency mortgage backed securities. For the period between purchase of a TBA and issuance of the underlying security, the Company’s position is accounted for as a derivative. The Company purchases TBAs in both long and short positions to enhance investment performance and as part of its overall investment strategy. The following table summarizes information on the fair values and notional values of the Company’s derivative instruments: Estimated Fair Value Asset Liability Derivatives Notional Value (1) December 31, 2019 Futures contracts (2) $ 10,065 $ (13,722 ) $ 4,104,559 Foreign currency forward contracts (2) 5,352 (5,327 ) 686,878 TBAs (3) 55,010 — 53,229 Other (2) 33,529 (20,701 ) 4,356,300 Total $ 103,956 $ (39,750 ) December 31, 2018 Futures contracts (2) $ 51,800 $ (2,115 ) $ 3,153,518 Foreign currency forward contracts (2) 8,147 (7,796 ) 1,008,907 TBAs (3) 8,292 — 8,132 Other (2) 13,946 (10,753 ) 2,213,981 Total $ 82,185 $ (20,664 ) (1) Represents the absolute notional value of all outstanding contracts, consisting of long and short positions. (2) The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’ Such amounts include risk in force on GSE credit-risk sharing transactions that are accounted for as derivatives. (3) The fair value of TBAs are included in ‘fixed maturities available for sale, at fair value.’ The Company did not hold any derivatives which were designated as hedging instruments at December 31, 2019 or 2018 . The Company’s derivative instruments can be traded under master netting agreements, which establish terms that apply to all derivative transactions with a counterparty. In the event of a bankruptcy or other stipulated event of default, such agreements provide that the non-defaulting party may elect to terminate all outstanding derivative transactions, in which case all individual derivative positions (loss or gain) with a counterparty are closed out and netted and replaced with a single amount, usually referred to as the termination amount, which is expressed in a single currency. The resulting single net amount, where positive, is payable to the party “in-the-money” regardless of whether or not it is the defaulting party, unless the parties have agreed that only the non-defaulting party is entitled to receive a termination payment where the net amount is positive and is in its favor. Effectively, contractual close-out netting reduces the derivatives credit exposure from a gross to a net exposure. At December 31, 2019 , $97.8 million and $37.8 million , respectively, of asset derivatives and liability derivatives were subject to a master netting agreement compared to $80.4 million and $18.9 million , respectively, at December 31, 2018 . The remaining derivatives included in the table above were not subject to a master netting agreement. All realized and unrealized contract gains and losses on the Company’s derivative instruments are reflected in net realized gains (losses) in the consolidated statements of income, as summarized in the following table: Derivatives not designated as hedging instruments Year Ended December 31, 2019 2018 2017 Net realized gains (losses): Futures contracts $ 114,123 $ 48,443 $ 9,318 Foreign currency forward contracts (9,499 ) (21,770 ) (14,495 ) TBAs 463 (133 ) 9 Other 14,654 (10,904 ) (2,188 ) Total $ 119,741 $ 15,636 $ (7,356 )

Variable Interest Entity and No

Variable Interest Entity and Noncontrolling Interests	12 Months Ended
	Dec. 31, 2019
Variable Interest Entity and Noncontrolling Interest Disclosure [Abstract]
Variable Interest Entity and Noncontrolling Interests	Variable Interest Entity and Noncontrolling Interests Watford Holdings Ltd. In March 2014, Watford raised approximately $1.1 billion of capital consisting of $907.3 million in common equity ( $895.6 million net of issuance costs) and $226.6 million in preference equity ( $219.2 million net of issuance costs and discount). The Company invested $100.0 million and acquired 2,500,000 common shares, and a warrant to purchase up to 975,503 additional common shares. The warrants expire on March 31, 2020, and are exercisable at any time. The exercise price of the warrants is determined on the date of exercise based on certain targeted returns for existing common shareholders. Watford’s common shares are listed on the Nasdaq Select Global Market under the ticker symbol “WTRE”. As of December 31, 2019 , the Company owns approximately 13% of Watford’s outstanding common equity. Subsidiaries of the Company act as Watford’s reinsurance and insurance underwriting managers. HPS Investment Partners, LLC (“HPS”) manages Watford’s non-investment grade credit portfolios, and the Company manages Watford’s investment grade portfolios, each under separate long term services agreements. John Rathgeber, previously Vice Chairman of Arch Worldwide Reinsurance Group, is CEO of Watford. In addition, Maamoun Rajeh and Nicolas Papadopoulo, both officers of the Company, serve on the board of directors of Watford. The Company concluded that Watford is a VIE and that the Company is the primary beneficiary. The Company includes the results of Watford in its consolidated financial statements. The Company concluded that Watford should be reflected in a separate operating segment (‘other’) and provides the income statement and total investable assets, total assets and total liabilities of Watford within Note 4 . Because Watford is an independent company, the assets of Watford can be used only to settle obligations of Watford and Watford is solely responsible for its own liabilities and commitments. The Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common shares and preferred shares and counterparty credit risk (mitigated by collateral) arising from the reinsurance transactions. The following table provides the carrying amount and balance sheet caption in which the assets and liabilities of Watford are reported: December 31, 2019 2018 Assets Investments accounted for using the fair value option $ 1,898,091 $ 2,312,003 Fixed maturities available for sale, at fair value 745,708 393,351 Equity securities, at fair value 65,338 32,206 Cash 102,437 63,529 Accrued investment income 14,025 19,461 Premiums receivable 273,657 227,301 Reinsurance recoverable on unpaid and paid losses and LAE 170,973 86,445 Ceded unearned premiums 132,577 61,587 Deferred acquisition costs, net 64,044 80,858 Receivable for securities sold 16,287 24,507 Goodwill and intangible assets 7,650 7,650 Other assets 60,070 63,959 Total assets of consolidated VIE $ 3,550,857 $ 3,372,857 Liabilities Reserves for losses and loss adjustment expenses $ 1,263,628 $ 1,032,760 Unearned premiums 438,907 390,114 Reinsurance balances payable 77,066 21,034 Revolving credit agreement borrowings 484,287 455,682 Senior notes 172,418 — Payable for securities purchased 18,180 60,142 Other liabilities 171,714 302,524 Total liabilities of consolidated VIE $ 2,626,200 $ 2,262,256 Redeemable noncontrolling interests $ 52,305 $ 220,992 The following table summarizes Watford’s cash flow from operating, investing and financing activities. Year Ended December 31, 2019 2018 2017 Total cash provided by (used for): Operating activities 239,284 229,315 286,558 Investing activities (140,620 ) (285,281 ) (467,418 ) Financing activities (61,433 ) (2,406 ) 162,152 Non-redeemable noncontrolling interests The Company accounts for the portion of Watford’s common equity attributable to third party investors in the shareholders’ equity section of its consolidated balance sheets. The noncontrolling ownership in Watford’s senior notes, common shares was approximately 87% at December 31, 2019 . The portion of Watford’s income or loss attributable to third party investors is recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests.’ The following table sets forth activity in the non-redeemable noncontrolling interests: December 31, 2019 2018 Balance, beginning of year $ 791,560 $ 843,411 Additional paid in capital attributable to non-redeemable noncontrolling interests (2,929 ) — Repurchases attributable to non-redeemable noncontrolling interests (1) (75,056 ) — Amounts attributable to non-redeemable noncontrolling interests 40,072 (48,507 ) Other comprehensive (income) loss attributable to non-redeemable noncontrolling interests 9,130 (3,344 ) Balance, end of year $ 762,777 $ 791,560 (1) During 2019, Watford’s board of directors authorized the investment in Watford’s common shares through a share repurchase program. Redeemable noncontrolling interests The Company accounts for redeemable noncontrolling interests in the mezzanine section of its consolidated balance sheets in accordance with applicable accounting guidance. Such redeemable noncontrolling interests primarily relate to the Watford Preference Shares issued in late March 2014 with a par value of $0.01 per share and a liquidation preference of $25.00 per share. The Watford Preference Shares were issued at a discounted amount of $24.50 per share. Holders of the Watford Preference Shares will be entitled to receive, if declared by Watford’s board, quarterly cash dividends on the last day of March, June, September, and December. Dividends accrued from the closing date to June 30, 2019 at a fixed rate of 8.5% per annum. From June 30, 2019 and subsequent, dividends will accrue based on a floating rate equal to the 3 month U.S. dollar LIBOR (with a 1% floor) plus a margin based on the difference between the fixed rate and the 5 year mid swap rate to the floating rate. Preferred dividends, including the accretion of the discount and issuance costs, are included in ‘net (income) loss attributable to noncontrolling interests’ in the Company’s consolidated statements of income. Because the redemption features are not solely within the control of Watford, the Company accounts for the redeemable noncontrolling interests in the Watford Preference Shares in the mezzanine section of its consolidated balance sheets. On August 1, 2019, Watford redeemed 6,919,998 of its 9,065,200 issued and outstanding preference shares (“Watford Preference Shares”) at a total redemption price of $25.19748 per share, inclusive of all declared and unpaid dividends. The Company received $11.5 million pursuant to the redemption of Watford Preference Shares. Preferred dividends on the Watford Preference Shares, including the accretion of the discount and issuance costs, was $17.8 million for 2019 , compared to $19.6 million for 2018 and 2017 . The following table sets forth activity in the redeemable noncontrolling interests: December 31, 2019 2018 2017 Balance, beginning of year $ 206,292 $ 205,922 $ 205,553 Redemption of redeemable noncontrolling interests (157,709 ) — — Accretion of preference share issuance costs 244 370 369 Other 6,577 — — Balance, end of year $ 55,404 $ 206,292 $ 205,922 The portion of income or loss attributable to third party investors is recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests’ as summarized in the table below: December 31, 2019 2018 2017 Amounts attributable to non-redeemable noncontrolling interests $ (40,072 ) $ 48,507 $ 7,913 Dividends attributable to redeemable noncontrolling interests (16,909 ) (18,357 ) (18,344 ) Net (income) loss attributable to noncontrolling interests $ (56,981 ) $ 30,150 $ (10,431 ) Bellemeade Re The Company has entered into various aggregate excess of loss mortgage reinsurance agreements with various special purpose reinsurance companies domiciled in Bermuda (the Bellemeade Agreements). At the time the Bellemeade Agreements were entered into, the applicability of the accounting guidance that addresses VIEs was evaluated. As a result of the evaluation of the Bellemeade Agreements, the Company concluded that these entities are VIEs. However, given that the ceding insurers do not have the unilateral power to direct those activities that are significant to their economic performance, the Company does not consolidate such entities in its consolidated financial statements. The following table presents the total assets of the Bellemeade entities, as well as the Company’s maximum exposure to loss associated with these VIEs, calculated as the maximum historical observable spread between the one month LIBOR, the basis for the contractual payments to bond holders, and short term invested trust asset yields. Maximum Exposure to Loss Total VIE Assets On-Balance Sheet (Asset) Liabilities Off-Balance Sheet Total December 31, 2019 Bellemeade 2017-1 Ltd. (Oct-17) $ 216,429 $ (442 ) $ 2,794 $ 2,352 Bellemeade 2018-1 Ltd. (Apr-18) 328,482 (1,574 ) 5,757 4,183 Bellemeade 2018-2 Ltd. (Aug-18) 437,009 (877 ) 2,524 1,647 Bellemeade 2018-3 Ltd. (Oct-18) 426,806 (1,113 ) 3,937 2,824 Bellemeade 2019-1 Ltd. (Mar-19) 257,358 (226 ) 3,027 2,801 Bellemeade 2019-2 Ltd. (Apr-19) 525,959 (78 ) 2,579 2,501 Bellemeade 2019-3 Ltd. (Jul-19) 656,523 (585 ) 9,273 8,688 Bellemeade 2019-4 Ltd. (Oct-19) 577,267 (302 ) 12,193 11,891 Total $ 3,425,833 $ (5,197 ) $ 42,084 $ 36,887 December 31, 2018 Bellemeade 2015-1 Ltd. (Jul-15) $ 43,246 $ 112 $ 498 $ 610 Bellemeade 2017-1 Ltd. (Oct-17) 304,373 165 1,312 1,477 Bellemeade 2018-1 Ltd. (Apr-18) 374,460 132 3,539 3,671 Bellemeade 2018-2 Ltd. (Aug-18) 653,278 874 4,005 4,879 Bellemeade 2018-3 Ltd. (Oct-18) 506,110 469 1,836 2,305 Total $ 1,881,467 $ 1,752 $ 11,190 $ 12,942 See Note 7, “Reinsurance.”

Other Comprehensive Income

Other Comprehensive Income	12 Months Ended
	Dec. 31, 2019
Comprehensive Income Note Disclosure [Abstract]
Other Comprehensive Income (Loss)	Other Comprehensive Income (Loss) The following table presents the changes in each component of AOCI, net of noncontrolling interests: Unrealized Appreciation on Available-For-Sale Investments Foreign Currency Translation Adjustments Total Year Ended December 31, 2019 Beginning balance $ (114,178 ) $ (64,542 ) $ (178,720 ) Other comprehensive income (loss) before reclassifications 491,605 18,147 509,752 Amounts reclassified from accumulated other comprehensive income (118,941 ) — (118,941 ) Net current period other comprehensive income (loss) 372,664 18,147 390,811 Ending balance $ 258,486 $ (46,395 ) $ 212,091 Year Ended December 31, 2018 Beginning balance $ 157,400 $ (39,356 ) $ 118,044 Cumulative effect of an accounting change (149,794 ) — (149,794 ) Other comprehensive income (loss) before reclassifications (266,357 ) (25,186 ) (291,543 ) Amounts reclassified from accumulated other comprehensive income 144,573 — 144,573 Net current period other comprehensive income (loss) (121,784 ) (25,186 ) (146,970 ) Ending balance $ (114,178 ) $ (64,542 ) $ (178,720 ) Year Ended December 31, 2017 Beginning balance $ (27,641 ) $ (86,900 ) $ (114,541 ) Other comprehensive income (loss) before reclassifications 252,904 47,544 300,448 Amounts reclassified from accumulated other comprehensive income (67,863 ) — (67,863 ) Net current period other comprehensive income (loss) 185,041 47,544 232,585 Ending balance $ 157,400 $ (39,356 ) $ 118,044 The following tables present details about amounts reclassified from accumulated other comprehensive income and the tax effects allocated to each component of other comprehensive income (loss): Consolidated Statement of Income Amounts Reclassified from AOCI Details About Line Item That Includes Year Ended December 31, AOCI Components Reclassification 2019 2018 2017 Unrealized appreciation on available-for-sale investments Net realized gains (losses) $ 131,043 $ (153,822 ) $ 82,542 Other-than-temporary impairment losses (3,165 ) (2,829 ) (7,138 ) Total before tax 127,878 (156,651 ) 75,404 Income tax (expense) benefit (8,937 ) 12,078 (7,541 ) Net of tax $ 118,941 $ (144,573 ) $ 67,863 Following are the related tax effects allocated to each component of other comprehensive income (loss): Before Tax Tax Expense Net of Tax Amount (Benefit) Amount Year Ended December 31, 2019 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ 562,576 $ 61,805 $ 500,771 Less reclassification of net realized gains (losses) included in net income 127,878 8,937 118,941 Foreign currency translation adjustments 18,463 353 18,110 Other comprehensive income (loss) $ 453,161 $ 53,221 $ 399,940 Year Ended December 31, 2018 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (294,267 ) $ (24,210 ) $ (270,057 ) Less reclassification of net realized gains (losses) included in net income (156,651 ) (12,078 ) (144,573 ) Foreign currency translation adjustments (25,006 ) (176 ) (24,830 ) Other comprehensive income (loss) $ (162,622 ) $ (12,308 ) $ (150,314 ) Year Ended December 31, 2017 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ 266,559 $ 13,655 $ 252,904 Less reclassification of net realized gains (losses) included in net income 75,404 7,541 67,863 Foreign currency translation adjustments 47,549 535 47,014 Other comprehensive income (loss) $ 238,704 $ 6,649 $ 232,055

Earnings Per Common Share

Earnings Per Common Share	12 Months Ended
	Dec. 31, 2019
Earnings Per Share [Abstract]
Earnings Per Common Share	Earnings Per Common Share The calculation of basic earnings per common share is computed by dividing income available to Arch common shareholders by the weighted average number of Common Shares and common share equivalents outstanding. The following table sets forth the computation of basic and diluted earnings per common share: Year Ended December 31, 2019 2018 2017 Numerator: Net income $ 1,693,300 $ 727,821 $ 629,709 Amounts attributable to noncontrolling interests (56,981 ) 30,150 (10,431 ) Net income available to Arch 1,636,319 757,971 619,278 Preferred dividends (41,612 ) (41,645 ) (46,041 ) Loss on redemption of preferred shares — (2,710 ) (6,735 ) Net income available to Arch common shareholders $ 1,594,707 $ 713,616 $ 566,502 Denominator: Weighted average common shares outstanding 401,802,815 401,036,376 377,531,628 Series D preferred securities (1) — 3,311,245 26,606,736 Weighted average common shares outstanding – basic 401,802,815 404,347,621 404,138,364 Effect of dilutive common share equivalents: Nonvested restricted shares 1,673,770 1,474,207 3,936,594 Stock options (2) 8,132,893 7,084,650 9,710,067 Weighted average common shares and common share equivalents outstanding – diluted 411,609,478 412,906,478 417,785,025 Earnings per common share: Basic $ 3.97 $ 1.76 $ 1.40 Diluted $ 3.87 $ 1.73 $ 1.36 (1) The company has determined that, based on a review of the terms, features and rights of the Company’s non-voting common equivalent preferred shares compared to the rights of the Company’s common shareholders, the underlying common shares that the convertible securities convert to were common share equivalents at the time of their issuance. (2) Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For 2019 , 2018 and 2017 , the number of stock options excluded were 1,302,017 , 5,673,821 and 2,603,451 , respectively.

Income Taxes

Income Taxes	12 Months Ended
	Dec. 31, 2019
Income Tax Disclosure [Abstract]
Income Taxes	Income Taxes Arch Capital is incorporated under the laws of Bermuda and, under current Bermuda law, is not obligated to pay any taxes in Bermuda based upon income or capital gains. The Company has received a written undertaking from the Minister of Finance in Bermuda under the Exempted Undertakings Tax Protection Act 1966 that, in the event that any legislation is enacted in Bermuda imposing any tax computed on profits, income, gain or appreciation on any capital asset, or any tax in the nature of estate duty or inheritance tax, such tax will not be applicable to Arch Capital or any of its operations until March 31, 2035. This undertaking does not, however, prevent the imposition of taxes on any person ordinarily resident in Bermuda or any company in respect of its ownership of real property or leasehold interests in Bermuda. Arch Capital and its non-U.S. subsidiaries will be subject to U.S. federal income tax only to the extent that they derive U.S. source income that is subject to U.S. withholding tax or income that is effectively connected with the conduct of a trade or business within the U.S. and is not exempt from U.S. tax under an applicable income tax treaty with the U.S. Arch Capital and its non-U.S. subsidiaries will be subject to a withholding tax on dividends from U.S. investments and interest from certain U.S. payors (subject to reduction by any applicable income tax treaty). Arch Capital and its non-U.S. subsidiaries intend to conduct their operations in a manner that will not cause them to be treated as engaged in a trade or business in the United States and, therefore, will not be required to pay U.S. federal income taxes (other than U.S. excise taxes on insurance and reinsurance premium and withholding taxes on dividends and certain other U.S. source investment income). However, because there is uncertainty as to the activities which constitute being engaged in a trade or business within the United States, there can be no assurances that the U.S. Internal Revenue Service will not contend successfully that Arch Capital or its non-U.S. subsidiaries are engaged in a trade or business in the United States. If Arch Capital or any of its non-U.S. subsidiaries were subject to U.S. income tax, Arch Capital’s shareholders’ equity and earnings could be materially adversely affected. Arch Capital has subsidiaries and branches that operate in various jurisdictions around the world that are subject to tax in the jurisdictions in which they operate. The significant jurisdictions in which Arch Capital’s subsidiaries and branches are subject to tax are the United States, United Kingdom, Ireland, Canada, Switzerland, Australia and Denmark. The components of income taxes attributable to operations were as follows: Year Ended December 31, 2019 2018 2017 Current expense (benefit): United States $ 139,407 $ 73,078 $ (51,705 ) Non-U.S. 4,954 12,785 5,969 144,361 85,863 (45,736 ) Deferred expense (benefit): United States 11,849 19,544 169,093 Non-U.S. (400 ) 8,544 4,211 11,449 28,088 173,304 Income tax expense $ 155,810 $ 113,951 $ 127,568 The Company’s income or loss before income taxes was earned in the following jurisdictions: Year Ended December 31, 2019 2018 2017 Income (Loss) Before Income Taxes: Bermuda $ 1,122,952 $ 388,492 $ 406,054 United States 701,480 440,823 381,157 Other 24,678 12,457 (29,934 ) Total $ 1,849,110 $ 841,772 $ 757,277 The expected tax provision computed on pre-tax income or loss at the weighted average tax rate has been calculated as the sum of the pre-tax income in each jurisdiction multiplied by that jurisdiction’s applicable statutory tax rate. The 2019 applicable statutory tax rates by jurisdiction were as follows: Bermuda ( 0.0% ), United States ( 21.0% ), United Kingdom ( 19.0% ), Ireland ( 12.5% ), Denmark ( 22.0% ), Canada ( 26.5% ), Gibraltar ( 10.0% ), Australia ( 30.0% ), Hong Kong ( 16.5% ) and the Netherlands ( 19.0% ). The United States rate was 35% in 2017. A reconciliation of the difference between the provision for income taxes and the expected tax provision at the weighted average tax rate follows: Year Ended December 31, 2019 2018 2017 Expected income tax expense (benefit) computed on pre-tax income at weighted average income tax rate $ 149,799 $ 91,529 $ 126,262 Addition (reduction) in income tax expense (benefit) resulting from: Tax-exempt investment income (3,091 ) (4,790 ) (13,330 ) Meals and entertainment 1,134 1,060 1,063 State taxes, net of U.S. federal tax benefit 3,314 2,086 732 Foreign branch taxes 1,231 5,428 5,752 Prior year adjustment 632 (2,522 ) (559 ) Foreign exchange gains & losses 436 1,293 (572 ) Changes in applicable tax rate — (128 ) 7,745 Dividend withholding taxes 6,510 6,594 232 Change in valuation allowance 1,628 18,396 14,798 Contingent consideration 190 740 3,785 Share based compensation (6,592 ) (5,356 ) (18,733 ) Other 619 (379 ) 393 Income tax expense (benefit) $ 155,810 $ 113,951 $ 127,568 The effect of a change in tax laws or rates on deferred taxes assets and liabilities is recognized in income in the period in which such change is enacted. On December 22, 2017, the Tax Cuts Act was signed into law which significantly changed the U.S. tax laws in many ways including a reduction of the U.S. federal income tax rate from 35% to 21% effective January 1, 2018. Also on December 22, 2017, the Securities and Exchange Commission issued Staff Accounting Bulletin No. 118 (“SAB 118”) which provided guidance on accounting for tax effects of the Tax Cuts Act. SAB 118 provided a measurement period of up to one year from the enactment date to complete the accounting. During 2018, the Company finalized its accounting for the income tax impact of the Tax Cuts Act resulting in a tax expense of $1.2 million , primarily attributable to the write down of temporary differences identified following the filing of the Company’s 2017 corporate tax return offset by AMT credits that were currently recoverable. Deferred income tax assets and liabilities reflect temporary differences based on enacted tax rates between the carrying amounts of assets and liabilities for financial reporting and income tax purposes. Significant components of the Company’s deferred income tax assets and liabilities were as follows: December 31, 2019 2018 Deferred income tax assets: Net operating loss $ 30,836 $ 24,089 Uncrystallized losses 1,565 7,960 AMT credit carryforward 1,323 2,652 Discounting of net loss reserves 52,582 43,130 Net unearned premium reserve 64,269 68,305 Compensation liabilities 21,693 20,492 Foreign tax credit carryforward 9,521 9,116 Interest expense — 1,387 Goodwill and intangible assets 11,644 17,127 Bad debt reserves 5,983 5,626 Lease liability 26,438 — Net unrealized foreign exchange losses 598 949 Net unrealized decline of investments — 13,453 Other, net 206 3,418 Deferred tax assets before valuation allowance 226,658 217,704 Valuation allowance (48,219 ) (44,659 ) Deferred tax assets net of valuation allowance 178,439 173,045 Deferred income tax liabilities: Depreciation and amortization (1,215 ) (2,559 ) Deposit accounting liability (2,169 ) (2,292 ) Contingency reserve (132,831 ) (112,852 ) Deferred policy acquisition costs (29,847 ) (32,105 ) Net unrealized appreciation of investments (38,764 ) — Right-of-use asset (23,416 ) — Other, net (3,680 ) (735 ) Total deferred tax liabilities (231,922 ) (150,543 ) Net deferred income tax assets (liabilities) $ (53,483 ) $ 22,502 The Company provides a valuation allowance to reduce certain deferred tax assets to an amount which management expects to more likely than not be realized. As of December 31, 2019 , the Company’s valuation allowance was $48.2 million , compared to $44.7 million at December 31, 2018 . The valuation allowance in both periods was primarily attributable to valuation allowance on the Company’s U.K. Canadian and Australian operations and certain other deferred tax assets relating to loss carryforwards that have a limited use. At December 31, 2019 , the Company’s net operating loss carryforwards and tax credits were as follows: Year Ended December 31, 2019 Expiration Operating Loss Carryforwards United Kingdom $ 89,000 No expiration Ireland 10,200 No expiration Australia 22,000 No expiration Hong Kong 17,600 No expiration Denmark 400 No expiration United States (1) (2) 23,100 2029 - 2038 Tax Credits U.K. foreign tax credits 9,521 No expiration U.S. refundable AMT credits 1,323 No expiration (1) Includes $0.6 million net operating loss carryforwards from Watford. (2) On January 30, 2014, the Company’s U.S. mortgage operations underwent an ownership change for U.S. federal income tax purposes as a result of the Company’s acquisition of the CMG Entities. As a result of this ownership change, a limitation has been imposed upon the utilization of approximately $8.9 million of the Company’s existing U.S. net operating loss carryforwards. Utilization is limited to approximately $0.6 million per year in accordance with Section 382 of the Internal Revenue Code of 1986 as amended (“the Code”). The Company’s U.S. mortgage operations are eligible for a tax deduction, subject to certain limitations, under Section 832(e) of the Code for amounts required by state law or regulation to be set aside in statutory contingency reserves. The deduction is allowed only to the extent that the Company purchases non-interest bearing U.S. Mortgage Guaranty Tax and Loss Bonds (“T&L Bonds”) issued by the U.S. Treasury Department in an amount equal to the tax benefit derived from deducting any portion of the statutory contingency reserves. T&L Bonds are reflected in ‘other assets’ on the Company’s balance sheet and totaled approximately $207.0 million at December 31, 2019 , compared to $183.0 million at December 31, 2018 . Deferred income tax liabilities have not been accrued with respect to the undistributed earnings of the Company's U.S., U.K. and Ireland subsidiaries as it is the Company’s intention that all such earnings will be indefinitely reinvested. If the earnings were to be distributed, as dividends or otherwise, such amounts may be subject to withholding tax in the jurisdiction of the paying entity. The Company no longer intends to indefinitely reinvest earnings from the Company's Canada subsidiary, however, no income or withholding taxes have been accrued as the Canada subsidiary does not have positive cumulative earnings and profits and therefore a distribution from this particular subsidiary would not be subject to income taxes or withholding taxes. Potential tax implications of repatriation from the Company’s unremitted earnings that are indefinitely reinvested are driven by facts at the time of distribution. Therefore it is not practicable to estimate the income tax liabilities that might be incurred if such earnings were remitted. Distributions from the U.K. or Ireland would not be subject to withholding tax and no deferred income tax liability would need to be accrued. The Company recognizes interest and penalties relating to unrecognized tax benefits in the provision for income taxes. As of December 31, 2019 , the Company’s total unrecognized tax benefits, including interest and penalties, were $2.0 million . If recognized, the full amount of the unrecognized tax benefit would impact the consolidated effective tax rate. A reconciliation of the beginning and ending amount of unrecognized tax benefits is as follows: December 31, 2019 2018 Balance at beginning of year $ 2,008 $ 2,008 Additions based on tax positions related to the current year — — Additions for tax positions of prior years — — Reductions for tax positions of prior years — — Settlements — — Balance at end of year $ 2,008 $ 2,008 The Company or its subsidiaries or branches files income tax returns in the U.S. federal jurisdiction and various state, local and foreign jurisdictions.The following table details open tax years that are potentially subject to examination by local tax authorities, in the following major jurisdictions: Jurisdiction Tax Years United States 2016-2019 United Kingdom 2018-2019 Ireland 2015-2019 Canada 2016-2019 Switzerland 2017-2019 Denmark 2015-2019 As of December 31, 2019 , the Company’s current income tax payable (included in “Other liabilities”) was $13.5 million .

Transactions with Related Parti

Transactions with Related Parties	12 Months Ended
	Dec. 31, 2019
Related Party Transactions [Abstract]
Transactions with Related Parties	Transactions with Related Parties I n 2017, the Company acquired approximately 25% of Premia Holdings Ltd. Premia Holdings Ltd. is the parent of Premia Reinsurance Ltd., a multi-line Bermuda reinsurance company (together with Premia Holdings Ltd., “Premia”). Premia’s strategy is to reinsure or acquire companies or reserve portfolios in the non-life property and casualty insurance and reinsurance run-off market. Arch Re Bermuda and certain Arch co-investors invested $100.0 million and acquired approximately 25% of Premia as well as warrants to purchase additional common equity. Arch has appointed two directors to serve on the seven person board of directors of Premia. Arch Re Bermuda is providing a 25% quota share reinsurance treaty on certain business written by Premia. In the 2019 fourth quarter, Barbican entered into certain reinsurance and related transactions with Premia pursuant to which Premia assumed a transfer of liability for the 2018 and prior years of account of Barbican as of July 1, 2019. Barbican recorded reinsurance recoverable on unpaid and paid losses and funds held liability of $177.7 million and $180.0 million , respectively, at December 31, 2019. Certain directors and executive officers of the Company own common and preference shares of Watford. See note 11, “Variable Interest Entity and Noncontrolling Interests,”

Leases (Notes)

Leases (Notes)	12 Months Ended
	Dec. 31, 2019
Leases [Abstract]
Leases	Leases In the ordinary course of business, the Company renews and enters into new leases for office property and equipment. At the lease inception date, the Company determines whether a contract contains a lease and its classification as a finance or operating lease. Primarily all of the Company’s leases are classified as operating leases. The Company’s operating leases have remaining lease terms of up to 11 years , some of which include options to extend the lease term. The Company considers these options when determining the lease term and measuring its lease liability and right-of-use asset. In addition, the Company’s lease agreements do not contain any material residual value guarantees or material restrictive covenants. Short-term operating leases with an initial term of twelve months or less were excluded on the Company's consolidated balance sheet and represent an inconsequential amount of operating lease expense. As most leases do not provide an implicit rate, the Company uses its incremental borrowing rate based on the information available at the lease commencement date in determining the present value of lease payments. Additional information regarding the Company’s operating leases is as follows: December 31, 2019 Operating lease costs $ 30,478 Cash payments included in the measurement of lease liabilities reported in operating cash flows $ 27,521 Right-of-use assets obtained in exchange for new lease liabilities $ 7,445 Right-of-use assets (1) $ 131,661 Operating lease liability (1) $ 150,519 Weighted average discount rate 3.9 % Weighted average remaining lease term 6.4 years (1) The right-of-use assets are included in ‘other assets’ while the operating lease liability is included in ‘other liabilities.’ The following table presents the contractual maturities of the Company's operating lease liabilities at December 31, 2019 : Years Ending December 31, 2020 $ 31,907 2021 30,842 2022 27,597 2023 23,027 2024 16,913 2025 and thereafter 40,167 Total undiscounted lease liability 170,453 Less: present value adjustment (19,934 ) Operating lease liability $ 150,519 At December 31, 2018, the future minimum rental commitments, exclusive of escalation clauses and maintenance costs and net of rental income, for all of the Company’s operating leases was as follows: Years Ending December 31, 2019 $ 31,088 2020 30,491 2021 29,351 2022 26,068 2023 21,408 2024 and thereafter 54,745 Total $ 193,151 All of these leases are for the rental of office space, with expiration terms that range from 2020 to 2030. Rental expense was approximately $30.5 million , $27.6 million and $31.1 million for 2019 , 2018 and 2017 , respectively. At December 31, 2019 , the Company has entered into certain financing lease agreements. The future lease payments for the Company’s financing leases are expected to be $4.8 million and $2.1 million for 2020 and 2021, respectively.

Commitments and Contingencies

Commitments and Contingencies	12 Months Ended
	Dec. 31, 2019
Commitments and Contingencies Disclosure [Abstract]
Commitments and Contingencies	Commitments and Contingencies Concentrations of Credit Risk The creditworthiness of a counterparty is evaluated by the Company, taking into account credit ratings assigned by independent agencies. The credit approval process involves an assessment of factors, including, among others, the counterparty, country and industry credit exposure limits. Collateral may be required, at the discretion of the Company, on certain transactions based on the creditworthiness of the counterparty. The areas where significant concentrations of credit risk may exist include unpaid losses and loss adjustment expenses recoverable, contractholder receivables, ceded unearned premiums, paid losses and loss adjustment expenses recoverable net of reinsurance balances payable, investments and cash and cash equivalent balances. A credit exposure exists with respect to reinsurance recoverables as they may become uncollectible. The Company manages its credit risk in its reinsurance relationships by transacting with reinsurers that it considers financially sound and, if necessary, the Company may hold collateral in the form of funds, trust accounts and/or irrevocable letters of credit. This collateral can be drawn on for amounts that remain unpaid beyond specified time periods on an individual reinsurer basis. In addition, certain insurance policies written by the Company’s insurance operations feature large deductibles, primarily in its construction and national accounts lines of business. Under such contracts, the Company is obligated to pay the claimant for the full amount of the claim. The Company is subsequently reimbursed by the policyholder for the deductible amount. These amounts are included on a gross basis in the consolidated balance sheet in contractholder payables and contractholder receivables, respectively. In the event that the Company is unable to collect from the policyholder, the Company would be liable for such defaulted amounts. Collateral, primarily in the form of letters of credit, cash and trusts, is obtained from the policyholder to mitigate the Company’s credit risk. In the instances where the company receives collateral in the form of cash, the Company records a related liability in “Collateral held for insured obligations.” In addition, the Company underwrites a significant amount of its business through brokers and a credit risk exists should any of these brokers be unable to fulfill their contractual obligations with respect to the payments of insurance and reinsurance balances owed to the Company. The following table summarizes the percentage of the Company’s gross premiums written generated from or placed by the largest brokers: Broker Year Ended December 31, 2019 2018 2017 Aon Corporation and its subsidiaries 12.2 % 11.4 % 11.3 % Marsh & McLennan Companies and its subsidiaries 9.6 % 9.3 % 10.7 % No other broker and no one insured or reinsured accounted for more than 10% of gross premiums written for 2019 , 2018 and 2017 . The Company’s available for sale investment portfolio is managed in accordance with guidelines that have been tailored to meet specific investment strategies, including standards of diversification, which limit the allowable holdings of any single issue. There were no investments in any entity in excess of 10% of the Company’s shareholders’ equity at December 31, 2019 other than investments issued or guaranteed by the United States government or its agencies. Investment Commitments The Company’s investment commitments, which are primarily related to agreements entered into by the Company to invest in funds and separately managed accounts when called upon, were approximately $1.69 billion and $1.77 billion at December 31, 2019 and 2018 , respectively. Contingent Consideration Liability Pursuant to the Company’s 2014 acquisition of the CMG Entities, the Company made a contingent consideration payment of $61.5 million in April 2019 and $71.7 million in April 2017. The maximum remaining amount of contingent consideration payments is $6.7 million over the remaining earn-out period. To the extent that the adjusted book value of the CMG Entities drops below the cumulative amount paid by the Company, no additional payments would be due. Purchase Obligations The Company has also entered into certain agreements which commit the Company to purchase goods or services, primarily related to software and computerized systems. Such purchase obligations were approximately $55.6 million and $39.5 million at December 31, 2019 and 2018 , respectively. Employment and Other Arrangements At December 31, 2019 , the Company has entered into employment agreements with certain of its executive officers. Such employment arrangements provide for compensation in the form of base salary, annual bonus, share-based awards, participation in the Company’s employee benefit programs and the reimbursements of expenses.

Debt and Financing Arrangements

Debt and Financing Arrangements	12 Months Ended
	Dec. 31, 2019
Debt Disclosure [Abstract]
Debt and Financing Arrangements	Debt and Financing Arrangements The Company’s senior notes payable at December 31, 2019 and 2018 were as follows: Carrying Amount at Interest Principal December 31, (Fixed) Amount 2019 2018 2034 notes (1) 7.350 % 300,000 297,254 297,150 2043 notes (2) 5.144 % 500,000 494,831 494,723 2026 notes (3) 4.011 % 500,000 496,806 496,417 2046 notes (4) 5.031 % 450,000 445,317 445,238 Watford notes (5) 6.500 % 140,000 137,418 — $ 1,890,000 $ 1,871,626 $ 1,733,528 (1) Senior notes of Arch Capital issued on May 4, 2004 and due May 1, 2034 (“2034 notes”). (2) Senior notes of Arch-U.S., a wholly-owned subsidiary of Arch Capital, issued on December 13, 2013 and due November 1, 2043 (“2043 notes”), fully and unconditionally guaranteed by Arch Capital. (3) Senior notes of Arch Capital Finance LLC (“Arch Finance”), a wholly-owned finance subsidiary of Arch Capital, issued on December 8, 2016 and due December 15, 2026 (“2026 notes”), fully and unconditionally guaranteed by Arch Capital. (4) Senior notes of Arch Finance issued on December 8, 2016 and due December 15, 2046 (“2046 notes”), fully and unconditionally guaranteed by Arch Capital (5) Senior notes of Watford issued on July 2, 2019 and due July 2, 2029, reflecting the elimination of amounts owned by Arch-U.S. The 2034 notes are Arch Capital’s senior unsecured obligations and rank equally with all of its existing and future senior unsecured indebtedness. Interest payments on the 2034 notes are due on May 1st and November 1st of each year. Arch Capital may redeem the 2034 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price. The 2043 notes are unsecured and unsubordinated obligations of Arch-U.S. and Arch Capital, respectively, and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch-U.S. and Arch Capital, respectively. Interest payments on the 2043 notes are due on May 1st and November 1st of each year. Arch-U.S. may redeem the 2043 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price. The 2026 notes are unsecured and unsubordinated obligations of Arch Finance and Arch Capital, respectively, and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch Finance and Arch Capital, respectively. Interest payments on the 2026 notes are due on June 15th and December 15th of each year. Arch Finance may redeem the 2026 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price. The 2046 notes are unsecured and unsubordinated obligations of Arch Finance and Arch Capital, respectively, and rank equally and ratably with the other unsecured and unsubordinated indebtedness of Arch Finance and Arch Capital, respectively. Interest payments on the 2046 notes are due on June 15th and December 15th of each year. Arch Finance may redeem the 2046 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price. On July 2, 2019, Watford completed an offering of $175.0 million in aggregate principal amount of its 6.5% senior notes, due July 2, 2029 (“Watford Senior Notes”). Interest on the Watford Senior Notes will be paid semi-annually in arrears on each January 2 and July 2, commencing January 2, 2020. The $172.4 million net proceeds from the offering were used to redeem a portion of Watford Preference Shares. The Company purchased $35.0 million in aggregate principal amount of the Watford Senior Notes. Letter of Credit and Revolving Credit Facilities In the normal course of its operations, the Company enters into agreements with financial institutions to obtain secured and unsecured credit facilities. On December 17, 2019, Arch Capital and certain of its subsidiaries entered into a $750.0 million five-year credit facility (the “Credit Facility”) with a syndication of lenders. The Credit Facility consists of a $250.0 million secured facility for letters of credit (the “Secured Facility”) and a $500.0 million unsecured facility for revolving loans and letters of credit (the “Unsecured Facility”). Obligations of each borrower under the Secured Facility for letters of credit are secured by cash and eligible securities of such borrower held in collateral accounts. Commitments under the Credit Facility may be increased up to, but not exceeding, an aggregate of $1.25 billion . Arch Capital has a one-time option to convert any or all outstanding revolving loans of Arch Capital and/or Arch-U.S. to term loans with the same terms as the revolving loans except that any prepayments may not be re-borrowed. Arch-U.S. guarantees the obligations of Arch Capital, and Arch Capital guarantees the obligations of Arch-U.S. Borrowings of revolving loans may be made at a variable rate based on LIBOR or an alternative base rate at the option of Arch Capital. Arch Capital and its lenders may agree on a LIBOR successor rate at the appropriate time to address the replacement of LIBOR. Secured letters of credit are available for issuance on behalf of certain Arch Capital subsidiaries. The Credit Facility is structured such that each party that requests a letter of credit or borrowing does so only for itself and its own obligations. The Credit Facility contains certain restrictive covenants customary for facilities of this type, including restrictions on indebtedness, consolidated tangible net worth, minimum shareholders’ equity levels and minimum financial strength ratings. Arch Capital and its subsidiaries which are party to the agreement were in compliance with all covenants contained therein at December 31, 2019 . Commitments under the Credit Facility will expire on December 17, 2024, and all loans then outstanding must be repaid. Letters of credit issued under the Unsecured Facility will not have an expiration date later than December 17, 2025. Under the $250.0 million secured letter of credit facility, Arch Capital’s subsidiaries had $225.4 million of letters of credit outstanding and remaining capacity of $24.6 million at December 31, 2019 . In addition, certain of Arch Capital’s subsidiaries had outstanding secured and unsecured letters of credit of $18.1 million and $195.0 million respectively, which were issued in the normal course of business. When issued, all secured letters of credit are secured by a portion of the investment portfolio. At December 31, 2019 , these letters of credit were secured by investments with a fair value of $255.4 million . Watford has access to a $100 million secured letter of credit facility expiring on May 16, 2020, a $100 million unsecured letter of credit facility which auto extends on September 20, 2020 and an $800 million secured credit facility expiring on November 30, 2021 that provides for borrowings and the issuance of letters of credit not to exceed $400 million . Borrowings of revolving loans may be made by Watford at a variable rate based on LIBOR or an alternative base rate at the option of Watford. At December 31, 2019 , Watford had $122.9 million in outstanding letters of credit under the two facilities and $484.3 million of borrowings outstanding under the secured credit facility, backed by Watford’s investment portfolio. Watford was in compliance with all covenants contained in these credit facilities at December 31, 2019 . The Company does not guarantee or provide credit support for Watford, and the Company’s financial exposure to Watford is limited to its investment in Watford’s senior notes, common and preferred shares and counterparty credit risk (mitigated by collateral) arising from the reinsurance transactions. The Company’s outstanding revolving credit agreement borrowings were as follows: Year Ended December 31, 2019 2018 Arch Capital $ — $ — Watford 484,287 455,682 Total $ 484,287 $ 455,682

Goodwill and Intangible Assets

Goodwill and Intangible Assets	12 Months Ended
	Dec. 31, 2019
Goodwill and Intangible Assets Disclosure [Abstract]
Goodwill and Intangible Assets	Goodwill and Intangible Assets The following table shows an analysis of goodwill and intangible assets: Goodwill Intangible assets (indefinite life) Intangible assets (finite life) Total Net balance at Dec. 31, 2017 $ 198,236 $ 68,174 $ 386,201 $ 652,611 Acquisitions 51,476 — 43,000 94,476 Amortization — — (105,670 ) (105,670 ) Impairment (1) — (6,300 ) — (6,300 ) Foreign currency movements and other adjustments (92 ) — (105 ) (197 ) Net balance at Dec. 31, 2018 249,620 61,874 323,426 634,920 Acquisitions (2) 74,780 24,431 82,482 181,693 Amortization — — (82,104 ) (82,104 ) Impairment (1) — (1,000 ) — (1,000 ) Foreign currency movements and other adjustments 2,151 605 1,817 4,574 Net balance at Dec. 31, 2019 $ 326,551 $ 85,910 $ 325,621 $ 738,083 Gross balance at Dec. 31, 2019 $ 331,448 $ 85,305 $ 744,583 $ 1,161,336 Accumulated amortization — — (419,294 ) (419,294 ) Foreign currency movements and other adjustments (4,897 ) 605 332 (3,959 ) Net balance at Dec. 31, 2019 $ 326,551 $ 85,910 $ 325,621 $ 738,083 (1) The impairment to the indefinite-lived intangible assets during the year ended December 31, 2019 and 2018 of $1.0 million and $6.3 million related to insurance licenses from the acquisition of UGC. (2) Certain amounts for the Company’s 2019 acquisitions are considered provisional. The following table presents the components of goodwill and intangible assets: Gross Balance Accumulated Foreign Currency Translation Adjustment and Other Net Balance Dec. 31, 2019 Acquired insurance contracts $ 452,470 $ (336,559 ) $ 310 $ 116,221 Operating platform 52,674 (39,571 ) (259 ) 12,844 Distribution relationships 243,838 (50,542 ) 212 193,508 Goodwill 331,448 — (4,897 ) 326,551 Insurance licenses 63,390 — — 63,390 Syndicate capacity 21,915 — 605 22,520 Unfavorable service contract (9,533 ) 8,657 — (876 ) Other 5,134 (1,279 ) 70 3,925 Total $ 1,161,336 $ (419,294 ) $ (3,959 ) $ 738,083 Dec. 31, 2018 Acquired insurance contracts $ 435,067 $ (271,981 ) $ (150 ) $ 162,936 Operating platform 47,400 (35,402 ) — 11,998 Distribution relationships 186,611 (36,718 ) (1,335 ) 148,558 Goodwill 256,668 — (7,048 ) 249,620 Insurance licenses 61,874 — — 61,874 Syndicate capacity — — — — Unfavorable service contract (9,533 ) 7,949 — (1,584 ) Other 2,556 (1,038 ) — 1,518 Total $ 980,643 $ (337,190 ) $ (8,533 ) $ 634,920 The estimated remaining amortization expense for the Company’s intangible assets with finite lives is as follows: 2020 $ 65,958 2021 48,063 2022 33,972 2023 31,731 2024 27,566 2025 and thereafter 118,331 Total $ 325,621 The estimated remaining useful lives of these assets range from one to seventeen years at December 31, 2019 . Other than the impairments described above, the Company’s annual impairment reviews for goodwill and intangible assets did not result in the recognition of impairment losses for 2019 , 2018 and 2017 .

Shareholders' Equity

Shareholders' Equity	12 Months Ended
	Dec. 31, 2019
Stockholders' Equity Note [Abstract]
Shareholders' Equity	Shareholders’ Equity Authorized and Issued The authorized share capital of Arch Capital consists of 1.8 billion Common Shares, par value of $0.0011 per share, and 50 million Preferred Shares, par value of $0.01 per share. Common Shares The following table presents a roll-forward of changes in Arch Capital’s issued and outstanding Common Shares: Year Ended December 31, 2019 2018 2017 Common Shares: Shares issued and outstanding, beginning of year 570,737,283 549,872,226 523,932,303 Shares issued (1) 2,835,994 2,757,506 3,388,344 Conversion of Series D preferred shares (2) — 17,022,600 21,265,860 Restricted shares issued, net of cancellations 1,043,918 1,084,951 1,285,719 Shares issued and outstanding, end of year 574,617,195 570,737,283 549,872,226 Common shares in treasury, end of year (168,997,994 ) (168,282,449 ) (156,938,409 ) Shares issued and outstanding, end of year 405,619,201 402,454,834 392,933,817 (1) Includes shares issued from the exercise of stock options and stock appreciation rights, and shares issued from the employee share purchase plan. (2) Such shares represent common shares that were issued upon conversion of the non-voting common equivalent preference shares issued in connection with the AIG acquisition. Three-For-One Common Share Split In May 2018, shareholders approved a proposal to amend the memorandum of association by sub-dividing the authorized common shares of Arch Capital to effect a three -for-one split of Arch Capital’s common shares. The share split changed the Company’s authorized common shares to 1.8 billion common shares ( 600 million previously), with a par value of $.0011 per share ( $.0033 previously). Information pertaining to the composition of the Company’s shareholders’ equity accounts, shares and earnings per share has been retroactively restated in the accompanying financial statements and notes to the consolidated financial statements to reflect the share split. Share Repurchase Program The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. At December 31, 2019 , $1.0 billion of share repurchases were available under the program. Repurchases under the program may be effected from time to time in open market or privately negotiated transactions through December 31, 2021. The timing and amount of the repurchase transactions under this program will depend on a variety of factors, including market conditions and corporate and regulatory considerations. Repurchases of Arch Capital’s common shares in connection with the share repurchase plan and other share-based transactions were held in the treasury under the cost method, and the cost of the common shares acquired is included in ‘Common shares held in treasury, at cost.’ At December 31, 2019 , Arch Capital held 169.0 million shares for an aggregate cost of $2.41 billion in treasury, at cost. The Company’s repurchases under the share repurchase program were as follows: Year Ended December 31, 2019 2018 2017 Aggregate cost of shares repurchased $ 2,871 $ 282,762 $ — Shares repurchased 110,598 10,559,850 — Average price per share repurchased $ 25.96 $ 26.78 $ — Since the inception of the share repurchase program through December 31, 2019 , Arch Capital has repurchased approximately 386.3 million common shares for an aggregate purchase price of $3.97 billion . Convertible Non-Voting Common Equivalent Preferred Shares On December 31, 2016, the Company completed the acquisition of all of the outstanding shares of capital stock of UGC. Based upon a formula set forth in the Stock Purchase Agreement, AIG received 1,276,282 of Arch Capital’s Series D convertible non-voting common equivalent preferred shares (“Series D Preferred Shares”). Each Series D Preferred Share converts to 10 shares of Arch Capital fully paid non-assessable common stock. The Company determined, based on a review of the terms features and rights of the series D preferred shares compared to the rights of the Company’s common shareholders, the underlying 38,288,460 common shares that the convertible securities convert to were common share equivalents at the time of their issuance . In June 2017, Arch Capital completed an underwritten public secondary offering of 21,265,860 common shares by AIG following transfer of 708,862 Series D Preferred Shares. In March 2018, Arch Capital completed an underwritten public secondary offering of 17,022,600 common shares by AIG following transfer of 567,420 Series D Preferred Shares. Proceeds from the sale of common shares pursuant to the public offering were received by AIG. At December 31, 2019 and 2018, no Series D Preferred Shares were outstanding. Series F Preferred Shares In August 2017 and November 2017, Arch Capital completed combined $330 million of underwritten public offerings ( $230 million in August 2017 and $100 million in November 2017) of 13.2 million depositary shares (the “Series F Depositary Shares”), each of which represents a 1/1,000th interest in a share of its 5.45% Non-Cumulative Preferred Shares, Series F, with a $0.01 par value and $25,000 liquidation preference per share (equivalent to $25 liquidation preference per Series F Depositary Share) (the “Series F Preferred Shares”). Each Series F Depositary Share, evidenced by a depositary receipt, entitles the holder, through the depositary, to a proportional fractional interest in all rights and preferences of the Series F Preferred Shares represented thereby (including any dividend, liquidation, redemption and voting rights). Holders of Series F Preferred Shares will be entitled to receive dividend payments only when, as and if declared by our board of directors or a duly authorized committee of the board. Any such dividends will be payable from, and including, the date of original issue on a noncumulative basis, quarterly in arrears on the last day of March, June, September and December of each year, at an annual rate of 5.45% . Dividends on the Series F Preferred Shares are not cumulative. The Company will be restricted from paying dividends on or repurchasing its common shares unless certain dividend payments are made on the Series F Preferred Shares. Except in specified circumstances relating to certain tax or corporate events, the Series F Preferred Shares are not redeemable prior to August 17, 2022 (the fifth anniversary of the issue date). On and after that date, the Series F Preferred Shares will be redeemable at the Company’s option, in whole or in part, at a redemption price of $25,000 per share of the Series F Preferred Shares (equivalent to $25 per depositary share), plus any declared and unpaid dividends, without accumulation of any undeclared dividends to, but excluding, the redemption date. The Series F Depositary Shares will be redeemed if and to the extent the related Series F Preferred Shares are redeemed by the Company. Neither the Series F Depositary Shares nor the Series F Preferred Shares have a stated maturity, nor will they be subject to any sinking fund or mandatory redemption. The Series F Preferred Shares are not convertible into any other securities. The Series F Preferred Shares will not have voting rights, except under limited circumstances. The net proceeds from the Series F Preferred Share offerings were used to redeem the Company’s outstanding 6.75% Series C Non-Cumulative Preferred Shares. Series E Preferred Shares On September 29, 2016, Arch Capital completed a $450 million underwritten public offering of 18.0 million depositary shares (the “Series E Depositary Shares”), each of which represents a 1/1,000th interest in a share of its 5.25% Non-Cumulative Preferred Shares, Series E, with a $0.01 par value and $25,000 liquidation preference per share (equivalent to $25 liquidation preference per Series E Depositary Share) (the “Series E Preferred Shares”). Each Series E Depositary Share, evidenced by a depositary receipt, entitles the holder, through the depositary, to a proportional fractional interest in all rights and preferences of the Series E Preferred Shares represented thereby (including any dividend, liquidation, redemption and voting rights). Holders of Series E Preferred Shares will be entitled to receive dividend payments only when, as and if declared by our board of directors or a duly authorized committee of the board. Any such dividends will be payable from, and including, the date of original issue on a non-cumulative basis, quarterly in arrears on the last day of March, June, September and December of each year, at an annual rate of 5.25% . Dividends on the Series E Preferred Shares are not cumulative. The Company will be restricted from paying dividends on or repurchasing its common shares unless certain dividend payments are made on the Series E preferred shares. Except in specified circumstances relating to certain tax or corporate events, the Series E Preferred Shares are not redeemable prior to September 29, 2021 (the fifth anniversary of the issue date). On and after that date, the Series E Preferred Shares will be redeemable at the Company’s option, in whole or in part, at a redemption price of $25,000 per share of the Series E Preferred Shares (equivalent to $25 per Series E Depositary Share), plus any declared and unpaid dividends, without accumulation of any undeclared dividends to, but excluding, the redemption date. The Series E Depositary Shares will be redeemed if and to the extent the related Series E Preferred Shares are redeemed by the Company. Neither the Series E Depositary Shares nor the Series E Preferred Shares have a stated maturity, nor will they be subject to any sinking fund or mandatory redemption. The Series E Preferred Shares are not convertible into any other securities. The Series E Preferred Shares will not have voting rights, except under limited circumstances. Series C Preferred Shares On January 2, 2018, Arch Capital redeemed all outstanding 6.75% Series C non-cumulative preferred shares. The preferred shares were redeemed at a redemption price equal to $25 per share, plus all declared and unpaid dividends to (but excluding) the redemption date. In accordance with GAAP, following the redemption, original issuance costs related to such shares have been removed from additional paid-in capital and recorded as a “loss on redemption of preferred shares.” Such adjustment had no impact on total shareholders’ equity or cash flows.

Share-Based Compensation

Share-Based Compensation	12 Months Ended
	Dec. 31, 2019
Share-based Payment Arrangement [Abstract]
Share-Based Compensation	Share-Based Compensation Long Term Incentive and Share Award Plans The Company utilizes share-based compensation plans for officers, other employees and directors of Arch Capital and its subsidiaries to provide competitive compensation opportunities, to encourage long-term service, to recognize individual contributions and reward achievement of performance goals and to promote the creation of long-term value for shareholders by aligning the interests of such persons with those of shareholders. The 2018 Long-Term Incentive and Share Award Plan (the “2018 Plan”) became effective as of May 9, 2018 following approval by shareholders of the Company. The 2018 Plan provides for the issuance of restricted stock units, performance units, restricted shares, performance shares, stock options and stock appreciation rights and other equity-based awards to our employees and directors. The 2018 Plan authorizes the issuance of 34,500,000 common shares and will terminate as to future awards on February 28, 2028. At December 31, 2019 , 25,201,143 shares are available for future issuance. The 2015 Long Term Incentive and Share Award Plan (the (“2015 Plan”) authorizes the issuance of 12,900,000 common shares and became effective as of May 7, 2015 following approval by shareholders of the Company. The 2015 Plan provides for the issuance of share-based awards to our employees and directors and will terminate as to future awards on February 26, 2025. At December 31, 2019 , 390,156 shares are available for future issuance. The 2012 Long Term Incentive and Share Award Plan (the “2012 Plan”) became effective as of May 9, 2012 following approval by shareholders of the Company. The 2012 Plan authorizes the issuance of 22,301,772 common shares and will terminate as to future awards on February 28, 2022. At December 31, 2019 , 606,589 shares are available for grant under the 2012 Plan. Upon shareholder approval on May 6, 2016, the Amended and Restated Arch Capital Group Ltd. 2007 Employee Share Purchase Plan (the “ESPP”) became effective and a total of 4,689,777 common shares were reserved for issuance. The purpose of the ESPP is to give employees of Arch Capital and its subsidiaries an opportunity to purchase common shares through payroll deductions, thereby encouraging employees to share in the economic growth and success of Arch Capital and its subsidiaries. The ESPP is designed to qualify as an “employee share purchase plan” under Section 423 of the Code. At December 31, 2019 , approximately 2,729,721 shares remain available for issuance. Stock Options and Stock Appreciation Rights The Company generally issues stock options and SARs to eligible employees, with exercise prices equal to the fair market values of the Company’s Common Shares on the grant dates. Such grants generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date. The grant date fair value is determined using the Black-Scholes option valuation model. The expected life assumption is based on an expected term analysis, which incorporates the Company’s historical exercise experience. Expected volatility is based on the Company’s daily historical trading data of its common shares. The table below summarizes the assumptions used. Year Ended December 31, 2019 2018 2017 Dividend yield — % — % — % Expected volatility 18.1 % 21.3 % 21.3 % Risk free interest rate 2.5 % 2.8 % 2.0 % Expected option life 6.0 years 6.0 years 6.0 years A summary of stock option and SAR activity under the Company’s Long Term Incentive and Share Award Plans during 2019 is presented below: Year Ended December 31, 2019 Number of Options / SARs Weighted Average Exercise Price Weighted Average Contractual Term Aggregate Intrinsic Value Outstanding, beginning of year 20,076,593 $ 19.37 Granted 1,228,280 $ 32.86 Exercised (2,355,216 ) $ 13.45 Forfeited or expired (96,639 ) $ 29.19 Outstanding, end of year 18,853,018 $ 20.94 5.03 $ 413,842 Exercisable, end of year 15,517,508 $ 19.05 4.28 $ 369,917 The aggregate intrinsic value of stock options and SARs exercised represents the difference between the exercise price of the stock options and SARs and the closing market price of the Company’s common shares on the exercise dates. During 2019 , the Company received proceeds of $13.1 million from the exercise of stock options and recognized a tax benefit of $6.9 million from the exercise of stock options and SARs. Year Ended December 31, 2019 2018 2017 Weighted average grant date fair value $ 7.90 $ 7.50 $ 8.15 Aggregate intrinsic value of Options/SARs exercised $ 51,350 $ 43,468 $ 64,173 Restricted Common Shares and Restricted Units The Company also issues restricted share and unit awards to eligible employees and directors, for which the fair value is equal to the fair market values of the Company’s Common Shares on the grant dates. Restricted share and unit awards generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date. A summary of restricted share and restricted unit activity under the Company’s Long Term Incentive and Share Award Plans for 2019 is presented below: Restricted Common Shares Restricted Unit Awards Unvested Shares: Unvested balance, beginning of year 1,619,285 1,254,558 Granted 384,926 810,815 Vested (931,696 ) (422,021 ) Forfeited (26,594 ) (80,340 ) Unvested balance, end of year 1,045,921 1,563,012 Weighted Average Grant Date Fair Value: Unvested balance, beginning of year $ 28.88 $ 27.58 Granted $ 33.43 $ 32.64 Vested $ 28.31 $ 27.75 Forfeited $ 30.15 $ 29.36 Unvested balance, end of year $ 31.02 $ 30.07 The following table presents the weighted average grant date fair value of restricted shares and restricted unit awards granted and the aggregate fair value of restricted shares and unit awards vesting in each year. Year Ended December 31, 2019 2018 2017 Restricted shares and restricted unit awards granted 1,195,741 1,563,287 1,747,176 Weighted average grant date fair value $ 32.89 $ 26.86 $ 32.02 Aggregate fair value of vested restricted share and unit awards $ 46,262 $ 39,898 $ 133,848 The aggregate intrinsic value of restricted units outstanding at December 31, 2019 was $67.0 million . Performance Awards The Company also issues performance share and unit awards (“performance awards”) to eligible employees, which are earned based on the achievement of pre-established threshold, target and maximum goals over three-year performance periods. Final payouts depend on the level of achievement along with each employees continued service through the vest date. The grant date fair value of the performance awards is measured using a Monte Carlo simulation model, which incorporated the assumptions summarized in the table below. Expected volatility is based on the Company’s daily historical trading data of its common shares. The cumulative compensation expense recognized and unrecognized as of any reporting period date represents the adjusted estimate of performance shares and units that will ultimately be awarded, valued at their original grant date fair values. Year Ended December 31, 2019 2018 2017 Expected volatility 17.1 % 16.2 % — % Risk free interest rate 2.5 % 2.6 % — % Performance Shares Performance Units Unvested Shares: Unvested balance, beginning of year 715,328 12,993 Granted 685,586 10,774 Vested — — Forfeited — — Unvested balance, end of year 1,400,914 23,767 Weighted Average Grant Date Fair Value: Unvested balance, beginning of year $ 24.77 $ 24.71 Granted $ 36.05 $ 35.83 Vested $ — $ — Forfeited $ — $ — Unvested balance, end of year $ 30.29 $ 29.75 The following table presents the weighted average grant date fair values of performance awards granted. Year Ended December 31, 2019 2018 2017 Performance awards 696,360 743,513 — Weighted average grant date fair value $ 36.05 $ 24.77 $ — The issuance of share-based awards and amortization thereon has no effect on the Company’s consolidated shareholders’ equity. Share-Based Compensation Expense The following tables present pre-tax and after-tax share-based compensation expense recognized as well as the unrecognized compensation cost associated with unvested awards and the weighted average period over which it is expected to be recognized. Year Ended December 31, 2019 2018 2017 Pre-Tax Stock options and SARs $ 12,866 $ 16,272 $ 18,536 Restricted share and unit awards 38,988 34,025 46,884 Performance awards 8,949 4,414 — ESPP 3,045 1,224 2,443 Total $ 63,848 $ 55,935 $ 67,863 After-Tax Stock options and SARs $ 11,450 $ 14,894 $ 16,219 Restricted share and unit awards 32,999 29,044 37,708 Performance awards 8,295 4,127 — ESPP 2,758 1,114 2,171 Total $ 55,502 $ 49,179 $ 56,098 December 31, 2019 Stock Options and SARs Restricted Common Shares and Units Performance Common Shares and Units Unrecognized compensation cost related to unvested awards $ 12,823 $ 39,606 $ 8,893 Weighted average recognition period (years) 1.23 1.31 1.06

Retirement Plans

Retirement Plans	12 Months Ended
	Dec. 31, 2019
Retirement Benefits [Abstract]
Retirement Plans	Retirement Plans For purposes of providing employees with retirement benefits, the Company maintains defined contribution retirement plans. Contributions are based on the participants’ eligible compensation. For 2019 , 2018 and 2017 , the Company expensed $44.8 million , $40.8 million and $40.7 million , respectively, related to these retirement plans.

Legal Proceedings

Legal Proceedings	12 Months Ended
	Dec. 31, 2019
Disclosure Legal Proceedings [Abstract]
Legal Proceedings	Legal Proceedings The Company, in common with the insurance industry in general, is subject to litigation and arbitration in the normal course of its business. As of December 31, 2019 , the Company was not a party to any litigation or arbitration which is expected by management to have a material adverse effect on the Company’s results of operations and financial condition and liquidity.

Statutory Information

Statutory Information	12 Months Ended
	Dec. 31, 2019
Disclosure Statutory Information [Abstract]
Statutory Information	Statutory Information The Company’s insurance and reinsurance subsidiaries are subject to insurance and/or reinsurance laws and regulations in the jurisdictions in which they operate. These regulations include certain restrictions on the amount of dividends or other distributions available to shareholders without prior approval of the insurance regulatory authorities. The actual and required statutory capital and surplus for the Company’s principal operating subsidiaries at December 31, 2019 and 2018 : December 31, 2019 2018 Actual capital and surplus (1): Bermuda $ 13,511,729 $ 11,605,652 Ireland 721,439 653,055 United States 4,440,848 4,195,477 United Kingdom 748,276 386,892 Canada 61,351 59,096 Required capital and surplus: Bermuda $ 5,492,968 $ 4,718,345 Ireland 542,703 429,117 United States 1,697,640 1,783,268 United Kingdom 349,328 271,864 Canada 32,763 33,189 (1) Such amounts include ownership interests in affiliated insurance and reinsurance subsidiaries. There were no state-prescribed or permitted regulatory accounting practices for any of the Company’s insurance or reinsurance entities that resulted in reported statutory surplus that differed from that which would have been reported under the prescribed practices of the respective regulatory authorities, including the National Association of Insurance Commissioners. The differences between statutory financial statements and statements prepared in accordance with GAAP vary by jurisdiction, however, with the primary differences being that statutory financial statements may not reflect deferred acquisition costs, certain net deferred tax assets, goodwill and intangible assets, unrealized appreciation or depreciation on debt securities and certain unauthorized reinsurance recoverables and include contingency reserves. The statutory net income (loss) for the Company’s principal operating subsidiaries for 2019 , 2018 and 2017 was as follows: Year Ended December 31, 2019 2018 2017 Statutory net income (loss): Bermuda $ 1,876,416 $ 919,554 $ 881,665 Ireland 26,367 29,223 (14,438 ) United States 481,188 292,831 500,412 United Kingdom (17,423 ) (18,467 ) (33,257 ) Canada (1,023 ) 2,525 158 Bermuda The Company has two Bermuda based subsidiaries: Arch Re Bermuda, a Class 4 insurer and long-term insurer, and Watford, a Class 4 insurer. Under the Bermuda Insurance Act 1978 (the “Insurance Act”), these subsidiaries are required to maintain minimum statutory capital and surplus equal to the greater of a minimum solvency margin and the enhanced capital requirement as determined by the Bermuda Monetary Authority (“BMA”). The enhanced capital requirement is calculated based on the Bermuda Solvency Capital Requirement model, a risk-based model that takes into account the risk characteristics of different aspects of the company’s business. At December 31, 2019 and 2018, all such requirements were met. The ability of these subsidiaries to pay dividends is limited under Bermuda law and regulations. Under the Insurance Act, Arch Re Bermuda is restricted with respect to the payment of dividends. Arch Re Bermuda is prohibited from declaring or paying in any financial year dividends of more than 25% of its total statutory capital and surplus (as shown on its previous financial year’s statutory balance sheet) unless it files, at least seven days before payment of such dividends, with the Bermuda Monetary Authority an affidavit stating that it will continue to meet the required margins following the declaration of those dividends. Accordingly, Arch Re Bermuda can pay approximately $3.10 billion to Arch Capital during 2020 without providing an affidavit to the BMA. Ireland The Company has two Irish subsidiaries: Arch Re Europe, an authorized life and non-life reinsurer, and Arch Insurance (EU), an authorized non-life insurer. Irish authorized reinsurers and insurers, such as Arch Re Europe and Arch Insurance (EU), are also subject to the general body of Irish laws and regulations including the provisions of the Companies Act 2014. Arch Re Europe and Arch Insurance (EU) are subject to the supervision of the Central Bank of Ireland (“CBOI”) and must comply with Irish insurance acts and regulations as well as with directions and guidance issued by the CBOI. These subsidiaries are required to maintain a minimum level of capital. At December 31, 2019 and 2018, these requirements were met. The amount of dividends these subsidiaries are permitted to declare is limited to accumulated, realized profits, so far as not previously utilized by distribution or capitalization, less its accumulated, realized losses, so far as not previously written off in a reduction or reorganization of capital duly made. The solvency and capital requirements must still be met following any distribution. Dividends or distributions, if any, made by Arch Re Europe would result in an increase in available capital at Arch Re Bermuda. United States The Company’s U.S. insurance and reinsurance subsidiaries are subject to insurance laws and regulations in the jurisdictions in which they operate. The ability of the Company’s regulated insurance subsidiaries to pay dividends or make distributions is dependent on their ability to meet applicable regulatory standards. These regulations include restrictions that limit the amount of dividends or other distributions, such as loans or cash advances, available to shareholders without prior approval of the insurance regulatory authorities. Dividends or distributions, if any, made by Arch Re U.S. would result in an increase in available capital at Arch-U.S., the Company’s U.S. holding company. Arch Re U.S. can declare a maximum of approximately $130.2 million of dividends during 2020 subject to the approval of the Commissioner of the Delaware Department of Insurance. Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company have each been approved as an eligible mortgage insurer by Fannie Mae and Freddie Mac, subject to maintaining certain ongoing requirements (“eligible mortgage insurers”). In April 2015, the GSEs published comprehensive, revised requirements, known as the Private Mortgage Insurer Eligibility Requirements or “PMIERs.” As clarified and revised by the Guidance Letters issued by the GSEs in December 2016 and March 2017, the PMIERs apply to the Company’s eligible mortgage insurers, but do not apply to Arch Mortgage Guaranty Company, which is not GSE-approved. The amount of assets required to satisfy the revised financial requirements of the PMIERs at any point in time will be affected by many factors, including macro-economic conditions, the size and composition of our eligible mortgage insurers’ mortgage insurance portfolio at the point in time, and the amount of risk ceded to reinsurers that may be deducted in our calculation of “minimum required assets.” The Company’s U.S. mortgage insurance subsidiaries are subject to detailed regulation by their domiciliary and primary regulators, the Wisconsin Office of the Commissioner of Insurance (“Wisconsin OCI”) for Arch Mortgage Insurance Company and Arch Mortgage Guaranty Company, the North Carolina Department of Insurance (“NC DOI”) for United Guaranty Residential Insurance Company, and by state insurance departments in each state in which they are licensed. As mandated by state insurance laws, mortgage insurers are generally mono-line companies restricted to writing a single type of insurance business, such as mortgage insurance business. Each company is subject to either Wisconsin or North Carolina statutory requirements as to payment of dividends. Generally, both Wisconsin and North Carolina law precludes any dividend before giving at least 30 days’ notice to the Wisconsin OCI or NC DOI, as applicable, and prohibits paying any dividend unless it is fair and reasonable to do so. In addition, the state regulators and the GSEs limit or restrict our eligible mortgage insurers’ ability to pay stockholder dividends or otherwise return capital to shareholders. Under respective states law, our U.S. mortgage subsidiaries can declare a maximum of approximately $338.9 million of ordinary dividends in 2020, however, dividend capacity is limited by the respective companies unassigned surplus amounts. As of December 31, 2019, the combined unassigned surplus amount of our U.S. mortgage insurance entities would limit the dividend capacity to $177.8 million . In certain instances, approval by the GSEs would be required for dividends or other forms of return of capital to shareholders due to the requirements under PMIERs, including the minimum required assets imposed on our eligible mortgage insurers by the GSEs. Such dividend would result in an increase in available capital at Arch U.S. MI Holdings Inc., a subsidiary of Arch-U.S. Mortgage insurance companies licensed in Wisconsin or North Carolina are required to establish contingency loss reserves for purposes of statutory accounting in an amount equal to at least 50% of net earned premiums. These amounts generally cannot be withdrawn for a period of 10 years and are separate liabilities for statutory accounting purposes, which affects the ability to pay dividends. However, with prior regulatory approval, a mortgage insurance company may make early withdrawals from the contingency reserve when incurred losses exceed 35% of net premiums earned in a calendar year. Under Wisconsin and North Carolina law, as well as that of 14 other states, a mortgage insurer must maintain a minimum amount of statutory capital relative to its risk in force in order for the mortgage insurer to continue to write new business. While formulations of minimum capital vary in certain jurisdictions, the most common measure applied allows for a maximum risk-to-capital ratio of 25 to 1. Wisconsin and North Carolina both require a mortgage insurer to maintain a “minimum policyholder position” calculated in accordance with their respective regulations. Policyholders' position consists primarily of statutory policyholders' surplus plus the statutory contingency reserve, less ceded reinsurance. While the statutory contingency reserve is reported as a liability on the statutory balance sheet, for risk-to-capital ratio calculations, it is included as capital for purposes of statutory capital. United Kingdom The Prudential Regulation Authority (“PRA”) and the Financial Conduct Authority (“FCA”) regulate insurance and reinsurance companies and the FCA regulates firms carrying on insurance mediation activities operating in the U.K., both under the Financial Services and Markets Act 2000. The Company’s European insurance operations are conducted through Arch Insurance (U.K.), Arch Syndicate 2012 and Barbican Syndicate 1955. Arch Syndicate 2012 has one corporate member, Arch Syndicate Investments Ltd. (“ASIL”), and is managed by Arch Underwriting at Lloyd’s Ltd (“AUAL”). The syndicates managed by BMAL have 11 corporate members. BMAL is the managing agent of Barbican Syndicate 1955. Arch Syndicate 2012 and Barbican Syndicate 1955 provide access to Lloyd’s extensive distribution network and worldwide licenses. All U.K. companies are also subject to a range of statutory provisions, including the laws and regulations of the Companies Acts 2006 (as amended) (the “U.K. Companies Acts”). Arch Insurance (U.K.), AUAL (on behalf of itself, Arch Syndicate 2012 and ASIL) and BMAL must maintain a margin of solvency at all times under the Solvency II Directive from the European Insurance and Occupational Pensions Authority. The regulations stipulate that insurers are required to maintain the minimum capital requirement and solvency capital requirement at all times. The capital requirements are calculated by reference to standard formulae defined in Solvency II. At December 31, 2019 and 2018, our subsidiaries were in compliance with these requirements. As corporate members of Lloyd’s, ASIL and others are subject to the oversight of the Council of Lloyd’s. The capital required to support a Syndicate’s underwriting capacity, or funds at Lloyd’s, is assessed annually and is determined by Lloyd’s in accordance with the capital adequacy rules established by the PRA. The Company has provided capital to support the underwriting of Arch Syndicate 2012 and Barbican Syndicate 1955 in the form of pledged assets provided by Arch Re Bermuda. The amount which the Company provides as funds at Lloyd’s is not available for distribution to the Company for the payment of dividends. Lloyd’s is supervised by the PRA and required to implement certain rules prescribed by the PRA under the Lloyd’s Act of 1982 regarding the operation of the Lloyd’s market. With respect to managing agents and corporate members, Lloyd’s prescribes certain minimum standards relating to management and control, solvency and other requirements and monitors managing agents’ compliance with such standards. Under U.K. law, all U.K. companies are restricted from declaring a dividend to their shareholders unless they have “profits available for distribution.” The calculation as to whether a company has sufficient profits is based on its accumulated realized profits minus its accumulated realized losses. U.K. insurance regulatory laws do not prohibit the payment of dividends, but the PRA or FCA, as applicable, requires that insurance companies and insurance intermediaries maintain certain solvency margins and may restrict the payment of a dividend by Arch Insurance (U.K.), AUAL, ASIL and BMAL. Canada Arch Insurance Canada and the Canadian branch of Arch Re U.S. (“Arch Re Canada”) are subject to federal, as well as provincial and territorial, regulation in Canada. The Office of the Superintendent of Financial Institutions (“OSFI”) is the federal regulatory body that, under the Insurance Companies Act (Canada), regulates federal Canadian and non-Canadian insurance companies operating in Canada. Arch Insurance Canada and Arch Re Canada are subject to regulation in the provinces and territories in which they underwrite insurance/reinsurance, and the primary goal of insurance/reinsurance regulation at the provincial and territorial levels is to govern the market conduct of insurance/reinsurance companies. Arch Insurance Canada is licensed to carry on insurance business by OSFI and in each province and territory. Arch Re Canada is licensed to carry-on reinsurance business by OSFI and in the provinces of Ontario and Quebec. Under the Insurance Companies Act (Canada), Arch Insurance Canada is required to maintain an adequate amount of capital in Canada, calculated in accordance with a test promulgated by OSFI called the Minimum Capital Test (“MCT”), and Arch Re Canada is required to maintain an adequate margin of assets over liabilities in Canada, calculated in accordance with a test promulgated by OSFI called the Branch Adequacy of Assets Test. Dividends or distributions, if any, made by Arch Insurance Canada would result in an increase in available capital at Arch Insurance Company (see “—United States” section).

Unaudited Condensed Quarterly F

Unaudited Condensed Quarterly Financial Information	12 Months Ended
	Dec. 31, 2019
Quarterly Financial Information Disclosure [Abstract]
Unaudited Condensed Quarterly Financial Information	Unaudited Condensed Quarterly Financial Information The following table summarizes the 2019 and 2018 unaudited condensed quarterly financial information: Fourth Quarter Third Quarter Second Quarter First Quarter Year Ended December 31, 2019 Net premiums written $ 1,455,453 $ 1,613,457 $ 1,444,898 $ 1,525,259 Net premiums earned 1,515,882 1,438,023 1,463,727 1,368,866 Net investment income 154,263 161,488 155,038 156,949 Net realized gains (losses) 41,474 62,518 120,806 141,565 Net impairment losses recognized in earnings (644 ) (1,163 ) (49 ) (1,309 ) Underwriting income (loss) 251,421 231,262 293,134 260,148 Net income (loss) attributable to Arch 326,384 392,453 468,954 448,528 Preferred dividends (10,403 ) (10,403 ) (10,403 ) (10,403 ) Net income (loss) available to Arch common shareholders 315,981 382,050 458,551 438,125 Net income (loss) per common share -- basic $ 0.78 $ 0.95 $ 1.14 $ 1.09 Net income (loss) per common share -- diluted $ 0.76 $ 0.92 $ 1.12 $ 1.07 Year Ended December 31, 2018 Net premiums written $ 1,301,754 $ 1,333,553 $ 1,298,896 $ 1,412,544 Net premiums earned 1,369,435 1,290,878 1,336,763 1,234,899 Net investment income 157,217 144,024 135,668 126,724 Net realized gains (losses) (166,030 ) (51,705 ) (76,611 ) (110,998 ) Net impairment losses recognized in earnings (1,705 ) (492 ) (470 ) (162 ) Underwriting income (loss) 166,955 234,581 235,465 236,997 Net income (loss) attributable to Arch 136,494 227,408 243,646 150,423 Preferred dividends (10,403 ) (10,402 ) (10,403 ) (10,437 ) Net income (loss) available to Arch common shareholders 126,091 217,006 233,243 137,276 Net income (loss) per common share -- basic $ 0.31 $ 0.54 $ 0.58 $ 0.34 Net income (loss) per common share -- diluted $ 0.31 $ 0.53 $ 0.56 $ 0.33

Guarantor Financial Information

Guarantor Financial Information	12 Months Ended
	Dec. 31, 2019
Condensed Financial Information Disclosure [Abstract]
Guarantor Financial Information	Guarantor Financial Information The following tables present condensed consolidating balance sheets at December 31, 2019 and 2018 and condensed consolidating statements of income, comprehensive income and cash flows for 2019 , 2018 and 2017 for Arch Capital, Arch-U.S., a 100% owned subsidiary of Arch Capital, and Arch Capital's other subsidiaries. December 31, 2019 Condensed Consolidating Balance Sheet Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Assets Total investments $ 42 $ 692,606 $ 23,748,432 $ (38,834 ) $ 24,402,246 Cash 18,113 54,518 653,599 — 726,230 Investments in subsidiaries 11,786,861 4,347,806 — (16,134,667 ) — Due from subsidiaries and affiliates 17 200,635 1,901,865 (2,102,517 ) — Premiums receivable — — 2,547,130 (768,413 ) 1,778,717 Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses — — 9,711,773 (5,364,957 ) 4,346,816 Contractholder receivables — — 2,119,460 — 2,119,460 Ceded unearned premiums — — 2,230,164 (995,481 ) 1,234,683 Deferred acquisition costs — — 675,917 (42,517 ) 633,400 Goodwill and intangible assets — — 738,083 — 738,083 Other assets 20,461 32,187 1,981,598 (128,520 ) 1,905,726 Total assets $ 11,825,494 $ 5,327,752 $ 46,308,021 $ (25,575,906 ) $ 37,885,361 Liabilities Reserve for losses and loss adjustment expenses $ — $ — $ 19,028,538 $ (5,136,696 ) $ 13,891,842 Unearned premiums — — 5,335,030 (995,481 ) 4,339,549 Reinsurance balances payable — — 1,435,485 (768,413 ) 667,072 Contractholder payables — — 2,119,460 — 2,119,460 Collateral held for insured obligations — — 206,698 206,698 Senior notes 297,254 494,831 1,114,541 (35,000 ) 1,871,626 Revolving credit agreement borrowings — — 484,287 — 484,287 Due to subsidiaries and affiliates — 536,805 1,565,712 (2,102,517 ) — Other liabilities 30,869 33,267 2,324,793 (399,654 ) 1,989,275 Total liabilities 328,123 1,064,903 33,614,544 (9,437,761 ) 25,569,809 Redeemable noncontrolling interests — — 58,882 (3,478 ) 55,404 Shareholders' Equity Total shareholders' equity available to Arch 11,497,371 4,262,849 11,871,818 (16,134,667 ) 11,497,371 Non-redeemable noncontrolling interests — — 762,777 — 762,777 Total shareholders' equity 11,497,371 4,262,849 12,634,595 (16,134,667 ) 12,260,148 Total liabilities, noncontrolling interests and shareholders' equity $ 11,825,494 $ 5,327,752 $ 46,308,021 $ (25,575,906 ) $ 37,885,361 December 31, 2018 Condensed Consolidating Balance Sheet Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Assets Total investments $ 104 $ 452,674 $ 21,307,206 $ (14,700 ) $ 21,745,284 Cash 6,125 5,940 634,491 — 646,556 Investments in subsidiaries 9,735,256 3,999,243 — (13,734,499 ) — Due from subsidiaries and affiliates 9 2 1,802,686 (1,802,697 ) — Premiums receivable — — 1,834,389 (535,239 ) 1,299,150 Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses — — 8,618,660 (5,699,288 ) 2,919,372 Contractholder receivables — — 2,079,111 — 2,079,111 Ceded unearned premiums — — 1,730,262 (754,793 ) 975,469 Deferred acquisition costs — — 618,535 (48,961 ) 569,574 Goodwill and intangible assets — — 634,920 — 634,920 Other assets 12,588 80,949 1,466,438 (211,082 ) 1,348,893 Total assets $ 9,754,082 $ 4,538,808 $ 40,726,698 $ (22,801,259 ) $ 32,218,329 Liabilities Reserve for losses and loss adjustment expenses $ — $ — $ 17,345,142 $ (5,491,845 ) $ 11,853,297 Unearned premiums — — 4,508,429 (754,793 ) 3,753,636 Reinsurance balances payable — — 928,346 (535,239 ) 393,107 Contractholder payables — — 2,079,111 — 2,079,111 Collateral held for insured obligations — — 236,630 — 236,630 Senior notes 297,150 494,723 941,655 — 1,733,528 Revolving credit agreement borrowings — — 455,682 — 455,682 Due to subsidiaries and affiliates — 536,805 1,265,892 (1,802,697 ) — Other liabilities 17,105 26,270 1,699,768 (467,484 ) 1,275,659 Total liabilities 314,255 1,057,798 29,460,655 (9,052,058 ) 21,780,650 Redeemable noncontrolling interests — — 220,992 (14,700 ) 206,292 Shareholders' Equity Total shareholders' equity available to Arch 9,439,827 3,481,010 10,253,491 (13,734,501 ) 9,439,827 Non-redeemable noncontrolling interests — — 791,560 — 791,560 Total shareholders' equity 9,439,827 3,481,010 11,045,051 (13,734,501 ) 10,231,387 Total liabilities, noncontrolling interests and shareholders' equity $ 9,754,082 $ 4,538,808 $ 40,726,698 $ (22,801,259 ) $ 32,218,329 Year Ended December 31, 2019 Condensed Consolidating Statement of Income and Comprehensive Income Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Revenues Net premiums earned $ — $ — $ 5,786,498 $ — $ 5,786,498 Net investment income 212 14,270 706,038 (92,782 ) 627,738 Net realized gains (losses) — 25,313 352,771 (11,721 ) 366,363 Net impairment losses recognized in earnings — — (3,165 ) — (3,165 ) Other underwriting income — — 24,861 — 24,861 Equity in net income (loss) of investments accounted for using the equity method — 779 122,893 — 123,672 Other income (loss) (762 ) — 2,995 — 2,233 Total revenues (550 ) 40,362 6,992,891 (104,503 ) 6,928,200 Expenses Losses and loss adjustment expenses — — 3,133,452 — 3,133,452 Acquisition expenses — — 840,945 — 840,945 Other operating expenses — — 800,997 — 800,997 Corporate expenses 62,701 7,221 10,189 — 80,111 Amortization of intangible assets — — 82,104 — 82,104 Interest expense 22,154 47,951 142,662 (91,895 ) 120,872 Net foreign exchange (gains) losses 1 — 22,188 (1,580 ) 20,609 Total expenses 84,856 55,172 5,032,537 (93,475 ) 5,079,090 Income (loss) before income taxes (85,406 ) (14,810 ) 1,960,354 (11,028 ) 1,849,110 Income tax (expense) benefit — 3,696 (159,506 ) — (155,810 ) Income (loss) before equity in net income of subsidiaries (85,406 ) (11,114 ) 1,800,848 (11,028 ) 1,693,300 Equity in net income of subsidiaries 1,721,725 564,657 — (2,286,382 ) — Net income 1,636,319 553,543 1,800,848 (2,297,410 ) 1,693,300 Net (income) loss attributable to noncontrolling interests — — (57,868 ) 887 (56,981 ) Net income available to Arch 1,636,319 553,543 1,742,980 (2,296,523 ) 1,636,319 Preferred dividends (41,612 ) — — — (41,612 ) Net income available to Arch common shareholders $ 1,594,707 $ 553,543 $ 1,742,980 $ (2,296,523 ) $ 1,594,707 Comprehensive income (loss) available to Arch $ 2,027,129 $ 751,210 $ 2,124,455 $ (2,875,665 ) $ 2,027,129 Year Ended December 31, 2018 Condensed Consolidating Statement of Income and Comprehensive Income Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Revenues Net premiums earned $ — $ — $ 5,231,975 $ — $ 5,231,975 Net investment income 49 3,902 649,394 (89,712 ) 563,633 Net realized gains (losses) 29 (2,676 ) (410,014 ) 7,317 (405,344 ) Net impairment losses recognized in earnings — — (2,829 ) — (2,829 ) Other underwriting income — — 15,073 — 15,073 Equity in net income (loss) of investments accounted for using the equity method — — 45,641 — 45,641 Other income (loss) 1,918 — 501 — 2,419 Total revenues 1,996 1,226 5,529,741 (82,395 ) 5,450,568 Expenses Losses and loss adjustment expenses — — 2,890,106 — 2,890,106 Acquisition expenses — — 805,135 — 805,135 Other operating expenses — — 677,809 — 677,809 Corporate expenses 64,279 2,422 12,293 — 78,994 Amortization of intangible assets — — 105,670 — 105,670 Interest expense 22,147 48,103 138,672 (88,438 ) 120,484 Net foreign exchange (gains) losses 30 — (59,607 ) (9,825 ) (69,402 ) Total expenses 86,456 50,525 4,570,078 (98,263 ) 4,608,796 Income (loss) before income taxes (84,460 ) (49,299 ) 959,663 15,868 841,772 Income tax (expense) benefit — 13,314 (127,265 ) — (113,951 ) Income (loss) before equity in net income of subsidiaries (84,460 ) (35,985 ) 832,398 15,868 727,821 Equity in net income of subsidiaries 842,431 388,260 — (1,230,691 ) — Net income 757,971 352,275 832,398 (1,214,823 ) 727,821 Net (income) loss attributable to noncontrolling interests — — 28,875 1,275 30,150 Net income available to Arch 757,971 352,275 861,273 (1,213,548 ) 757,971 Preferred dividends (41,645 ) — — — (41,645 ) Loss on repurchase of preferred shares (2,710 ) — — — (2,710 ) Net income available to Arch common shareholders $ 713,616 $ 352,275 $ 861,273 $ (1,213,548 ) $ 713,616 Comprehensive income (loss) available to Arch $ 611,003 $ 292,973 $ 730,828 $ (1,023,801 ) $ 611,003 Year Ended December 31, 2017 Condensed Consolidating Statement of Income and Comprehensive Income Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Revenues Net premiums earned $ — $ — $ 4,844,532 $ — $ 4,844,532 Net investment income 243 1,420 559,963 (90,754 ) 470,872 Net realized gains (losses) — — 149,141 — 149,141 Net impairment losses recognized in earnings — — (7,138 ) — (7,138 ) Other underwriting income — — 30,253 — 30,253 Equity in net income (loss) of investments accounted for using the equity method — — 142,286 — 142,286 Other income (loss) (482 ) — (2,089 ) — (2,571 ) Total revenues (239 ) 1,420 5,716,948 (90,754 ) 5,627,375 Expenses Losses and loss adjustment expenses — — 2,967,446 — 2,967,446 Acquisition expenses — — 775,458 — 775,458 Other operating expenses — — 684,451 — 684,451 Corporate expenses 67,450 4,152 12,150 — 83,752 Amortization of intangible assets — — 125,778 — 125,778 Interest expense 23,560 47,993 135,342 (89,464 ) 117,431 Net foreign exchange (gains) losses 2 — 68,900 46,880 115,782 Total expenses 91,012 52,145 4,769,525 (42,584 ) 4,870,098 Income (loss) before income taxes (91,251 ) (50,725 ) 947,423 (48,170 ) 757,277 Income tax (expense) benefit — 10,333 (137,901 ) — (127,568 ) Income (loss) before equity in net income of subsidiaries (91,251 ) (40,392 ) 809,522 (48,170 ) 629,709 Equity in net income of subsidiaries 710,529 303,991 — (1,014,520 ) — Net income 619,278 263,599 809,522 (1,062,690 ) 629,709 Net (income) loss attributable to noncontrolling interests — — (11,721 ) 1,290 (10,431 ) Net income available to Arch 619,278 263,599 797,801 (1,061,400 ) 619,278 Preferred dividends (46,041 ) — — — (46,041 ) Loss on repurchase of preferred shares (6,735 ) — — — (6,735 ) Net income available to Arch common shareholders $ 566,502 $ 263,599 $ 797,801 $ (1,061,400 ) $ 566,502 Comprehensive income (loss) available to Arch $ 851,863 $ 288,752 $ 983,475 $ (1,272,227 ) $ 851,863 Year Ended December 31, 2019 Condensed Consolidating Statement of Cash Flows Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Operating Activities Net Cash Provided By (Used For) Operating Activities $ 52,487 $ 486,252 $ 2,138,195 $ (628,475 ) $ 2,048,459 Investing Activities Purchases of fixed maturity investments — (878,577 ) (29,347,333 ) 172,133 (30,053,777 ) Purchases of equity securities — (155,890 ) (726,820 ) 70,743 (811,967 ) Purchases of other investments — (28,490 ) (1,442,055 ) — (1,470,545 ) Proceeds from the sales of fixed maturity investments — 806,603 27,937,616 (148,354 ) 28,595,865 Proceeds from the sales of equity securities — 7,441 493,120 (70,743 ) 429,818 Proceeds from the sales, redemptions and maturities of other investments — 1,634 1,207,925 — 1,209,559 Proceeds from redemptions and maturities of fixed maturity investments — — 643,265 — 643,265 Net settlements of derivative instruments — — 59,982 — 59,982 Net (purchases) sales of short-term investments 61 34,372 5,400 — 39,833 Change in cash collateral related to securities lending — — (62,193 ) — (62,193 ) Contributions to subsidiaries (2,121 ) (6,000 ) (57,039 ) 65,160 — Issuance of intercompany loans — (200,000 ) (87,783 ) 287,783 — Purchases of fixed assets (162 ) — (37,675 ) — (37,837 ) Other — (18,767 ) (329,719 ) — (348,486 ) Net Cash Provided By (Used For) Investing Activities (2,222 ) (437,674 ) (1,743,309 ) 376,722 (1,806,483 ) Financing Activities Purchases of common shares under share repurchase program (2,871 ) — — — (2,871 ) Proceeds from common shares issued, net 6,203 — 65,160 (65,160 ) 6,203 Proceeds from intercompany borrowings — — 287,783 (287,783 ) — Proceeds from borrowings — — 235,083 (35,000 ) 200,083 Repayments of borrowings — — (49,182 ) — (49,182 ) Change in cash collateral related to securities lending — — 62,193 — 62,193 Change in third party investment in non-redeemable noncontrolling interests — — (75,056 ) — (75,056 ) Change in third party investment in redeemable noncontrolling interests — — (173,103 ) 11,221 (161,882 ) Dividends paid to redeemable noncontrolling interests — — (13,402 ) 887 (12,515 ) Dividends paid to parent (1) — — (627,588 ) 627,588 — Other — — (6,023 ) — (6,023 ) Preferred dividends paid (41,612 ) — — — (41,612 ) Net Cash Provided By (Used For) Financing Activities (38,280 ) — (294,135 ) 251,753 (80,662 ) Effects of exchange rate changes on foreign currency cash and restricted cash — — 17,741 — 17,741 Increase (decrease) in cash and restricted cash 11,985 48,578 118,492 — 179,055 Cash and restricted cash, beginning of year 6,159 5,940 712,544 — 724,643 Cash and restricted cash, end of period $ 18,144 $ 54,518 $ 831,036 $ — $ 903,698 (1) Included in net cash provided by (used for) operating activities in the Arch Capital (Parent Guarantor) and/or Arch-U.S. (Subsidiary Issuer) columns. Year Ended December 31, 2018 Condensed Consolidating Statement of Cash Flows Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Operating Activities Net Cash Provided By (Used For) Operating Activities $ 324,319 $ 481,751 $ 1,703,181 $ (949,929 ) $ 1,559,322 Investing Activities Purchases of fixed maturity investments — (906,482 ) (33,662,541 ) 1,241,363 (33,327,660 ) Purchases of equity securities — (44,830 ) (956,319 ) — (1,001,149 ) Purchases of other investments — — (2,014,622 ) — (2,014,622 ) Proceeds from the sales of fixed maturity investments — 535,947 32,218,687 (1,241,363 ) 31,513,271 Proceeds from the sales of equity securities — — 1,118,445 — 1,118,445 Proceeds from the sales, redemptions and maturities of other investments — — 1,561,958 — 1,561,958 Proceeds from redemptions and maturities of fixed maturity investments — — 892,755 — 892,755 Net settlements of derivative instruments — — 44,699 — 44,699 Net (purchases) sales of short-term investments 96,476 7,674 381,323 — 485,473 Change in cash collateral related to securities lending — — 180,883 — 180,883 Contributions to subsidiaries — (98,500 ) 98,500 — — Purchases of fixed assets (110 ) — (29,699 ) — (29,809 ) Other (4 ) — 21,740 — 21,736 Net Cash Provided By (Used For) Investing Activities 96,362 (506,191 ) (144,191 ) — (554,020 ) Financing Activities Redemption of preferred shares (92,555 ) — — — (92,555 ) Purchases of common shares under share repurchase program (282,762 ) — — — (282,762 ) Proceeds from common shares issued, net (7,608 ) — — — (7,608 ) Proceeds from borrowings — — 218,259 — 218,259 Repayments of borrowings — — (576,401 ) — (576,401 ) Change in cash collateral related to securities lending — — (180,883 ) — (180,883 ) Dividends paid to redeemable noncontrolling interests — — (19,264 ) 1,275 (17,989 ) Dividends paid to parent (1) — — (948,654 ) 948,654 — Other — — (7,226 ) — (7,226 ) Preferred dividends paid (41,645 ) — — — (41,645 ) Net Cash Provided By (Used For) Financing Activities (424,570 ) — (1,514,169 ) 949,929 (988,810 ) Effects of exchange rate changes on foreign currency cash and restricted cash — — (19,133 ) — (19,133 ) Increase (decrease) in cash and restricted cash (3,889 ) (24,440 ) 25,688 — (2,641 ) Cash and restricted cash, beginning of year 10,048 30,380 686,856 — 727,284 Cash and restricted cash, end of period $ 6,159 $ 5,940 $ 712,544 $ — $ 724,643 (1) Included in net cash provided by (used for) operating activities in the Arch Capital (Parent Guarantor) and/or Arch-U.S. (Subsidiary Issuer) columns. Year Ended December 31, 2017 Condensed Consolidating Statement of Cash Flows Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Operating Activities Net Cash Provided By (Used For) Operating Activities $ 159,130 $ (10,289 ) $ 1,649,751 $ (703,714 ) $ 1,094,878 Investing Activities Purchases of fixed maturity investments — — (36,806,913 ) — (36,806,913 ) Purchases of equity securities — — (1,021,016 ) — (1,021,016 ) Purchases of other investments — — (2,020,624 ) — (2,020,624 ) Proceeds from the sales of fixed maturity investments — — 35,686,779 — 35,686,779 Proceeds from the sales of equity securities — — 1,056,401 — 1,056,401 Proceeds from the sales, redemptions and maturities of other investments — — 1,528,617 — 1,528,617 Proceeds from redemptions and maturities of fixed maturity investments — — 907,417 — 907,417 Net settlements of derivative instruments — — (28,563 ) — (28,563 ) Proceeds from investment in joint venture — — — — — Net (purchases) sales of short-term investments (93,864 ) (4,586 ) (636,104 ) — (734,554 ) Change in cash collateral related to securities lending — — 12,540 — 12,540 Contributions to subsidiaries 20,457 (73,700 ) (423,998 ) 477,241 — Issuance of intercompany loans — — (47,000 ) 47,000 — Repayment of intercompany loans — 47,000 80,840 (127,840 ) — Purchases of fixed assets (18 ) — (22,823 ) — (22,841 ) Other — — 111,516 (20,641 ) 90,875 Net Cash Provided By (Used For) Investing Activities (73,425 ) (31,286 ) (1,622,931 ) 375,760 (1,351,882 ) Financing Activities Proceeds from issuance of Series C preferred shares issued, net 319,694 — — — 319,694 Redemption of preferred shares (230,000 ) — — — (230,000 ) Purchases of common shares under share repurchase program — — — — — Proceeds from common shares issued, net (21,048 ) — 477,244 (477,244 ) (21,048 ) Proceeds from intercompany borrowings — — 47,000 (47,000 ) — Proceeds from borrowings — — 253,415 — 253,415 Repayments of intercompany borrowings — — (127,840 ) 127,840 — Repayments of borrowings (100,000 ) — (97,000 ) — (197,000 ) Change in cash collateral relating to securities lending — — (12,540 ) — (12,540 ) Dividends paid to redeemable noncontrolling — — (19,264 ) 1,275 (17,989 ) Dividends paid to parent (1) — — (702,442 ) 702,442 — Other — — (72,537 ) 20,641 (51,896 ) Preferred dividends paid (46,041 ) — — — (46,041 ) Net Cash Provided By (Used For) Financing Activities (77,395 ) — (253,964 ) 327,954 (3,405 ) Effects of exchange rate changes on foreign currency cash and restricted cash — — 18,124 — 18,124 Increase (decrease) in cash and restricted cash 8,310 (41,575 ) (209,020 ) — (242,285 ) Cash and restricted cash, beginning of year 1,738 71,955 895,876 — 969,569 Cash and restricted cash, end of period $ 10,048 $ 30,380 $ 686,856 $ — $ 727,284 (1) Included in net cash provided by (used for) operating activities in the Arch Capital (Parent Guarantor) and/or Arch-U.S. (Subsidiary Issuer) columns.

Subsequent Event

Subsequent Event	12 Months Ended
	Dec. 31, 2019
Subsequent Events [Abstract]
Subsequent event	Subsequent Event On February 25, 2020, the Company announced that it has entered into a share purchase agreement with Natixis to purchase a 29.5% stake in Coface, a France-based leader in the global trade credit insurance market. The transaction will be completed at a price of €10.70 per share (dividend until closing attached), corresponding to a transaction value of approximately €480 million based on the current number of shares. As part of the transaction, Natixis’ seven representatives on Coface’s board of directors will resign and be replaced by four Arch nominees. Among other things, this transaction remains subject to antitrust and regulatory approvals, including in particular, approval by the French prudential regulator, the Autorité de Controle Prudentiel et de Résolution.

Schedule III - Supplementary In

Schedule III - Supplementary Insurance Information	12 Months Ended
	Dec. 31, 2019
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Abstract]
Supplementary Insurance Information	SCHEDULE III ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES SUPPLEMENTARY INSURANCE INFORMATION (U.S. dollars in thousands) Deferred Acquisition Costs Reserves for Losses and Loss Adjustment Expenses Unearned Premiums Net Premiums Earned Net Investment Income (1) Net Losses and Loss Adjustment Expenses Incurred Amortization of Deferred Acquisition Costs Other Operating Expenses (2) Net Premiums Written December 31, 2019 Insurance $188,684 $7,900,328 $1,991,496 $2,397,080 NM $1,615,475 $361,614 $454,770 $2,641,726 Reinsurance 197,856 4,270,013 971,776 1,466,389 NM 1,011,329 239,032 141,484 1,602,723 Mortgage 182,816 457,872 937,370 1,366,340 NM 53,513 134,319 153,092 1,261,756 Other 64,044 1,263,629 438,907 556,689 NM 453,135 105,980 51,651 532,862 Total $633,400 $13,891,842 $4,339,549 $5,786,498 NM $3,133,452 $840,945 $800,997 $6,039,067 December 31, 2018 Insurance $152,360 $7,093,018 $1,549,183 $2,205,661 NM $1,520,680 $349,702 $364,138 $2,212,125 Reinsurance 166,276 3,215,909 710,774 1,261,216 NM 846,882 211,280 133,350 1,372,572 Mortgage 170,080 511,610 1,103,565 1,186,236 NM 81,289 118,595 142,432 1,157,875 Other 80,858 1,032,760 390,114 578,862 NM 441,255 125,558 37,889 604,175 Total $569,574 $11,853,297 $3,753,636 $5,231,975 NM $2,890,106 $805,135 $677,809 $5,346,747 December 31, 2017 Insurance $159,224 $6,952,676 $1,451,390 $2,113,018 NM $1,622,444 $323,639 $359,524 $2,122,440 Reinsurance 150,582 3,053,694 633,810 1,142,621 NM 773,923 221,250 146,663 1,174,474 Mortgage 140,057 579,160 1,206,470 1,057,166 NM 134,677 100,598 146,336 1,111,342 Other 85,961 798,262 330,644 531,727 NM 436,402 129,971 31,928 553,117 Total $535,824 $11,383,792 $3,622,314 $4,844,532 NM $2,967,446 $775,458 $684,451 $4,961,373 (1) The Company does not manage its assets by segment and, accordingly, net investment income is not allocated to each underwriting segment. See note 4, “Segment Information,” to our consolidated financial statements in Item 8 for information related to the ‘other’ segment. (2) Certain other operating expenses relate to the Company’s corporate segment (non-underwriting). Such amounts are not reflected in the table above. See note 4, “Segment Information,” to our consolidated financial statements in Item 8 for information related to the corporate segment.

Schedule IV - Reinsurance

Schedule IV - Reinsurance	12 Months Ended
	Dec. 31, 2019
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Abstract]
Reinsurance	SCHEDULE IV ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES REINSURANCE (U.S. dollars in thousands) Gross Amount Ceded to Other Companies (1) Assumed From Other Companies (1) Net Percentage of Amount Assumed to Net Year Ended December 31, 2019 Premiums Written: Insurance $ 3,879,752 $ (1,266,267 ) $ 28,241 $ 2,641,726 1.1 % Reinsurance 238,229 (720,500 ) 2,084,994 1,602,723 130.1 % Mortgage 1,224,373 (204,509 ) 241,892 1,261,756 19.2 % Other 339,169 (222,019 ) 415,712 532,862 78.0 % Total $ 5,681,523 $ (2,099,893 ) $ 2,457,437 $ 6,039,067 40.7 % Year Ended December 31, 2018 Premiums Written: Insurance $ 3,232,234 $ (1,050,207 ) $ 30,098 $ 2,212,125 1.4 % Reinsurance 213,809 (539,950 ) 1,698,713 1,372,572 123.8 % Mortgage 1,139,099 (202,833 ) 221,609 1,157,875 19.1 % Other 253,760 (130,840 ) 481,255 604,175 79.7 % Total $ 4,838,902 $ (1,614,257 ) $ 2,122,102 $ 5,346,747 39.7 % Year Ended December 31, 2017 Premiums Written: Insurance $ 3,050,876 $ (958,646 ) $ 30,210 $ 2,122,440 1.4 % Reinsurance 152,404 (465,925 ) 1,487,995 1,174,474 126.7 % Mortgage 1,110,319 (256,796 ) 257,819 1,111,342 23.2 % Other 133,858 (47,187 ) 466,446 553,117 84.3 % Total $ 4,447,457 $ (1,407,052 ) $ 1,920,968 $ 4,961,373 38.7 % (1) Certain amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

Schedule VI - Supplementary Inf

Schedule VI - Supplementary Information For Property and Casualty Insurance Underwriters	12 Months Ended
	Dec. 31, 2019
SEC Schedule, 12-18, Supplemental Information, Property-Casualty Insurance Underwriters [Abstract]
Supplementary Information for Property and Casualty Insurance Underwriters	SCHEDULE VI ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES SUPPLEMENTARY INFORMATION FOR PROPERTY AND CASUALTY INSURANCE UNDERWRITERS (U.S. dollars in thousands) Column A Column B Column C Column D Column E Column F Column G Column H Column I Column J Column K Affiliation with Registrant Deferred Acquisition Costs Reserves for Losses and Loss Adjustment Expenses Discount, if any, deducted in Column C Unearned Premiums Net Net Investment Income Net Losses and Loss Adjustment Expenses Incurred Related to Amortization Net Paid Losses and Loss Adjustment Expenses Net (a) Current Year (b) Prior Years Consolidated Subsidiaries 2019 $ 633,400 $ 13,891,842 $ 22,012 $ 4,339,549 $ 5,786,498 $ 627,738 $ 3,297,037 $ (163,585 ) $ 840,945 $ 2,383,255 $ 6,039,067 2018 569,574 11,853,297 21,145 3,753,636 5,231,975 563,633 3,162,818 (272,712 ) 805,135 2,206,164 5,346,747 2017 535,824 11,383,792 20,016 3,622,314 4,844,532 470,872 3,205,428 (237,982 ) 775,458 2,352,912 4,961,373

Significant Accounting Polici_2

Significant Accounting Policies (Policies)	12 Months Ended
	Dec. 31, 2019
Accounting Policies [Abstract]
Basis of presentation	The consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”) and include the accounts of Arch Capital and its subsidiaries, including Arch Reinsurance Ltd. (“Arch Re Bermuda”), Arch Reinsurance Company (“Arch Re U.S.”), Arch-U.S., Arch Insurance Company, Arch Specialty Insurance Company, Arch Excess & Surplus Insurance Company, Arch Indemnity Insurance Company, Arch Insurance Canada Ltd. (“Arch Insurance Canada”), Arch Reinsurance Europe Underwriting Designated Activity Company (“Arch Re Europe”), Arch Mortgage Insurance Company, Arch Mortgage Guaranty Company, United Guaranty Residential Insurance Company, Arch Insurance (EU) Designated Activity Company (formerly, Arch Mortgage Insurance Designated Activity Company) (“Arch Insurance (EU)”), Arch Insurance (UK) Limited (formerly Arch Insurance Company (Europe) Limited)(“Arch Insurance (U.K.)”), Lloyd’s of London syndicate 2012 and related companies (“Arch Syndicate 2012”), Barbican and Watford. All significant intercompany transactions and balances have been eliminated in consolidation.
Use of estimates	The preparation of financial statements in conformity with GAAP requires management to make estimates and assumptions that affect the reported amounts of assets and liabilities and disclosure of contingent assets and liabilities at the date of the financial statements and the reported amounts of revenues and expenses during the reporting period. Actual results could differ materially from those estimates and assumptions. The Company’s principal estimates include: • The reserve for losses and loss adjustment expenses; • Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses, including the provision for uncollectible amounts; • Estimates of written and earned premiums; • The valuation of the investment portfolio and assessment of other-than-temporary impairments (“OTTI”); • The valuation of purchased intangible assets; • The assessment of goodwill and intangible assets for impairment; and • the valuation of deferred tax assets.
Premiums	Insurance. Insurance premiums written are generally recorded at the policy inception and are primarily earned on a pro rata basis over the terms of the policies for all products, usually 12 months . Premiums written include estimates in the Company’s programs, specialty lines, lenders products business and for participation in involuntary pools. Such premium estimates are derived from multiple sources which include the historical experience of the underlying business, similar business and available industry information. Unearned premium reserves represent the portion of premiums written that relates to the unexpired terms of in-force insurance policies. Reinsurance. Reinsurance premiums written include amounts reported by brokers and ceding companies, supplemented by the Company’s own estimates of premiums where reports have not been received. The determination of premium estimates requires a review of the Company’s experience with the ceding companies, familiarity with each market, the timing of the reported information, an analysis and understanding of the characteristics of each line of business, and management’s judgment of the impact of various factors, including premium or loss trends, on the volume of business written and ceded to the Company. On an ongoing basis, the Company’s underwriters review the amounts reported by these third parties for reasonableness based on their experience and knowledge of the subject class of business, taking into account the Company’s historical experience with the brokers or ceding companies. In addition, reinsurance contracts under which the Company assumes business generally contain specific provisions which allow the Company to perform audits of the ceding company to ensure compliance with the terms and conditions of the contract, including accurate and timely reporting of information. Based on a review of all available information, management establishes premium estimates where reports have not been received. Premium estimates are updated when new information is received and differences between such estimates and actual amounts are recorded in the period in which estimates are changed or the actual amounts are determined. Reinsurance premiums written are recorded based on the type of contracts the Company writes. Premiums on the Company’s excess of loss and pro rata reinsurance contracts are estimated when the business is underwritten. For excess of loss contracts, premiums are recorded as written based on the terms of the contract. Estimates of premiums written under pro rata contracts are recorded in the period in which the underlying risks are expected to incept and are based on information provided by the brokers and the ceding companies. For multi-year reinsurance treaties which are payable in annual installments, generally, only the initial annual installment is included as premiums written at policy inception due to the ability of the reinsured to commute or cancel coverage during the term of the policy. The remaining annual installments are included as premiums written at each successive anniversary date within the multi-year term. Reinstatement premiums for the Company’s insurance and reinsurance operations are recognized at the time a loss event occurs, where coverage limits for the remaining life of the contract are reinstated under pre-defined contract terms. Reinstatement premiums, if obligatory, are fully earned when recognized. The accrual of reinstatement premiums is based on an estimate of losses and loss adjustment expenses, which reflects management’s judgment. Premium estimates are reviewed by management at least quarterly. Such review includes a comparison of actual reported premiums to expected ultimate premiums along with a review of the aging and collection of premium estimates. Based on management’s review, the appropriateness of the premium estimates is evaluated, and any adjustment to these estimates is recorded in the period in which it becomes known. Adjustments to premium estimates could be material and such adjustments could directly and significantly impact earnings favorably or unfavorably in the period they are determined because the estimated premium may be fully or substantially earned. A significant portion of amounts included as premiums receivable, which represent estimated premiums written, net of commissions, are not currently due based on the terms of the underlying contracts. Reinsurance premiums written, irrespective of the class of business, are generally earned on a pro rata basis over the terms of the underlying policies or reinsurance contracts. Contracts and policies written on a “losses occurring” basis cover claims that may occur during the term of the contract or policy, which is typically 12 months . Accordingly, the premium is earned evenly over the term. Contracts which are written on a “risks attaching” basis cover claims which attach to the underlying insurance policies written during the terms of such contracts. Premiums earned on such contracts usually extend beyond the original term of the reinsurance contract, typically resulting in recognition of premiums earned over a 24 -month period. Certain of the Company’s reinsurance contracts include provisions that adjust premiums or acquisition expenses based upon the experience under the contracts. Premiums written and earned, as well as related acquisition expenses, are recorded based upon the projected experience under such contracts. The Company also writes certain reinsurance business that is intended to provide insurers with risk management solutions that complement traditional reinsurance. Under these contracts, the Company assumes a measured amount of insurance risk in exchange for an anticipated margin, which is typically lower than on traditional reinsurance contracts. The terms and conditions of these contracts may include additional or return premiums based on loss experience, loss corridors, sublimits and caps. Examples of such business include aggregate stop-loss coverages, financial quota share coverages and multi-year retrospectively rated excess of loss coverages. If these contracts are deemed to transfer risk, they are accounted for as reinsurance. Otherwise, such contracts are accounted for under the deposit method. Mortgage. Mortgage guaranty insurance policies are contracts that are generally non-cancelable by the insurer, are renewable at a fixed price, and provide for payment of premiums on a monthly, annual or single basis. Upon renewal, the Company is not able to re-underwrite or re-price its policies. Consistent with industry accounting practices, premiums written on a monthly basis are earned as coverage is provided. Premiums written on an annual basis are amortized on a monthly pro rata basis over the year of coverage. Primary mortgage insurance premiums written on policies covering more than one year are referred to as single premiums. A portion of the revenue from single premiums is recognized in premiums earned in the current period, and the remaining portion is deferred as unearned premiums and earned over the estimated expiration of risk of the policy. If single premium policies related to insured loans are canceled due to repayment by the borrower and the policy is a non-refundable product, the remaining unearned premium related to each canceled policy is recognized as earned premium upon notification of the cancellation. Unearned premiums represent the portion of premiums written that is applicable to the estimated unexpired risk of insured loans. A portion of premium payments may be refundable if the insured cancels coverage, which generally occurs when the loan is repaid, the loan amortizes to a sufficiently low amount to trigger a lender permitted or legally required cancellation, or the value of the property has increased sufficiently in accordance with the terms of the contract. Premium refunds reduce premiums earned in the consolidated statements of income. Generally, only unearned premiums are refundable.
Acquisition costs	Acquisition Costs. Acquisition costs that are directly related and incremental to the successful acquisition or renewal of business are deferred and amortized based on the type of contract. The Company’s insurance and reinsurance operations capitalize incremental direct external costs that result from acquiring a contract but do not capitalize salaries, benefits and other internal underwriting costs. For the Company’s mortgage insurance operations, which include a substantial direct sales force, both external and certain internal direct costs are deferred and amortized. For property and casualty insurance and reinsurance contracts, deferred acquisition costs are amortized over the period in which the related premiums are earned. Consistent with mortgage insurance industry accounting practice, amortization of acquisition costs related to the mortgage insurance contracts for each underwriting year’s book of business is recorded in proportion to estimated gross profits. Estimated gross profits are comprised of earned premiums and losses and loss adjustment expenses. For each underwriting year, the Company estimates the rate of amortization to reflect actual experience and any changes to persistency or loss development. Deferred acquisition costs are carried at their estimated realizable value and take into account anticipated losses and loss adjustment expenses, based on historical and current experience, and anticipated investment income. A premium deficiency occurs if the sum of anticipated losses and loss adjustment expenses, unamortized acquisition costs and maintenance costs exceed unearned premiums (including expected future premiums) and anticipated investment income. A premium deficiency reserve (“PDR”) is recorded by charging any unamortized acquisition costs to expense to the extent required in order to eliminate the deficiency. If the premium deficiency exceeds unamortized acquisition costs then a liability is accrued for the excess deficiency. To assess the need for a PDR on mortgage exposures, the Company develops loss projections based on modeled loan defaults related to its current policies in force. This projection is based on recent trends in default experience, severity and rates of defaulted loans moving to claim, as well as recent trends in the rate at which loans are prepaid, and incorporates anticipated interest income. Evaluating the expected profitability of the Company’s existing mortgage insurance business and the need for a PDR for its mortgage business involves significant reliance upon assumptions and estimates with regard to the likelihood, magnitude and timing of potential losses and premium revenues. No premium deficiency charges were recorded by the Company during 2019 , 2018 or 2017 .
Deposit accounting	Certain assumed reinsurance contracts that are deemed not to transfer insurance risk, are accounted for using the deposit method of accounting. However, it is possible that the Company could incur financial losses on such contracts. Management exercises significant judgment in the assumptions used in determining whether assumed contracts should be accounted for as reinsurance contracts or deposit contracts. For those contracts that contain only significant underwriting risk, the estimated profit margin is deferred and amortized over the contract period and such amount is included in the Company’s underwriting results. When the estimated profit margin is explicit, the margin is reflected as other underwriting income and any adverse financial results on such contracts are reflected as incurred losses. When the estimated profit margin is implicit, the margin is reflected as an offset to paid losses and any adverse financial results on such contracts are reflected as incurred losses. Additional judgments are required when applying the accounting guidance with respect to the revenue recognition criteria for contracts deemed to transfer only significant underwriting risk. For those contracts that contain only significant timing risk, an accretion rate is established at inception of the contract based on actuarial estimates whereby the deposit accounting liability is increased to the estimated amount payable over the contract term. The accretion on the deposit is based on the expected rate of return required to fund the expected future payment obligations. Periodically the Company reassesses the estimated ultimate liability and the related expected rate of return. The accretion of the deposit accounting liability as well as changes to the estimated ultimate liability and the accretion rate would be reflected as part of interest expense in the Company’s results of operations. Any negative accretion in a deposit accounting liability is shown in other underwriting income in the Company’s results of operations. Under some of these contracts, the ceding company retains the related assets on a funds-held basis. Such amounts are included in “Other assets” on the Company’s balance sheet. Interest income produced by those assets are recorded as part of net investment income in the Company's results of operations.
Retroactive accounting	Retroactive reinsurance reimburses a ceding company for liabilities incurred as a result of past insurable events covered by the underlying policies reinsured. In certain instances, reinsurance contracts cover losses both on a prospective basis and on a retroactive basis and, accordingly, the Company bifurcates the prospective and retrospective elements of these reinsurance contracts and accounts for each element separately where practical. Underwriting income generated in connection with retroactive reinsurance contracts is deferred and amortized into income over the settlement period while losses are charged to income immediately. Subsequent changes in estimated amount or timing of cash flows under such retroactive reinsurance contracts are accounted for by adjusting the previously deferred amount to the balance that would have existed had the revised estimate been available at the inception of the reinsurance transaction, with a corresponding charge or credit to income.
Reinsurance ceded	In the normal course of business, the Company purchases reinsurance to increase capacity and to limit the impact of individual losses and events on its underwriting results by reinsuring certain levels of risk with other insurance enterprises or reinsurers. The Company uses pro rata, excess of loss and facultative reinsurance contracts. Reinsurance ceding commissions that represent a recovery of acquisition costs are recognized as a reduction to acquisition costs while the remaining portion is deferred. The accompanying consolidated statement of income reflects premiums and losses and loss adjustment expenses and acquisition costs, net of reinsurance ceded. See note 7, “Reinsurance” for information on the Company's reinsurance usage. Reinsurance premiums ceded and unpaid losses and loss adjustment expenses recoverable are estimated in a manner consistent with that of the original policies issued and the terms of the reinsurance contracts. If the reinsurers are unable to satisfy their obligations under the agreements, the Company’s insurance or reinsurance subsidiaries would be liable for such defaulted amounts.
Cash	Cash includes cash equivalents, which are investments with original maturities of three months or less
Investments	The Company currently classifies substantially all of its fixed maturity investments and short-term investments as “available for sale” and, accordingly, they are carried at estimated fair value (also known as fair value) with the changes in fair value recorded as an unrealized gain or loss component of accumulated other comprehensive income in shareholders’ equity. The fair value of fixed maturity securities and equity securities is generally determined from quotations received from nationally recognized pricing services, or when such prices are not available, by reference to broker or underwriter bid indications. Short-term investments comprise securities due to mature within one year of the date of issue. Short-term investments include certain cash equivalents which are part of investment portfolios under the management of external and internal investment managers. The Company enters into securities lending agreements with financial institutions to enhance investment income whereby it loans certain of its securities to third parties, primarily major brokerage firms, for short periods of time through a lending agent. Such securities have been reclassified as “Securities pledged under securities lending, at fair value.” The Company maintains legal control over the securities it lends, retains the earnings and cash flows associated with the loaned securities and receives a fee from the borrower for the temporary use of the securities. Collateral received is required at a rate of 102% or greater of the fair value of the loaned securities including accrued investment income and is monitored and maintained by the lending agent. Such collateral is reflected as “Collateral received under securities lending, at fair value.” The Company’s investment portfolio includes certain funds that, due to their ownership structure, are accounted for by the Company using the equity method. In applying the equity method, these investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the fair value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. Changes in the carrying value of such investments are recorded in net income as “Equity in net income (loss) of investments accounted for using the equity method.” As such, fluctuations in the carrying value of the investments accounted for using the equity method may increase the volatility of the Company’s reported results of operations. The Company’s investment portfolio includes equity securities that are accounted for at fair value. Such holdings primarily include publicly traded common stocks. Dividend income on equities is reflected in net investment income. Changes in fair value on equity securities are included in “Net realized gains (losses)” in the consolidated statement of income. The Company elected to carry certain fixed maturity securities, equity securities and other investments at fair value under the fair value option afforded by accounting guidance regarding the fair value option for financial assets and liabilities. The fair value for certain of the Company’s other investments are determined using net asset values (“NAVs”) as advised by external fund managers. The NAV is based on the fund manager’s valuation of the underlying holdings in accordance with the fund’s governing documents. Changes in fair value of investments accounted for using the fair value option are included in “Net realized gains (losses).” The primary reasons for electing the fair value option were to address simplification and cost-benefit considerations. The Company invests in limited partner interests and shares of limited liability companies. Such amounts are included in investments accounted for using the equity method, other investments available for sale and investments accounted for using the fair value option. These investments can often have characteristics of a variable interest entity (“VIE”). A VIE refers to entities that have characteristics such as (i) insufficient equity at risk to allow the entity to finance its activities without additional financial support or (ii) instances where the equity investors, as a group, do not have the characteristic of a controlling financial interest. If the Company is determined to be the primary beneficiary, it is required to consolidate the VIE. The primary beneficiary is defined as the variable interest holder that is determined to have the controlling financial interest as a result of having both (i) the power to direct the activities of a VIE that most significantly impact the economic performance of the VIE and (ii) the obligation to absorb losses or right to receive benefits from the VIE that could potentially be significant to the VIE. At inception of the VIE as well as on an ongoing basis, the Company determines whether it is the primary beneficiary based on an analysis of the Company’s level of involvement in the VIE, the contractual terms, and the overall structure of the VIE. The Company's maximum exposure to loss with respect to these investments is limited to the investment carrying amounts reported in the Company's consolidated balance sheet and any unfunded commitment. The Company performs quarterly reviews of its investments to determine whether declines in fair value below the cost basis are considered other-than-temporary in accordance with applicable accounting guidance regarding the recognition and presentation of OTTI. The process of determining whether a security is other-than-temporarily impaired requires judgment and involves analyzing many factors. These factors include (i) an analysis of the liquidity, business prospects and overall financial condition of the issuer, (ii) the time period in which there was a significant decline in value, (iii) the significance of the decline and (iv) the analysis of specific credit events. When there are credit-related losses associated with debt securities for which the Company does not have an intent to sell and it is more likely than not that it will not be required to sell the security before recovery of its cost basis, the amount of the OTTI related to a credit loss is recognized in earnings and the amount of the OTTI related to other factors ( e.g. , interest rates, market conditions, etc.) is recorded as a component of other comprehensive income (loss). The amount of the credit loss of an impaired debt security is the difference between the amortized cost and the greater of (i) the present value of expected future cash flows and (ii) the fair value of the security. In instances where no credit loss exists but it is more likely than not that the Company will have to sell the debt security prior to the anticipated recovery, the decline in fair value below amortized cost is recognized as an OTTI in earnings. In periods after the recognition of an OTTI on debt securities, the Company accounts for such securities as if they had been purchased on the measurement date of the OTTI at an amortized cost basis equal to the previous amortized cost basis less the OTTI recognized in earnings. For debt securities for which OTTI were recognized in earnings, the difference between the new amortized cost basis and the cash flows expected to be collected will be accreted or amortized into net investment income. See note 8, “Investment Information” for additional information. Net investment income includes interest and dividend income together with amortization of market premiums and discounts and is net of investment management and custody fees. Anticipated prepayments and expected maturities are used in applying the interest method for certain investments such as mortgage and other asset-backed securities. When actual prepayments differ significantly from anticipated prepayments, the effective yield is recalculated to reflect actual payments to date and anticipated future payments. The net investment in such securities is adjusted to the amount that would have existed had the new effective yield been applied since the acquisition of the security. Such adjustments, if any, are included in net investment income when determined. Investment gains or losses realized on the sale of investments, except for certain fund investments, are determined on a first-in, first-out basis and are reflected in net income. Investment gains or losses realized on the sale of certain fund investments are determined on an average cost basis. Unrealized appreciation or decline in the value of available for sale securities, which are carried at fair value, is excluded from net income and recorded as a separate component of accumulated other comprehensive income, net of applicable deferred income tax.
Derivative instruments	The Company recognizes all derivative instruments, including embedded derivative instruments, at fair value in its consolidated balance sheets. The Company employs the use of derivative instruments within its operations to mitigate risks arising from assets and liabilities held in foreign currencies as well as part of its overall investment strategy. For such instruments, changes in assets and liabilities measured at fair value are recorded as “Net realized gains” in the consolidated statements of income. In addition, the Company’s derivative instruments include amounts related to underwriting activities where an insurance or reinsurance contract meets the accounting definition of a derivative instrument. For such contracts, changes in fair value are reflected in “Other underwriting income” in the consolidated statements of income as the underlying contract originates from the Company’s underwriting operations. For the periods ended 2019 , 2018 , and 2017 , the Company did not designate any derivative instruments as hedges under the relevant accounting guidance. See note 10, “Derivative Instruments” for additional information.
Reserves for losses and loss adjustment expenses	Insurance and Reinsurance. The reserve for losses and loss adjustment expenses consists of estimates of unpaid reported losses and loss adjustment expenses and estimates for losses incurred but not reported. The reserve for unpaid reported losses and loss adjustment expenses, established by management based on reports from ceding companies and claims from insureds, excludes estimates of amounts related to losses under high deductible policies, and represents the estimated ultimate cost of events or conditions that have been reported to or specifically identified by the Company. Such reserves are supplemented by management’s estimates of reserves for losses incurred for which reports or claims have not been received. The Company’s reserves are based on a combination of reserving methods, incorporating both Company and industry loss development patterns. The Company selects the initial expected loss and loss adjustment expense ratios based on information derived by its underwriters and actuaries during the initial pricing of the business, supplemented by industry data where appropriate. Such ratios consider, among other things, rate changes and changes in terms and conditions that have been observed in the market. These estimates are reviewed regularly and, as experience develops and new information becomes known, the reserves are adjusted as necessary. Such adjustments, if any, are reflected in income in the period in which they are determined. As actual loss information has been reported, the Company has developed its own loss experience and its reserving methods include other actuarial techniques. Over time, such techniques have been given further weight in its reserving process based on the continuing maturation of the Company’s reserves. Inherent in the estimates of ultimate losses and loss adjustment expenses are expected trends in claims severity and frequency and other factors which may vary significantly as claims are settled. Accordingly, ultimate losses and loss adjustment expenses may differ materially from the amounts recorded in the accompanying consolidated financial statements. Losses and loss adjustment expenses are recorded on an undiscounted basis, except for excess workers’ compensation and employers’ liability business written by the Company’s insurance operations. Mortgage. The reserves for mortgage guaranty insurance losses and loss adjustment expenses are the estimated claim settlement costs on notices of delinquency that have been received by the Company, as well as loan delinquencies that have been incurred but have not been reported by the lenders. Consistent with primary mortgage insurance industry accounting practice, the Company does not establish loss reserves for future claims on insured loans that are not currently delinquent (defined as two consecutive missed payments). The Company establishes loss reserves on a case-by-case basis when insured loans are reported delinquent using estimated claim rates and average claim sizes for each cohort, net of any salvage recoverable. The Company also reserves for delinquencies that have occurred but have not yet been reported to the Company prior to the close of an accounting period. To determine this reserve, the Company estimates the number of delinquencies not yet reported using historical information regarding late reported delinquencies and applies estimated claim rates and claim sizes for the estimated delinquencies not yet reported. The establishment of reserves across the Company’s segments is an inherently uncertain process, are necessarily based on estimates, and the ultimate net cost may vary from such estimates. The methods for making such estimates and for establishing the resulting liability are reviewed and updated using the most current information available. Any resulting adjustments, which may be material, are reflected in current operations.
Contractholders receivables and payables	Certain insurance policies written by the Company’s insurance operations feature large deductibles, primarily in its construction and national accounts lines of business. Under such contracts, the Company is obligated to pay the claimant for the full amount of the claim. The Company is subsequently reimbursed by the policyholder for the deductible amount. These amounts are included on a gross basis in the consolidated balance sheet in contractholder payables and contractholder receivables, respectively. In the event that the Company is unable to collect from the policyholder, the Company would be liable for such defaulted amounts. Collateral, primarily in the form of letters of credit, cash and trusts, is obtained from the policyholder to mitigate the Company’s credit risk. In the instances where the Company receives collateral in the form of cash, the Company reflects it in “Collateral held for insured obligations.”
Foreign exchange	Assets and liabilities of foreign operations whose functional currency is not the U.S. Dollar are translated at the prevailing exchange rates at each balance sheet date. Revenues and expenses of such foreign operations are translated at average exchange rates during the year. The net effect of the translation adjustments for foreign operations is included in accumulated other comprehensive income, net of applicable deferred income tax. Monetary assets and liabilities, such as premiums receivable and the reserve for losses and loss adjustment expenses, denominated in foreign currencies are revalued at the exchange rate in effect at the balance sheet date with the resulting foreign exchange gains and losses included in net income. Accounts that are classified as non-monetary, such as deferred acquisition costs and the unearned premium reserves, are not revalued. In the case of foreign currency denominated fixed maturity securities which are classified as “available for sale,” the change in exchange rates between the local currency in which the investments are denominated and the Company’s functional currency at each balance sheet date is included in unrealized appreciation or decline in value of securities, a component of accumulated other comprehensive income, net of applicable deferred income tax.
Income taxes	Deferred income taxes reflect the expected future tax consequences of temporary differences between the carrying amounts of assets and liabilities for financial reporting purposes and amounts used for income tax purposes. A valuation allowance is recorded if it is more likely than not that some or all of a deferred tax asset may not be realized. The Company considers future taxable income and feasible tax planning strategies in assessing the need for a valuation allowance. In the event the Company determines that it will not be able to realize all or part of its deferred income tax assets in the future, an adjustment to the deferred income tax assets would be charged to income in the period in which such determination is made. In addition, if the Company subsequently assesses that the valuation allowance is no longer needed, a benefit would be recorded to income in the period in which such determination is made. See note 14, “Income Taxes” for additional information. The Company recognizes a tax benefit where it concludes that it is more likely than not that the tax benefit will be sustained on audit by the taxing authority based solely on the technical merits of the associated tax position. If the recognition threshold is met, the Company recognizes a tax benefit measured at the largest amount of the tax benefit that, in the Company’s judgment, is greater than 50% likely to be realized. The Company records interest and penalties related to unrecognized tax benefits in the provision for income taxes.
Share-based payment arrangements	The Company applies a fair value based measurement method in accounting for its share-based payment arrangements with eligible employees and directors. Compensation expense is estimated based on the fair value of the award at the grant date and is recognized in net income over the requisite service period with a corresponding increase in shareholders’ equity. No value is attributed to awards that employees forfeit because they fail to satisfy vesting conditions. The Company’s (i) time-based awards generally vest over a three year period with one-third vesting on the first, second and third anniversaries of the grant date and (ii) performance-based awards cliff vest after each three year performance period based on achievement of the specified performance criteria. The share-based compensation expense associated with awards that have graded vesting features and vest based on service conditions only is calculated on a straight-line basis over the requisite service period for the entire award. Compensation expense recognized in connection with performance awards is based on the achievement of the specified performance and service conditions. The final measure of compensation expense recognized over the requisite service period reflects the final performance outcome. During the recognition period compensation expense is accrued based on the performance condition that is probable of achievement. For awards granted to retirement-eligible employees where no service is required for the employee to retain the award, the grant date fair value is immediately recognized as compensation expense at the grant date because the employee is able to retain the award without continuing to provide service. For employees near retirement eligibility, attribution of compensation cost is over the period from the grant date to the retirement eligibility date. These charges had no impact on the Company’s cash flows or total shareholders’ equity. See note 21, “Share-Based Compensation” for information relating to the Company’s share-based payment awards.
Guaranty fund and other related assessments	Liabilities for guaranty fund and other related assessments in the Company’s insurance and reinsurance operations are accrued when the Company receives notice that an amount is payable, or earlier if a reasonable estimate of the assessment can be made.
Treasury shares	Treasury shares are common shares purchased by the Company and not subsequently canceled. These shares are recorded at cost and result in a reduction of the Company’s shareholders’ equity in its Consolidated Balance Sheets.
Goodwill and intangible assets	Goodwill represents the excess of the purchase price of an acquisition over the fair value of the net assets acquired and is assigned to the applicable reporting unit at acquisition. Goodwill is evaluated for impairment on an annual basis. Impairment tests may be performed more frequently if the facts and circumstances indicate a possible impairment. In performing impairment tests, the Company may first assess qualitative factors to determine whether it is more likely than not (that is, more than a 50% probability) that the fair value of a reporting unit exceeds its carrying amount as a basis for determining whether it is necessary to perform the two-step goodwill impairment test described in the accounting guidance. Indefinite-lived intangible assets, such as insurance licenses are evaluated for impairment similar to goodwill. Finite-lived intangible assets and liabilities include the value of acquired insurance and reinsurance contracts, which are estimated based on the present value of future expected cash flows and amortized in proportion to the estimated profits expected to be realized. Other finite-lived intangible assets or liabilities, including favorable or unfavorable contracts, are amortized over their useful lives. Finite-lived intangible assets and liabilities are periodically reviewed for indicators of impairment. An impairment is recognized when the carrying amount is not recoverable from its undiscounted cash flows and is measured as the difference between the carrying amount and fair value. If goodwill or intangible assets are impaired, such assets are written down to their fair values with the related expense recorded in the Company’s results of operations.
Recent accounting pronouncements	Recently Issued Accounting Standards Adopted The Company adopted ASU 2016-02, “Leases (Topic 842)”, which provides a new comprehensive model for lease accounting. Topic 842 requires a lessee to recognize a liability to make lease payments (the lease liability) and a right-of-use asset representing its right to use the underlying asset for the lease term. The Company adopted the modified retrospective approach of this standard, that resulted in the recognition of a right-of-use asset of $147.9 million as part of other assets and a lease liability of $163.6 million as part of other liabilities in the consolidated balance sheet as of January 1, 2019. The Company de-recognized the liability for deferred rent that was required under the previous guidance. In addition, the Company adopted ASU 2018-11, “Leases: Targeted Improvements (Topic 842),” which provides an additional (optional) transition method to adopt the new lease standard. The Company adopted the alternative transition method and elected to utilize a cumulative-effect adjustment to the opening balance of the retained earnings for the year of adoption. As such, the Company’s reporting for the comparative periods prior to the adoption continue to be presented in the financial statements in accordance with previous lease accounting guidance. The Company also adopted the practical expedients as a package which allows the Company to not reassess (1) whether any expired or existing contracts are or contain leases (2) the lease classification for any expired or existing leases (3) initial direct costs for any existing leases and (4) to account for the lease and non-lease components as a single lease component. In addition to electing the practical expedients as a package, the Company elected to include hindsight to determine the lease term of existing leases, and made an accounting policy election to not apply the recognition requirements to short-term leases (lease term of less than twelve months). The cumulative effect adjustment to the opening balance of retained earnings was zero. The adoption of the updated guidance did not have a material effect on the Company’s results of operations or liquidity. The Company adopted ASU 2018-07 “Improvements to Nonemployee Share-Based Payment Accounting,” which was issued in June 2018 to simplify the accounting for share-based payments granted to nonemployees for goods and services. Under this ASU, most of the guidance on such payments to nonemployees would be aligned with the requirements for share-based payments granted to employees. The ASU is effective for reporting periods beginning after December 15, 2018. This guidance and the adoption of this provision did not have a material effect on the Company's financial position, results of operations or cash flows. The Company adopted ASU 2018-02 “Income Statement Reporting Comprehensive Income (Topic 220) - Reclassification of Certain Tax Effects from Accumulated Other Comprehensive Income,” which was issued in February 2018 to allow the reclassification of the stranded tax effects in accumulated other comprehensive income (“AOCI”) resulting from the Tax Cuts and Jobs Act of 2017 (“Tax Cuts Act”). Current guidance requires the effect of a change in tax laws or rates on deferred tax balances to be reported in income from continuing operations in the accounting period that includes the period of enactment, even if the related income tax effects were originally charged or credited directly to AOCI. The amount of the reclassification would include the effect of the change in the U.S. federal corporate income tax rate on the gross deferred tax amounts and related valuation allowances, if any, at the date of the enactment of the Tax Cuts Act related to items in AOCI. The updated guidance is effective for reporting periods beginning after December 15, 2018 and is to be applied retrospectively to each period in which the effect of the Tax Cuts Act related to items remaining in AOCI are recognized or at the beginning of the period of adoption. The adoption of this ASU did not have a material effect on the Company’s results of operations, financial position or liquidity. The Company adopted ASU 2017-08 “Receivables - Nonrefundable Fees and Other Costs (Subtopic 310-20), Premium Amortization on Purchased Callable Debt Securities,” which was issued in March 2017. This ASU shortens the amortization period for certain callable debt securities held at a premium and requires the premium to be amortized to the earliest call date. However, the new guidance does not require an accounting change for securities held at a discount whose discount continues to be amortized to maturity. The standard is effective for financial statements issued for fiscal years, and interim periods within those fiscal years, beginning after December 15, 2018, with early adoption permitted. The adoption of the guidance requires a modified retrospective approach with a cumulative-effect adjustment to retained earnings. The adoption of this ASU did not have a material effect on the Company’s consolidated financial statements. Recently Issued Accounting Standards Not Yet Adopted ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326),” was issued in June 2016. The ASU changes how entities will measure credit losses for most financial assets and certain other instruments that aren’t measured at fair value through net income. The ASU requires an entity to estimate its lifetime “expected credit loss” and record an allowance that, when deducted from the amortized cost basis of the financial asset, presents the net amount expected to be collected on the financial asset. The ASU is effective for the 2020 first quarter, and should be applied on a modified retrospective basis for the majority of the provisions with a cumulative-effect adjustment to retained earnings at the beginning of the year of adoption. Upon adoption, the Company expects the new standard to have an impact on certain type of investment securities, reinsurance recoverables and contractholder receivables. The Company will adopt the ASU on January 1, 2020 by applying the modified retrospective approach. The Company anticipates recording a cumulative-effect adjustment to the opening balance of retained earnings, which is not expected to have a material effect on the consolidated financial statements. ASU 2018-13, “Fair Value Measurement (Topic 820): Disclosure Framework - Changes to the Disclosure Requirements for Fair Value Measurement,” was issued in August, 2018. The ASU modifies the disclosure requirements on fair value measurement as part of the disclosure framework project with the objective to improve the effectiveness of disclosures in the notes to the financial statements. The amendments in this update allow for removal of (1) the amount and reasons for transfer between Level 1 and Level 2 of the fair value hierarchy; (2) the policy for transfers between levels; and (3) the valuation processes for Level 3 fair value measurements. The ASU is effective for fiscal years beginning after December 15, 2019 and interim periods within those fiscal years. The Company is currently evaluating the impact of the new guidance on its consolidated financial statements and does not expect this guidance to have a material effect on the Company’s consolidated financial statements. ASU 2018-15, “Intangibles - Goodwill and Other - Internal-Use Software (Subtopic 350-40) ,” was issued in the 2018 third quarter. This ASU aligns the requirements for capitalizing certain implementation costs incurred in a cloud computing arrangement that is a service contract with the requirements for capitalizing implementation costs incurred to develop or obtain internal-use software. The standard is effective for financial statements issued for fiscal years, and interim periods within those fiscal years, beginning after December 15, 2019, with early adoption permitted. The guidance provides flexibility in adoption, allowing for either retrospective adjustment or prospective adjustment for all implementation costs incurred after the date of adoption. The Company is currently evaluating the impact of the new guidance on the consolidated financial statements. The Company is currently evaluating the impact of the new guidance on its consolidated financial statements and does not expect this guidance to have a material effect on the Company’s consolidated financial statements.

Segment Information (Tables)

Segment Information (Tables)	12 Months Ended
	Dec. 31, 2019
Segment Reporting [Abstract]
Analysis of underwriting income (loss) by segment and reconciliation to net income (loss) available to common shareholders	The following tables summarize the Company’s underwriting income or loss by segment, together with a reconciliation of underwriting income or loss to net income available to Arch common shareholders, summary information regarding net premiums written and earned by major line of business and net premiums written by location: Year Ended December 31, 2019 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 3,907,993 $ 2,323,223 $ 1,466,265 $ 7,695,645 $ 754,881 $ 8,138,960 Premiums ceded (1,266,267 ) (720,500 ) (204,509 ) (2,189,440 ) (222,019 ) (2,099,893 ) Net premiums written 2,641,726 1,602,723 1,261,756 5,506,205 532,862 6,039,067 Change in unearned premiums (244,646 ) (136,334 ) 104,584 (276,396 ) 23,827 (252,569 ) Net premiums earned 2,397,080 1,466,389 1,366,340 5,229,809 556,689 5,786,498 Other underwriting income (loss) — 6,444 16,005 22,449 2,412 24,861 Losses and loss adjustment expenses (1,615,475 ) (1,011,329 ) (53,513 ) (2,680,317 ) (453,135 ) (3,133,452 ) Acquisition expenses (361,614 ) (239,032 ) (134,319 ) (734,965 ) (105,980 ) (840,945 ) Other operating expenses (454,770 ) (141,484 ) (153,092 ) (749,346 ) (51,651 ) (800,997 ) Underwriting income (loss) $ (34,779 ) $ 80,988 $ 1,041,421 1,087,630 (51,665 ) 1,035,965 Net investment income 491,067 136,671 627,738 Net realized gains (losses) 351,202 15,161 366,363 Net impairment losses recognized in earnings (3,165 ) — (3,165 ) Equity in net income (loss) of investments accounted for using the equity method 123,672 — 123,672 Other income (loss) 2,233 — 2,233 Corporate expenses (65,667 ) — (65,667 ) Transaction costs and other (14,444 ) — (14,444 ) Amortization of intangible assets (82,104 ) — (82,104 ) Interest expense (93,735 ) (27,137 ) (120,872 ) Net foreign exchange gains (losses) (9,252 ) (11,357 ) (20,609 ) Income (loss) before income taxes 1,787,437 61,673 1,849,110 Income tax expense (155,790 ) (20 ) (155,810 ) Net income (loss) 1,631,647 61,653 1,693,300 Dividends attributable to redeemable noncontrolling interests — (16,909 ) (16,909 ) Amounts attributable to nonredeemable noncontrolling interests — (40,072 ) (40,072 ) Net income (loss) available to Arch 1,631,647 4,672 1,636,319 Preferred dividends (41,612 ) — (41,612 ) Loss on redemption of preferred shares — — — Net income (loss) available to Arch common shareholders $ 1,590,035 $ 4,672 $ 1,594,707 Underwriting Ratios Loss ratio 67.4 % 69.0 % 3.9 % 51.3 % 81.4 % 54.2 % Acquisition expense ratio 15.1 % 16.3 % 9.8 % 14.1 % 19.0 % 14.5 % Other operating expense ratio 19.0 % 9.6 % 11.2 % 14.3 % 9.3 % 13.8 % Combined ratio 101.5 % 94.9 % 24.9 % 79.7 % 109.7 % 82.5 % Goodwill and intangible assets $ 289,021 $ 2,516 $ 438,896 $ 730,433 $ 7,650 $ 738,083 Total investable assets $ 22,285,676 $ 2,704,589 $ 24,990,265 Total assets 34,374,468 3,510,893 37,885,361 Total liabilities 22,977,636 2,592,173 25,569,809 (1) Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total. Year Ended December 31, 2018 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 3,262,332 $ 1,912,522 $ 1,360,708 $ 6,534,423 $ 735,015 $ 6,961,004 Premiums ceded (1,050,207 ) (539,950 ) (202,833 ) (1,791,851 ) (130,840 ) (1,614,257 ) Net premiums written 2,212,125 1,372,572 1,157,875 4,742,572 604,175 5,346,747 Change in unearned premiums (6,464 ) (111,356 ) 28,361 (89,459 ) (25,313 ) (114,772 ) Net premiums earned 2,205,661 1,261,216 1,186,236 4,653,113 578,862 5,231,975 Other underwriting income — (682 ) 13,033 12,351 2,722 15,073 Losses and loss adjustment expenses (1,520,680 ) (846,882 ) (81,289 ) (2,448,851 ) (441,255 ) (2,890,106 ) Acquisition expenses, net (349,702 ) (211,280 ) (118,595 ) (679,577 ) (125,558 ) (805,135 ) Other operating expenses (364,138 ) (133,350 ) (142,432 ) (639,920 ) (37,889 ) (677,809 ) Underwriting income (loss) $ (28,859 ) $ 69,022 $ 856,953 897,116 (23,118 ) 873,998 Net investment income 437,958 125,675 563,633 Net realized gains (losses) (284,429 ) (120,915 ) (405,344 ) Net impairment losses recognized in earnings (2,829 ) — (2,829 ) Equity in net income (loss) of investments accounted for using the equity method 45,641 — 45,641 Other income (loss) 2,419 — 2,419 Corporate expenses (58,608 ) — (58,608 ) Transaction costs and other (11,386 ) (9,000 ) (20,386 ) Amortization of intangible assets (105,670 ) — (105,670 ) Interest expense (101,019 ) (19,465 ) (120,484 ) Net foreign exchange gains (losses) 58,711 10,691 69,402 Income (loss) before income taxes 877,904 (36,132 ) 841,772 Income tax (expense) benefit (113,924 ) (27 ) (113,951 ) Net income (loss) 763,980 (36,159 ) 727,821 Dividends attributable to redeemable noncontrolling interests — (18,357 ) (18,357 ) Amounts attributable to nonredeemable noncontrolling interests — 48,507 48,507 Net income (loss) available to Arch 763,980 (6,009 ) 757,971 Preferred dividends (41,645 ) — (41,645 ) Loss on redemption of preferred shares (2,710 ) — (2,710 ) Net income (loss) available to Arch common shareholders $ 719,625 $ (6,009 ) $ 713,616 Underwriting Ratios Loss ratio 68.9 % 67.1 % 6.9 % 52.6 % 76.2 % 55.2 % Acquisition expense ratio 15.9 % 16.8 % 10.0 % 14.6 % 21.7 % 15.4 % Other operating expense ratio 16.5 % 10.6 % 12.0 % 13.8 % 6.5 % 13.0 % Combined ratio 101.3 % 94.5 % 28.9 % 81.0 % 104.4 % 83.6 % Goodwill and intangible assets $ 114,012 $ — $ 513,258 $ 627,270 $ 7,650 $ 634,920 Total investable assets $ 19,566,861 $ 2,757,663 $ 22,324,524 Total assets 28,845,473 3,372,856 32,218,329 Total liabilities 19,518,395 2,262,255 21,780,650 (1) Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total. Year Ended December 31, 2017 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 3,081,086 $ 1,640,399 $ 1,368,138 $ 6,088,254 $ 600,304 $ 6,368,425 Premiums ceded (958,646 ) (465,925 ) (256,796 ) (1,679,998 ) (47,187 ) (1,407,052 ) Net premiums written 2,122,440 1,174,474 1,111,342 4,408,256 553,117 4,961,373 Change in unearned premiums (9,422 ) (31,853 ) (54,176 ) (95,451 ) (21,390 ) (116,841 ) Net premiums earned 2,113,018 1,142,621 1,057,166 4,312,805 531,727 4,844,532 Other underwriting income — 11,336 15,737 27,073 3,180 30,253 Losses and loss adjustment expenses (1,622,444 ) (773,923 ) (134,677 ) (2,531,044 ) (436,402 ) (2,967,446 ) Acquisition expenses, net (323,639 ) (221,250 ) (100,598 ) (645,487 ) (129,971 ) (775,458 ) Other operating expenses (359,524 ) (146,663 ) (146,336 ) (652,523 ) (31,928 ) (684,451 ) Underwriting income (loss) $ (192,589 ) $ 12,121 $ 691,292 510,824 (63,394 ) 447,430 Net investment income 382,072 88,800 470,872 Net realized gains (losses) 148,798 343 149,141 Net impairment losses recognized in earnings (7,138 ) — (7,138 ) Equity in net income (loss) of investments accounted for using the equity method 142,286 — 142,286 Other income (loss) (2,571 ) — (2,571 ) Corporate expenses (61,602 ) — (61,602 ) Transaction costs and other (22,150 ) — (22,150 ) Amortization of intangible assets (125,778 ) — (125,778 ) Interest expense (103,592 ) (13,839 ) (117,431 ) Net foreign exchange gains (losses) (113,345 ) (2,437 ) (115,782 ) Income (loss) before income taxes 747,804 9,473 757,277 Income tax benefit (127,547 ) (21 ) (127,568 ) Net income 620,257 9,452 629,709 Dividends attributable to redeemable noncontrolling interests — (18,344 ) (18,344 ) Amounts attributable to nonredeemable noncontrolling interests — 7,913 7,913 Net income (loss) available to Arch 620,257 (979 ) 619,278 Preferred dividends (46,041 ) — (46,041 ) Loss on redemption of preferred shares (6,735 ) — (6,735 ) Net income (loss) available to Arch common shareholders $ 567,481 $ (979 ) $ 566,502 Underwriting Ratios Loss ratio 76.8 % 67.7 % 12.7 % 58.7 % 82.1 % 61.3 % Acquisition expense ratio 15.3 % 19.4 % 9.5 % 15.0 % 24.4 % 16.0 % Other operating expense ratio 17.0 % 12.8 % 13.8 % 15.1 % 6.0 % 14.1 % Combined ratio 109.1 % 99.9 % 36.0 % 88.8 % 112.5 % 91.4 % Goodwill and intangible assets $ 22,310 $ 211 $ 622,440 $ 644,961 $ 7,650 $ 652,611 Total investable assets $ 19,716,421 $ 2,440,067 $ 22,156,488 Total assets 29,037,004 3,014,654 32,051,658 Total liabilities 19,959,574 1,846,149 21,805,723 (1) Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.
Summary of information regarding net premiums written and earned by major line of business and net premiums written by location	The following tables provide summary information regarding net premiums earned by major line of business and net premiums written by underwriting location: INSURANCE SEGMENT Year Ended December 31, 2019 2018 2017 Net premiums earned (1) Professional lines (2) $ 499,224 $ 458,425 $ 444,137 Programs 414,103 389,186 364,639 Property, energy, marine and aviation 298,966 205,069 173,779 Construction and national accounts 325,687 322,440 324,517 Travel, accident and health 305,085 297,147 257,358 Excess and surplus casualty (3) 200,615 172,424 195,154 Lenders products 66,079 94,248 97,043 Other (4) 287,321 266,722 256,391 Total $ 2,397,080 $ 2,205,661 $ 2,113,018 Net premiums written by underwriting location (1) United States $ 1,983,476 $ 1,736,651 $ 1,715,467 Europe 559,214 401,974 344,836 Other 99,036 73,500 62,137 Total $ 2,641,726 $ 2,212,125 $ 2,122,440 (1) Insurance segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions. (2) Includes professional liability, executive assurance and healthcare business. (3) Includes casualty and contract binding business. (4) Includes alternative markets, excess workers' compensation and surety business. REINSURANCE SEGMENT Year Ended December 31, 2019 2018 2017 Net premiums earned (1) Other specialty (2) $ 478,517 $ 474,568 $ 408,566 Casualty (3) 429,288 347,034 341,122 Property excluding property catastrophe 362,841 287,788 255,453 Property catastrophe 90,934 75,249 73,300 Marine and aviation 48,274 39,238 36,214 Other (4) 56,535 37,339 27,966 Total $ 1,466,389 $ 1,261,216 $ 1,142,621 Net premiums written by underwriting location (1) United States $ 529,943 $ 413,550 $ 399,379 Bermuda 578,618 487,523 350,681 Europe and other 494,162 471,499 424,414 Total $ 1,602,723 $ 1,372,572 $ 1,174,474 (1) Reinsurance segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions. (2) Includes proportional motor, surety, accident and health, workers’ compensation catastrophe, agriculture, trade credit and other. (3) Includes executive assurance, professional liability, workers’ compensation, excess motor, healthcare and other. (4) Includes life, casualty clash and other. MORTGAGE SEGMENT Year Ended December 31, 2019 2018 2017 Net premiums earned by underwriting location United States $ 1,134,849 $ 1,009,765 $ 901,858 Other 231,491 176,471 155,308 Total $ 1,366,340 $ 1,186,236 $ 1,057,166 Net premiums written by underwriting location United States $ 1,032,868 $ 948,323 $ 903,329 Other 228,888 209,552 208,013 Total $ 1,261,756 $ 1,157,875 $ 1,111,342 OTHER SEGMENT Year Ended December 31, 2019 2018 2017 Net premiums earned (1) Casualty (2) $ 246,894 $ 277,589 $ 333,275 Other specialty (3) 185,547 204,485 135,855 Property catastrophe 13,399 10,998 12,690 Property excluding property catastrophe 3,503 2,802 1,392 Other (4) 107,346 82,988 48,515 Total $ 556,689 $ 578,862 $ 531,727 Net premiums written by underwriting location (1) United States $ 127,176 $ 49,800 $ 11,750 Europe 52,065 91,635 91,463 Bermuda 353,621 462,740 449,904 Total $ 532,862 $ 604,175 $ 553,117 (1) Other segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions. (2) Includes professional liability, excess motor, programs and other. (3) Includes proportional motor and other. (4) Includes mortgage and other.

Reserve for Losses and Loss A_2

Reserve for Losses and Loss Adjustment Expenses (Tables)	12 Months Ended
	Dec. 31, 2019
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]
Analysis of losses and loss adjustment expenses and reconciliation of beginning and ending reserve balances	The following table represents an analysis of losses and loss adjustment expenses and a reconciliation of the beginning and ending reserve for losses and loss adjustment expenses: Year Ended December 31, 2019 2018 2017 Reserve for losses and loss adjustment expenses at beginning of year $ 11,853,297 $ 11,383,792 $ 10,200,960 Unpaid losses and loss adjustment expenses recoverable 2,814,291 2,464,910 2,083,575 Net reserve for losses and loss adjustment expenses at beginning of year 9,039,006 8,918,882 8,117,385 Net incurred losses and loss adjustment expenses relating to losses occurring in: Current year 3,297,037 3,162,818 3,205,428 Prior years (163,585 ) (272,712 ) (237,982 ) Total net incurred losses and loss adjustment expenses 3,133,452 2,890,106 2,967,446 Net losses and loss adjustment expense reserves of acquired business (1) 209,486 — — Retroactive reinsurance transactions (2) (225,500 ) (420,404 ) — Foreign exchange (gains) losses 36,003 (143,414 ) 186,963 Net paid losses and loss adjustment expenses relating to losses occurring in: Current year (621,202 ) (524,048 ) (505,424 ) Prior years (1,762,053 ) (1,682,116 ) (1,847,488 ) Total net paid losses and loss adjustment expenses (2,383,255 ) (2,206,164 ) (2,352,912 ) Net reserve for losses and loss adjustment expenses at end of year 9,809,192 9,039,006 8,918,882 Unpaid losses and loss adjustment expenses recoverable 4,082,650 2,814,291 2,464,910 Reserve for losses and loss adjustment expenses at end of year $ 13,891,842 $ 11,853,297 $ 11,383,792 (1) The 2019 amount primarily related to the acquisition of Barbican. (2) During the 2019 first quarter and 2018 second quarter, a subsidiary of the Company entered into two separate retroactive reinsurance transactions with third party reinsurers to reinsure run-off liabilities associated with certain U.S. insurance exposures.

Short Duration Contracts (Table

Short Duration Contracts (Tables)	12 Months Ended
	Dec. 31, 2019
Short Duration Contracts Disclosure [Abstract]
Levels of disaggregation	The Company’s reserves for losses and loss adjustment expenses primarily relate to short-duration contracts with various characteristics ( e.g. , type of coverage, geography, claims duration). The Company considered such information in determining the level of disaggregation for disclosures related to its short-duration contracts, as detailed in the table below: Reportable segment Level of disaggregation Included lines of business Insurance Property energy, marine and aviation Property energy, marine and aviation Third party occurrence business Excess and surplus casualty (excluding contract binding); construction and national accounts; and other (including alternative market risks, excess workers’ compensation and employer’s liability insurance coverages) Third party claims-made business Professional lines Multi-line and other specialty Programs; contract binding (part of excess and surplus casualty); travel, accident and health; lenders products; and other (c ontract and commercial surety coverages) Reinsurance Casualty Casualty Property catastrophe Property catastrophe Property excluding property catastrophe Property excluding property catastrophe Marine and aviation Marine and aviation Other specialty Other specialty Mortgage Direct mortgage insurance in the U.S. Mortgage insurance on U.S. primary exposures
Claims Development [Line Items]
Reconciliation of claims development to liability	The following table represents a reconciliation of the disclosures of net incurred and paid loss development tables to the reserve for losses and loss adjustment expenses at December 31, 2019 : December 31, 2019 Net outstanding liabilities Insurance Property, energy, marine and aviation $ 340,714 Third party occurrence business 2,264,839 Third party claims-made business 1,225,121 Multi-line and other specialty 887,227 Reinsurance Casualty 1,707,696 Property catastrophe 113,053 Property excluding property catastrophe 458,581 Marine and aviation 131,895 Other specialty 637,789 Mortgage U.S. primary 255,238 Other short duration lines not included in disclosures (1) 1,514,373 Total for short duration lines 9,536,526 Unpaid losses and loss adjustment expenses recoverable Insurance Property, energy, marine and aviation 213,004 Third party occurrence business 1,105,669 Third party claims-made business 728,511 Multi-line and other specialty 189,613 Reinsurance Casualty 532,387 Property catastrophe 282,910 Property excluding property catastrophe 48,554 Marine and aviation 28,893 Other specialty 206,022 Mortgage U.S. primary 21,875 Other short duration lines not included in disclosures (2) 1,472,777 Intercompany eliminations (696,931 ) Total for short duration lines 4,133,284 Lines other than short duration 55,989 Discounting (22,012 ) Unallocated claims adjustment expenses 188,055 222,032 Total gross reserves for losses and loss adjustment expenses $ 13,891,842 (1) Includes net outstanding liabilities of $1.1 billion for the ‘other’ segment. (2) Includes unpaid loss and loss adjustment expenses recoverable related to the acquisition of Barbican and $319.3 million related to the loss portfolio transfer reinsurance agreement.
Insurance
Claims Development [Line Items]
Claims development tables	The following tables present information on the insurance segment’s short-duration insurance contracts: Property, energy, marine and aviation ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2019 Total of IBNR liabilities plus expected development on reported claims Cumulative number of reported claims Year ended December 31, Accident year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2010 $ 197,399 $ 187,305 $ 151,937 $ 139,757 $ 128,475 $ 128,799 $ 127,530 $ 124,974 $ 120,813 $ 118,570 $ 1,310 3,676 2011 266,725 269,790 229,244 217,753 208,494 205,344 198,763 198,956 198,370 868 4,219 2012 230,399 229,820 203,408 197,187 194,746 190,930 188,649 178,394 2,487 4,266 2013 156,936 154,313 146,777 140,967 132,839 132,211 128,247 752 4,279 2014 146,391 143,825 145,065 134,055 133,482 129,973 6,769 3,930 2015 110,867 108,260 102,535 102,221 97,361 5,669 4,613 2016 102,910 99,899 104,246 100,542 560 6,388 2017 278,549 247,072 235,152 14,830 6,744 2018 185,486 179,262 29,117 5,333 2019 161,850 59,863 5,688 Total $ 1,527,721 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2010 $ 28,433 $ 65,846 $ 87,476 $ 105,887 $ 110,892 $ 117,737 $ 119,953 $ 118,437 $ 119,276 $ 116,822 2011 34,002 98,616 140,555 165,950 198,128 199,943 195,613 196,272 196,056 2012 20,301 92,034 137,179 159,862 165,488 177,945 179,138 173,058 2013 31,874 83,689 109,088 118,131 120,385 123,392 123,696 2014 25,620 53,060 76,774 83,080 86,518 99,041 2015 23,271 63,990 75,340 84,964 88,433 2016 24,442 82,357 97,147 97,674 2017 29,915 138,525 196,290 2018 29,641 102,798 2019 26,014 Total 1,219,882 All outstanding liabilities before 2010, net of reinsurance 32,875 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 340,714 Third party occurrence business ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2019 Total of IBNR liabilities plus expected development on reported claims Cumulative number of reported claims Year ended December 31, Accident year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2010 $ 217,431 $ 235,241 $ 230,710 $ 230,859 $ 233,204 $ 229,534 $ 223,618 $ 215,332 $ 218,374 $ 211,046 $ 33,176 62,757 2011 233,958 240,406 253,691 258,348 252,227 253,598 246,721 239,395 233,563 44,601 71,101 2012 240,917 262,373 267,980 270,603 257,059 252,497 242,648 242,454 60,258 65,806 2013 282,629 296,492 306,358 301,403 281,437 275,101 271,116 74,749 66,990 2014 329,448 335,281 338,194 342,455 340,408 341,595 98,049 75,526 2015 358,478 391,198 398,185 394,268 388,744 146,656 77,727 2016 389,333 393,991 406,785 397,914 193,182 77,100 2017 416,856 419,456 421,414 254,057 82,458 2018 434,854 450,950 315,814 74,221 2019 454,723 390,054 62,988 Total $ 3,413,519 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2010 $ 6,753 $ 25,511 $ 45,550 $ 72,696 $ 102,391 $ 117,250 $ 132,818 $ 142,380 $ 148,140 $ 158,370 2011 7,006 25,142 43,309 73,268 113,283 134,342 152,472 160,326 171,744 2012 6,962 30,799 58,387 83,193 108,087 129,369 142,932 153,263 2013 6,842 29,214 71,328 101,148 122,043 148,951 162,910 2014 9,204 40,232 71,397 112,434 161,780 188,871 2015 11,112 44,522 88,383 139,283 179,435 2016 11,684 41,893 87,424 135,617 2017 13,392 52,283 99,225 2018 16,994 62,762 2019 18,202 Total 1,330,399 All outstanding liabilities before 2010, net of reinsurance 181,719 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 2,264,839 Third party claims-made business ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2019 Total of IBNR liabilities plus expected development on reported claims Cumulative number of reported claims Year ended December 31, Accident year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2010 $ 286,202 $ 311,709 $ 332,779 $ 338,238 $ 331,006 $ 314,388 $ 298,444 $ 280,497 $ 283,530 $ 284,427 $ 8,775 12,335 2011 281,448 323,369 314,961 309,684 315,118 294,367 281,487 284,242 279,909 14,003 11,762 2012 309,654 312,143 310,359 305,362 283,903 268,765 271,663 272,826 17,820 14,759 2013 295,759 313,601 317,165 313,738 288,506 286,280 271,290 29,604 14,542 2014 260,698 275,172 293,467 273,876 278,182 287,424 42,805 13,935 2015 254,540 272,413 271,343 257,902 246,366 43,026 13,815 2016 270,537 286,677 306,837 304,266 81,707 15,716 2017 266,526 284,875 300,710 131,795 15,904 2018 272,655 301,247 177,552 14,934 2019 271,824 224,119 9,698 Total $ 2,820,289 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2010 $ 13,811 $ 70,583 $ 127,531 $ 162,490 $ 197,142 $ 213,530 $ 229,824 $ 233,085 $ 241,887 $ 252,119 2011 13,510 71,038 128,011 171,354 204,215 223,458 235,181 248,524 259,416 2012 17,307 67,314 117,891 160,480 185,656 204,240 221,391 240,281 2013 18,557 85,442 134,509 175,328 193,704 212,488 230,377 2014 13,572 62,308 127,683 170,331 204,330 223,907 2015 8,845 51,064 98,371 124,381 168,664 2016 10,371 67,446 125,740 156,030 2017 9,180 66,582 111,532 2018 12,123 67,567 2019 11,443 Total 1,721,336 All outstanding liabilities before 2010, net of reinsurance 126,168 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 1,225,121 Multi-line and other specialty ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2019 Total of IBNR liabilities plus expected development on reported claims Cumulative number of reported claims Year ended December 31, Accident year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2010 $ 173,984 $ 176,796 $ 169,307 $ 166,892 $ 158,092 $ 154,716 $ 153,526 $ 153,598 $ 151,951 $ 150,342 $ 2,508 37,891 2011 182,372 187,924 182,213 175,794 171,923 171,691 168,243 169,851 169,467 3,097 44,881 2012 252,699 263,326 257,420 255,055 254,155 246,077 246,482 243,042 4,255 55,403 2013 263,349 271,603 262,837 263,097 251,187 252,713 247,659 7,096 71,701 2014 300,962 324,736 317,210 317,161 316,047 312,400 11,578 109,295 2015 333,519 356,543 355,484 363,627 355,095 17,097 147,950 2016 406,309 428,530 425,281 413,668 25,881 173,735 2017 479,694 498,860 488,276 46,435 217,360 2018 573,827 621,724 123,652 243,725 2019 604,356 299,028 169,915 Total $ 3,606,029 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2010 $ 49,906 $ 91,265 $ 111,143 $ 125,897 $ 135,981 $ 140,372 $ 143,459 $ 146,357 $ 146,482 $ 146,413 2011 51,145 102,910 117,372 136,078 147,466 151,126 156,619 158,902 161,887 2012 78,178 165,305 189,330 208,372 222,024 230,929 232,064 235,461 2013 86,403 150,432 179,785 212,713 224,665 233,572 235,784 2014 107,529 196,081 232,950 265,927 279,950 290,702 2015 137,561 235,193 276,608 304,464 319,788 2016 174,366 302,470 339,125 360,602 2017 179,777 339,753 378,500 2018 213,065 399,443 2019 213,559 Total 2,742,139 All outstanding liabilities before 2010, net of reinsurance 23,337 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 887,227
Percentage annual payout by age	The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2019 : Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Property, energy, marine and aviation 19.1 % 39.1 % 19.2 % 9.1 % 5.3 % 5.1 % 0.1 % (1.5 )% 0.3 % (2.1 )% Third party occurrence business 3.1 % 8.8 % 10.9 % 12.0 % 12.3 % 8.5 % 6.5 % 4.1 % 3.8 % 4.8 % Third party claims-made business 4.6 % 19.3 % 19.1 % 13.4 % 11.6 % 6.6 % 5.7 % 4.3 % 3.5 % 3.6 % Multi-line and other specialty 35.2 % 29.9 % 10.5 % 9.4 % 5.4 % 3.2 % 1.7 % 1.6 % 0.9 % — %
Reinsurance
Claims Development [Line Items]
Claims development tables	The following tables present information on the reinsurance segment’s short-duration insurance contracts: Casualty ($000’s) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2019 Total of IBNR liabilities plus expected development on reported claims Cumulative number of reported claims Year ended December 31, Accident year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2010 $ 189,406 $ 190,639 $ 193,935 $ 185,429 $ 175,107 $ 164,530 $ 158,797 $ 154,969 $ 149,360 $ 145,012 $ 22,988 N/A 2011 149,186 152,793 146,786 141,854 137,580 134,486 128,535 125,712 127,056 23,269 N/A 2012 142,523 140,694 136,540 124,626 114,660 109,376 118,026 121,306 32,311 N/A 2013 165,465 158,693 154,478 148,223 136,163 134,615 130,954 39,769 N/A 2014 216,073 221,252 218,392 232,303 228,802 238,510 52,506 N/A 2015 222,008 220,835 229,481 236,743 240,762 65,978 N/A 2016 213,803 226,214 249,540 264,406 73,050 N/A 2017 264,219 250,550 265,751 78,119 N/A 2018 278,129 292,526 167,212 N/A 2019 326,258 254,304 N/A Total $ 2,152,541 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2010 $ 2,135 $ 20,781 $ 37,608 $ 51,467 $ 69,362 $ 79,732 $ 90,611 $ 98,414 $ 106,944 $ 108,584 2011 2,300 11,403 21,541 38,315 54,298 63,712 70,578 75,747 81,596 2012 1,294 8,458 14,648 25,468 36,497 47,732 59,423 69,776 2013 2,466 9,902 22,998 43,009 54,496 63,035 70,674 2014 3,912 16,038 40,763 63,376 90,965 114,226 2015 4,457 20,254 47,198 70,956 96,592 2016 5,735 25,643 51,641 86,681 2017 6,425 29,376 59,262 2018 7,579 31,572 2019 16,101 Total 735,064 All outstanding liabilities before 2010, net of reinsurance 290,219 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 1,707,696 Property catastrophe ($000’s) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2019 Total of IBNR liabilities plus expected development on reported claims Cumulative number of reported claims Year ended December 31, Accident year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2010 $ 92,632 $ 47,218 $ 38,916 $ 38,823 $ 42,333 $ 42,732 $ 42,535 $ 42,738 $ 42,544 $ 43,500 $ — N/A 2011 203,903 183,897 165,402 152,784 148,956 148,230 146,028 141,950 140,905 — N/A 2012 149,918 122,948 108,624 102,158 99,931 99,118 97,084 97,192 164 N/A 2013 66,695 47,409 36,133 31,664 29,119 28,400 27,532 (125 ) N/A 2014 44,896 30,625 25,114 22,263 20,527 19,822 (10 ) N/A 2015 32,159 16,787 10,497 4,546 2,715 184 N/A 2016 23,411 16,786 13,044 9,370 639 N/A 2017 78,418 45,467 42,594 (3,620 ) N/A 2018 72,769 59,033 4,671 N/A 2019 43,497 15,329 N/A Total $ 486,160 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2010 $ 8,464 $ 23,406 $ 31,371 $ 37,332 $ 38,527 $ 40,092 $ 41,357 $ 41,411 $ 41,593 $ 41,901 2011 59,545 82,065 113,275 127,960 133,439 135,928 137,967 138,355 138,911 2012 25,850 70,836 83,869 90,774 92,933 94,062 94,672 95,359 2013 12,126 19,095 23,872 25,704 27,450 27,690 27,694 2014 13,657 19,823 18,280 19,108 18,699 18,892 2015 (3,689 ) (3,422 ) 784 1,044 569 2016 (7,324 ) 1,331 1,593 2,778 2017 28,735 27,463 31,558 2018 25,481 11,872 2019 3,903 Total 373,437 All outstanding liabilities before 2010, net of reinsurance 330 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 113,053 Property excluding property catastrophe ($000’s) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2019 Total of IBNR liabilities plus expected development on reported claims Cumulative number of reported claims Year ended December 31, Accident year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2010 $ 142,466 $ 128,147 $ 117,919 $ 112,249 $ 110,319 $ 108,188 $ 104,403 $ 101,224 $ 100,442 $ 99,299 $ 821 N/A 2011 206,803 179,479 166,987 163,262 159,117 157,811 155,539 154,519 153,198 1,531 N/A 2012 156,087 121,698 123,613 119,040 114,617 112,398 110,927 108,374 850 N/A 2013 115,375 76,856 70,499 66,121 64,397 63,616 62,423 787 N/A 2014 143,307 117,304 99,198 90,708 88,436 84,134 3,430 N/A 2015 213,740 188,293 183,977 188,219 187,493 13,082 N/A 2016 176,017 145,251 137,493 136,298 19,522 N/A 2017 256,757 239,608 226,555 21,691 N/A 2018 222,345 240,094 31,217 N/A 2019 213,206 94,880 N/A Total $ 1,511,074 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2010 $ 37,776 $ 76,429 $ 88,196 $ 93,354 $ 95,571 $ 96,718 $ 97,363 $ 97,793 $ 97,733 $ 97,842 2011 47,605 121,234 141,120 145,621 147,675 148,777 149,019 149,291 150,305 2012 26,109 77,957 93,165 101,831 102,801 103,435 102,612 102,552 2013 25,955 42,669 49,753 52,931 53,730 55,609 61,118 2014 23,500 62,790 71,691 76,632 78,271 78,659 2015 75,325 118,655 149,122 160,029 165,186 2016 33,282 94,875 98,708 104,085 2017 25,258 116,304 145,172 2018 29,478 107,496 2019 45,380 Total 1,057,795 All outstanding liabilities before 2010, net of reinsurance 5,302 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 458,581 Marine and aviation ($000’s) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2019 Total of IBNR liabilities plus expected development on reported claims Cumulative number of reported claims Year ended December 31, Accident year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2010 $ 40,973 $ 42,297 $ 38,520 $ 35,428 $ 33,524 $ 31,910 $ 31,160 $ 30,331 $ 28,521 $ 28,347 $ 32 N/A 2011 39,323 32,910 35,848 32,405 28,785 27,188 27,253 24,863 23,783 1,541 N/A 2012 59,013 58,857 55,027 52,261 51,053 49,697 46,019 43,000 4,052 N/A 2013 39,025 37,841 36,796 35,364 35,265 34,528 34,084 8,204 N/A 2014 30,949 29,140 27,334 25,633 23,635 23,270 6,819 N/A 2015 33,831 37,614 31,831 31,770 30,822 5,769 N/A 2016 27,366 22,752 23,569 19,279 10,917 N/A 2017 28,796 26,342 23,806 10,283 N/A 2018 28,164 26,206 13,754 N/A 2019 39,801 23,090 N/A Total $ 292,398 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2010 $ 8,523 $ 13,402 $ 16,752 $ 18,478 $ 20,220 $ 26,535 $ 27,182 $ 27,544 $ 27,119 $ 27,118 2011 4,420 12,121 16,529 19,231 15,952 16,626 21,979 21,903 21,965 2012 2,657 11,434 27,518 33,294 35,033 36,232 37,719 38,010 2013 4,932 13,845 18,511 21,500 22,510 23,778 24,155 2014 4,151 7,946 11,538 12,410 14,583 15,016 2015 5 13,436 19,052 20,888 22,663 2016 (7,317 ) (1,676 ) 523 3,258 2017 1,657 6,516 9,339 2018 2,001 7,015 2019 9,074 Total 177,613 All outstanding liabilities before 2010, net of reinsurance 17,110 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 131,895 Other specialty ($000’s) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2019 Total of IBNR liabilities plus expected development on reported claims Cumulative number of reported claims Year ended December 31, Accident year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2010 $ 43,160 $ 32,881 $ 26,070 $ 23,827 $ 22,821 $ 22,461 $ 22,222 $ 21,990 $ 21,382 $ 21,171 $ 670 N/A 2011 112,256 97,229 93,206 91,553 89,670 88,313 87,708 85,812 86,232 2,679 N/A 2012 221,101 210,448 200,482 194,895 192,692 195,632 193,811 188,044 12,317 N/A 2013 251,978 225,620 215,711 212,088 213,089 210,698 210,201 15,212 N/A 2014 275,419 256,819 258,738 251,960 246,896 248,573 19,791 N/A 2015 210,183 201,558 199,726 196,972 197,337 24,609 N/A 2016 223,625 221,177 215,354 210,053 26,895 N/A 2017 275,721 265,098 255,873 44,453 N/A 2018 333,228 328,750 80,916 N/A 2019 372,747 170,179 N/A Total $ 2,118,981 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2010 $ 4,049 $ 13,424 $ 16,559 $ 17,584 $ 18,366 $ 18,943 $ 19,165 $ 19,783 $ 19,802 $ 19,818 2011 28,875 57,832 69,981 74,604 78,073 79,803 81,984 83,080 82,787 2012 45,128 120,600 143,106 154,202 161,902 166,066 170,374 172,137 2013 56,857 118,642 144,491 160,651 170,279 175,474 182,911 2014 68,948 146,900 182,625 195,903 202,401 213,450 2015 54,762 114,768 138,794 145,820 154,816 2016 64,928 138,782 162,836 174,625 2017 74,926 167,782 197,699 2018 74,550 208,755 2019 83,456 Total 1,490,454 All outstanding liabilities before 2010, net of reinsurance 9,262 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 637,789
Percentage annual payout by age	The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2019 : Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Casualty 2.2 % 7.5 % 9.7 % 11.4 % 10.8 % 8.0 % 7.1 % 6.0 % 5.2 % 1.1 % Property catastrophe 10.7 % 25.5 % 28.8 % 9.2 % (0.7 )% 1.7 % 1.2 % 0.4 % 0.4 % 0.7 % Property excluding property catastrophe 27.2 % 38.8 % 11.6 % 5.3 % 1.7 % 1.2 % 2.2 % 0.2 % 0.3 % 0.1 % Marine and aviation 8.7 % 25.0 % 17.3 % 9.1 % 2.4 % 6.7 % 7.3 % 0.5 % (0.6 )% — % Other specialty 26.4 % 35.7 % 12.9 % 5.5 % 3.9 % 2.8 % 2.4 % 1.7 % (0.1 )% 0.1 %
Mortgage
Claims Development [Line Items]
Claims development tables	The following table presents information on the mortgage segment’s short-duration insurance contracts: Direct mortgage insurance business in the U.S. ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2019 Total of IBNR liabilities plus expected development on reported claims Cumulative number of paid claims Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2012 520,835 480,592 475,317 469,238 467,296 459,467 458,065 456,286 46 15,052 2013 469,311 419,668 411,793 405,809 395,693 393,149 390,987 38 9,445 2014 316,095 297,151 279,434 266,027 265,992 261,091 68 6,250 2015 222,790 197,238 198,001 194,677 189,235 67 4,490 2016 183,556 170,532 148,715 140,608 111 3,334 2017 179,376 132,220 107,255 212 2,241 2018 132,318 96,357 616 1,006 2019 108,424 11,315 87 Total $ 1,750,243 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 (106,065 ) 186,605 327,605 395,695 426,024 441,577 448,151 452,348 2013 41,447 203,957 308,956 353,189 373,909 382,200 386,853 2014 20,099 129,159 201,925 233,879 247,038 254,175 2015 16,159 92,431 151,222 171,337 180,321 2016 11,462 72,201 113,357 127,286 2017 8,622 48,112 78,650 2018 3,966 31,478 2019 2,899 1,514,010 All outstanding liabilities before 2012, net of reinsurance 19,005 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 255,238
Percentage annual payout by age	The following table presents the average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance, as of December 31, 2019 : Average annual percentage payout of incurred losses and allocated loss adjustment expenses by age, net of reinsurance Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 U.S. Primary 3.3 % 42.3 % 29.1 % 11.8 % 5.4 % 2.8 % 1.3 % 0.9 %

Reinsurance (Tables)

Reinsurance (Tables)	12 Months Ended
	Dec. 31, 2019
Reinsurance Disclosures [Abstract]
Effects of reinsurance	The effects of reinsurance on the Company’s written and earned premiums and losses and loss adjustment expenses with unaffiliated reinsurers were as follows: Year Ended December 31, 2019 2018 2017 Premiums Written Direct $ 5,681,523 $ 4,838,902 $ 4,447,457 Assumed 2,457,437 2,122,102 1,920,968 Ceded (2,099,893 ) (1,614,257 ) (1,407,052 ) Net $ 6,039,067 $ 5,346,747 $ 4,961,373 Premiums Earned Direct $ 5,447,829 $ 4,799,842 $ 4,379,131 Assumed 2,337,950 1,988,038 1,856,573 Ceded (1,999,281 ) (1,555,905 ) (1,391,172 ) Net $ 5,786,498 $ 5,231,975 $ 4,844,532 Losses and Loss Adjustment Expenses Direct $ 2,953,072 $ 2,472,133 $ 2,568,327 Assumed 1,602,528 1,307,317 1,442,077 Ceded (1,422,148 ) (889,344 ) (1,042,958 ) Net $ 3,133,452 $ 2,890,106 $ 2,967,446
Summary of reinsurance recoverables on paid and unpaid losses	The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums) at December 31, 2019 and 2018 : December 31, 2019 2018 Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses $ 4,346,816 $ 2,919,372 % due from carriers with A.M. Best rating of “A-” or better 61.2 % 63.0 % % due from unrated fully collateralized reinsurers (1) 13.5 % 12.9 % % due from all other carriers with no A.M. Best rating (2) 25.3 % 24.1 % Largest balance due from any one carrier as % of total shareholders’ equity 1.7 % 2.7 % (1) Such amount is fully collateralized through reinsurance trusts. (2) Over 90% of such amount is collateralized through reinsurance trusts or letters of credit.
Coverage and retention	The following table summarizes the respective coverages and retentions at December 31, 2019 : Initial Coverage at Issuance Coverage at Dec. 31, 2019 First Layer Retention Bellemeade 2017-1 Ltd. (1) 368,114 216,429 165,652 Bellemeade 2018-1 Ltd. (2) 374,460 328,482 168,510 Bellemeade 2018-2 Ltd. (3) 653,278 437,009 352,258 Bellemeade 2018-3 Ltd. (4) 506,110 426,806 179,331 Bellemeade 2019-1 Ltd. (5) 341,790 257,358 208,046 Bellemeade 2019-2 Ltd. (6) 621,022 525,959 221,794 Bellemeade 2019-3 Ltd. (7) 700,920 656,523 232,093 Bellemeade 2019-4 Ltd. (8) 577,267 577,267 162,357 Total $ 4,142,961 $ 3,425,833 $ 1,690,041 (1) Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017. (2) Issued in April 2018, covering in-force policies issued between July 1, 2017 and December 31, 2017. (3) Issued in August 2018, covering in-force policies issued between April 1, 2013 and December 31, 2015. (4) Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018. (5) Issued in March 2019, covering in-force policies primarily issued between 2005 to 2008 under United Guaranty Residential Insurance Company (“UGRIC”); as well as policies issued through 2015 under both UGRIC and Arch Mortgage Insurance Company. (6) Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018. (7) Issued in July 2019, covering in-force policies issued in 2016. (8) Issued in October 2019, covering in-force policies issued between January 1, 2019 and June 30, 2019.

Investment Information (Tables)

Investment Information (Tables)	12 Months Ended
	Dec. 31, 2019
Disclosure Investment Information [Abstract]
Summary of fair value and cost or amortized cost of available for sale securities	The following table summarizes the fair value and cost or amortized cost of the Company’s securities classified as available for sale: Estimated Fair Value Gross Unrealized Gains Gross Unrealized Losses Cost or Amortized Cost OTTI Unrealized Losses (2) December 31, 2019 Fixed maturities (1): Corporate bonds $ 6,406,591 $ 191,889 $ (12,793 ) $ 6,227,495 $ — Mortgage backed securities 562,309 9,669 (931 ) 553,571 (6 ) Municipal bonds 881,926 24,628 (2,213 ) 859,511 — Commercial mortgage backed securities 733,108 14,951 (2,330 ) 720,487 — U.S. government and government agencies 4,916,592 36,600 (10,134 ) 4,890,126 — Non-U.S. government securities 2,078,757 48,549 (20,330 ) 2,050,538 — Asset backed securities 1,683,753 24,017 (4,724 ) 1,664,460 — Total 17,263,036 350,303 (53,455 ) 16,966,188 (6 ) Short-term investments 956,546 811 (1,548 ) 957,283 — Total $ 18,219,582 $ 351,114 $ (55,003 ) $ 17,923,471 $ (6 ) December 31, 2018 Fixed maturities (1): Corporate bonds $ 5,537,548 $ 14,476 $ (105,428 ) $ 5,628,500 $ (69 ) Mortgage backed securities 541,193 3,991 (3,216 ) 540,418 (6 ) Municipal bonds 1,013,395 5,380 (11,891 ) 1,019,906 — Commercial mortgage backed securities 729,442 2,650 (10,751 ) 737,543 — U.S. government and government agencies 3,758,698 27,189 (8,474 ) 3,739,983 — Non-U.S. government securities 1,771,338 14,477 (50,948 ) 1,807,809 — Asset backed securities 1,600,896 8,060 (14,798 ) 1,607,634 — Total 14,952,510 76,223 (205,506 ) 15,081,793 (75 ) Short-term investments 955,880 36 (394 ) 956,238 — Total $ 15,908,390 $ 76,259 $ (205,900 ) $ 16,038,031 $ (75 ) (1) In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.” (2) Represents the total OTTI recognized in accumulated other comprehensive income (“AOCI”). It does not include the change in fair value subsequent to the impairment measurement date. At December 31, 2019 and 2018, the net unrealized gain related to securities for which a non-credit OTTI was recognized in AOCI was nil .
Summary of available for sale securities in a continual unrealized loss position	The following table summarizes, for all available for sale securities in an unrealized loss position, the fair value and gross unrealized loss by length of time the security has been in a continual unrealized loss position: Less than 12 Months 12 Months or More Total Estimated Fair Value Gross Unrealized Losses Estimated Fair Value Gross Unrealized Losses Estimated Fair Value Gross Unrealized Losses December 31, 2019 Fixed maturities (1): Corporate bonds $ 675,131 $ (12,350 ) $ 37,671 $ (443 ) $ 712,802 $ (12,793 ) Mortgage backed securities 102,887 (927 ) 203 (4 ) 103,090 (931 ) Municipal bonds 220,296 (2,213 ) — — 220,296 (2,213 ) Commercial mortgage backed securities 147,290 (2,302 ) 2,683 (28 ) 149,973 (2,330 ) U.S. government and government agencies 1,373,127 (10,089 ) 32,058 (45 ) 1,405,185 (10,134 ) Non-U.S. government securities 1,224,243 (20,163 ) 37,610 (167 ) 1,261,853 (20,330 ) Asset backed securities 441,522 (3,334 ) 48,313 (1,390 ) 489,835 (4,724 ) Total 4,184,496 (51,378 ) 158,538 (2,077 ) 4,343,034 (53,455 ) Short-term investments 95,777 (1,548 ) — — 95,777 (1,548 ) Total $ 4,280,273 $ (52,926 ) $ 158,538 $ (2,077 ) $ 4,438,811 $ (55,003 ) December 31, 2018 Fixed maturities (1): Corporate bonds $ 2,983,195 $ (68,910 ) $ 1,234,865 $ (36,518 ) $ 4,218,060 $ (105,428 ) Mortgage backed securities 84,296 (695 ) 109,009 (2,521 ) 193,305 (3,216 ) Municipal bonds 233,081 (2,074 ) 408,155 (9,817 ) 641,236 (11,891 ) Commercial mortgage backed securities 223,341 (2,831 ) 193,956 (7,920 ) 417,297 (10,751 ) U.S. government and government agencies 635,049 (1,354 ) 391,102 (7,120 ) 1,026,151 (8,474 ) Non-U.S. government securities 1,028,340 (35,524 ) 389,671 (15,424 ) 1,418,011 (50,948 ) Asset backed securities 533,592 (8,832 ) 368,095 (5,966 ) 901,687 (14,798 ) Total 5,720,894 (120,220 ) 3,094,853 (85,286 ) 8,815,747 (205,506 ) Short-term investments 122,878 (394 ) — — 122,878 (394 ) Total $ 5,843,772 $ (120,614 ) $ 3,094,853 $ (85,286 ) $ 8,938,625 $ (205,900 ) (1) In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received and reinvested and included the fixed maturities pledged. See “—Securities Lending Agreements.”
Contractual maturities of the Company's fixed maturities and fixed maturities pledged under securities lending arrangements	December 31, 2019 December 31, 2018 Maturity Estimated Fair Value Amortized Cost Estimated Fair Value Amortized Cost Due in one year or less $ 428,659 $ 423,617 $ 276,682 $ 279,135 Due after one year through five years 10,126,403 9,996,206 8,666,297 8,738,944 Due after five years through 10 years 3,317,535 3,219,567 2,919,232 2,951,582 Due after 10 years 411,269 388,280 218,768 226,537 14,283,866 14,027,670 12,080,979 12,196,198 Mortgage backed securities 562,309 553,571 541,193 540,418 Commercial mortgage backed securities 733,108 720,487 729,442 737,543 Asset backed securities 1,683,753 1,664,460 1,600,896 1,607,634 Total (1) $ 17,263,036 $ 16,966,188 $ 14,952,510 $ 15,081,793 (1) In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received and reinvested and included the fixed maturities pledged. See “—Securities Lending Agreements.”
Summary of securities lending transactions accounted for as secured borrowings, with significant investment categories	The Company’s securities lending transactions were accounted for as secured borrowings with significant investment categories as follows: Remaining Contractual Maturity of the Agreements Overnight and Continuous Less than 30 Days 30-90 Days 90 Days or More Total December 31, 2019 U.S. government and government agencies $ 240,332 $ — $ 115,973 $ — $ 356,305 Corporate bonds 2,570 — — — 2,570 Equity securities 29,491 — — — 29,491 Total $ 272,393 $ — $ 115,973 $ — $ 388,366 Gross amount of recognized liabilities for securities lending in offsetting disclosure in Note 10 — Amounts related to securities lending not included in offsetting disclosure in Note 10 $ 388,366 December 31, 2018 U.S. government and government agencies $ 219,276 $ — $ 32,583 $ — $ 251,859 Corporate bonds 7,129 — — — 7,129 Equity securities 15,137 — — — 15,137 Total $ 241,542 $ — $ 32,583 $ — $ 274,125 Gross amount of recognized liabilities for securities lending in offsetting disclosure in Note 10 — Amounts related to securities lending not included in offsetting disclosure in Note 10 $ 274,125
Summary of other investments, including available for sale and fair value option components	The following table summarizes the Company’s other investments, which are included in investments accounted for using the fair value option, by strategy: December 31, 2019 2018 Term loan investments 1,326,018 1,282,287 Lending 602,841 524,112 Credit related funds 123,020 202,123 Energy 97,402 117,509 Investment grade fixed income 151,594 101,902 Infrastructure 61,786 45,371 Private equity 49,376 24,383 Real estate 17,279 14,252 Total $ 2,429,316 $ 2,311,939
Summary information for investments accounted for using the equity method	The following table summarizes the Company’s investments accounted for using the equity method, by strategy: December 31, 2019 2018 Credit related funds $ 428,437 $ 429,402 Equities 293,686 375,273 Real estate 246,851 232,647 Lending 202,690 125,041 Private equity 144,983 114,019 Infrastructure 235,033 113,748 Energy 108,716 103,661 Total $ 1,660,396 $ 1,493,791 In applying the equity method, investments are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of the net income or loss of the funds (which include changes in the fair value of the underlying securities in the funds). Such investments are generally recorded on a one to three month lag based on the availability of reports from the investment funds. A summary of financial information for the Company’s investment funds accounted for using the equity method is as follows: December 31, 2019 2018 Invested assets $ 26,383,370 $ 28,299,386 Total assets 28,039,181 29,833,681 Total liabilities 3,595,695 3,406,612 Net assets $ 24,443,486 $ 26,427,069 Year Ended December 31, 2019 2018 2017 Total revenues $ 164,669 $ 4,565,354 $ 3,867,874 Total expenses 528,762 1,135,602 782,773 Net income (loss) $ (364,093 ) $ 3,429,752 $ 3,085,101
Summary of assets and liabilities accounted for using the fair value option	The following table summarizes the Company’s assets which are accounted for using the fair value option: December 31, 2019 2018 Fixed maturities $ 754,452 $ 1,245,562 Other investments 2,429,316 2,311,939 Short-term investments 377,014 322,177 Equity securities 102,695 103,893 Investments accounted for using the fair value option $ 3,663,477 $ 3,983,571
Summary of investments in limited partnership interests where the Company has a variable interest	The following table summarizes investments in limited partnership interests where the Company has a variable interest by balance sheet item: December 31, 2019 2018 Investments accounted for using the equity method (1) $ 1,660,396 $ 1,493,791 Investments accounted for using the fair value option (2) 188,283 162,398 Total $ 1,848,679 $ 1,656,189 (1) Aggregate unfunded commitments were $1.36 billion at December 31, 2019 , compared to $1.22 billion at December 31, 2018 . (2) Aggregate unfunded commitments were $41.7 million at December 31, 2019 , compared to $117.5 million at December 31, 2018 .
Components of net investment income	The components of net investment income were derived from the following sources: Year Ended December 31, 2019 2018 2017 Fixed maturities $ 505,399 $ 470,912 $ 385,919 Term loans 98,949 87,926 86,017 Equity securities 15,857 13,154 11,752 Short-term investments 15,820 18,793 10,964 Other (1) 80,618 64,942 68,249 Gross investment income 716,643 655,727 562,901 Investment expenses (88,905 ) (92,094 ) (92,029 ) Net investment income $ 627,738 $ 563,633 $ 470,872 (1) Includes income distributions from investment funds and other items.
Summary of net realized gains (losses)	Net realized gains (losses) were as follows, excluding the other-than-temporary impairment provisions: Year Ended December 31, 2019 2018 2017 Available for sale securities: Gross gains on investment sales $ 235,655 $ 69,299 $ 286,415 Gross losses on investment sales (104,612 ) (223,123 ) (203,873 ) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities 41,910 (90,898 ) 29,451 Other investments (35,734 ) (90,778 ) 51,124 Equity securities 15,869 (5,984 ) 18,707 Short-term investments 3,801 (461 ) 272 Equity securities, at fair value (1): Net realized gains (losses) on securities sold 11,313 (40,117 ) — Net unrealized gains (losses) on equity securities still held at reporting date 97,768 (22,828 ) — Derivative instruments (2) 119,741 15,636 (7,356 ) Other (3) (19,348 ) (16,090 ) (25,599 ) Net realized gains (losses) $ 366,363 $ (405,344 ) $ 149,141 (1) Effective January 1, 2018, changes in fair value on equity securities are recorded through net income. (2) See Note 10 for information on the Company’s derivative instruments. (3) Includes the re-measurement of contingent consideration liability amounts.
Summary of OTTI recognized in earnings by asset class	The following table details the net impairment losses recognized in earnings by asset class: Year Ended December 31, 2019 2018 2017 Fixed maturities: Mortgage backed securities $ (915 ) $ (437 ) $ (1,488 ) Corporate bonds (1,256 ) (1,232 ) (2,884 ) Non-U.S. government securities — (290 ) (376 ) Asset backed securities (994 ) (811 ) — U.S. government and government agencies — — (426 ) Municipal bonds — — (375 ) Total (3,165 ) (2,770 ) (5,549 ) Short-term investments — (59 ) — Equity securities — — (1,422 ) Other investments — — (167 ) Net impairment losses recognized in earnings $ (3,165 ) $ (2,829 ) $ (7,138 )
Rollforward of the amount related to credit losses recognized in earnings for which a portion was recognized in AOCI	The following table provides a roll forward of the amount related to credit losses recognized in earnings for which a portion of an OTTI was recognized in accumulated other comprehensive income: Year Ended December 31, 2019 2018 2017 Balance at start of year $ 637 $ 767 $ 13,138 Credit loss impairments recognized on securities not previously impaired — — 31 Credit loss impairments recognized on securities previously impaired — — 210 Reductions for increases in cash flows expected to be collected that are recognized over the remaining life of the security — — — Reductions for securities sold during the period (291 ) (130 ) (12,612 ) Balance at end of year $ 346 $ 637 $ 767
Summary of restricted assets	The following table details the value of the Company’s restricted assets: December 31, 2019 2018 Assets used for collateral or guarantees: Affiliated transactions $ 4,526,761 $ 4,623,483 Third party agreements 2,278,248 2,181,682 Deposits with U.S. regulatory authorities 797,371 689,114 Deposits with non-U.S. regulatory authorities 119,238 59,624 Total restricted assets $ 7,721,618 $ 7,553,903
Reconciliation of cash and restricted cash	The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets: December 31, 2019 2018 2017 Cash $ 726,230 $ 646,556 $ 606,199 Restricted cash (included in ‘other assets’) 177,468 78,087 121,085 Cash and restricted cash $ 903,698 $ 724,643 $ 727,284

Fair Value (Tables)

Fair Value (Tables)	12 Months Ended
	Dec. 31, 2019
Fair Value Disclosures [Abstract]
Fair value hierarchy	The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2019 : Fair Value Measurement Using: Estimated Fair Value Quoted Prices in Active Markets for Identical Assets (Level 1) Significant Other Observable Inputs (Level 2) Significant Unobservable Inputs (Level 3) Assets measured at fair value (1): Available for sale securities: Fixed maturities: Corporate bonds $ 6,406,591 $ — $ 6,397,740 $ 8,851 Mortgage backed securities 562,309 — 562,055 254 Municipal bonds 881,926 — 881,926 — Commercial mortgage backed securities 733,108 — 733,108 — U.S. government and government agencies 4,916,592 4,805,581 111,011 — Non-U.S. government securities 2,078,757 — 2,078,757 — Asset backed securities 1,683,753 — 1,678,791 4,962 Total 17,263,036 4,805,581 12,443,388 14,067 Short-term investments 956,546 904,804 51,742 — Equity securities, at fair value 850,283 789,596 4,798 55,889 Derivative instruments (4) 48,946 — 48,946 — Fair value option: Corporate bonds 488,402 — 487,470 932 Non-U.S. government bonds 50,465 — 50,465 — Mortgage backed securities 11,947 — 11,947 — Municipal bonds 377 — 377 — Commercial mortgage backed securities 1,134 — 1,134 — Asset backed securities 200,163 — 200,163 — U.S. government and government agencies 1,962 1,852 110 — Short-term investments 377,014 333,320 43,694 — Equity securities 102,697 43,962 641 58,094 Other investments 1,418,273 53,287 1,296,169 68,817 Other investments measured at net asset value (2) 1,011,043 Total 3,663,477 432,421 2,092,170 127,843 Total assets measured at fair value $ 22,782,288 $ 6,932,402 $ 14,641,044 $ 197,799 Liabilities measured at fair value: Contingent consideration liabilities $ (7,998 ) $ — $ — $ (7,998 ) Securities sold but not yet purchased (3) (66,257 ) — (66,257 ) — Derivative instruments (4) (39,750 ) — (39,750 ) — Total liabilities measured at fair value $ (114,005 ) $ — $ (106,007 ) $ (7,998 ) (1) In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See Note 8 . (2) In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets. (3) Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets. (4) See Note 10 . The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2018 : Fair Value Measurement Using: Estimated Fair Value Quoted Prices in Active Markets for Identical Assets (Level 1) Significant Other Observable Inputs (Level 2) Significant Unobservable Inputs (Level 3) Assets measured at fair value (1): Available for sale securities: Fixed maturities: Corporate bonds $ 5,537,548 $ — $ 5,529,407 $ 8,141 Mortgage backed securities 541,193 — 540,884 309 Municipal bonds 1,013,395 — 1,013,395 — Commercial mortgage backed securities 729,442 — 729,438 4 U.S. government and government agencies 3,758,698 3,657,181 101,517 — Non-U.S. government securities 1,771,338 — 1,771,338 — Asset backed securities 1,600,896 — 1,600,896 — Total 14,952,510 3,657,181 11,286,875 8,454 Equity securities 353,794 321,927 31,867 — Short-term investments 955,880 875,881 79,999 — Derivative instruments (4) 73,893 — 73,893 — Fair value option: Corporate bonds 852,585 — 846,827 5,758 Non-U.S. government bonds 79,066 — 79,066 — Mortgage backed securities 16,731 — 16,731 — Municipal bonds 7,144 — 7,144 — Commercial mortgage backed securities — — — — Asset backed securities 178,790 — 178,790 — U.S. government and government agencies 111,246 111,138 108 — Short-term investments 322,177 278,579 43,598 — Equity securities 103,893 48,827 55,066 — Other investments 1,254,220 39,107 1,152,408 62,705 Other investments measured at net asset value (2) 1,057,719 Total 3,983,571 477,651 2,379,738 68,463 Total assets measured at fair value $ 20,319,648 $ 5,332,640 $ 13,852,372 $ 76,917 Liabilities measured at fair value: Contingent consideration liabilities $ (66,665 ) $ — $ — $ (66,665 ) Securities sold but not yet purchased (3) (7,790 ) — (7,790 ) — Derivative instruments (4) (20,664 ) — (20,664 ) — Total liabilities measured at fair value $ (95,119 ) $ — $ (28,454 ) $ (66,665 ) (1) In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See Note 8 . (2) In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets. (3) Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets. (4) See Note 10 .
Rollforward of Level 3 investments	The following table presents a reconciliation of the beginning and ending balances for all financial assets and liabilities measured at fair value on a recurring basis using Level 3 inputs for 2019 and 2018 : Assets Liabilities Available For Sale Fair Value Option Fair Value Structured Securities (1) Corporate Bonds Corporate Bonds Other Investments Equity Securities Equity Securities Contingent Consideration Liabilities Year Ended December 31, 2019 Balance at beginning of year $ 313 $ 8,141 $ 5,758 $ 62,705 $ — $ — $ (66,665 ) Total gains or (losses) (realized/unrealized) Included in earnings (2) 1,760 2 (162 ) (8,119 ) 1,949 (3,418 ) (1,478 ) Included in other comprehensive income 3 (267 ) — — — — — Purchases, issuances, sales and settlements Purchases — 881 — 3,746 — 36,077 — Issuances — — — — — — (548 ) Sales (1,757 ) — (28,583 ) (20,495 ) — (27,982 ) — Settlements (552 ) (1,766 ) — (600 ) — — 60,693 Transfers in and/or out of Level 3 5,449 1,860 23,919 31,580 56,145 51,212 — Balance at end of year $ 5,216 $ 8,851 $ 932 $ 68,817 $ 58,094 $ 55,889 $ (7,998 ) Year Ended December 31, 2018 Balance at beginning of year $ 5,927 $ 9,460 $ 12,217 $ 59,167 $ — $ — $ (60,996 ) Total gains or (losses) (realized/unrealized) Included in earnings (2) 4 (1 ) (334 ) (1,416 ) — — (5,669 ) Included in other comprehensive income (11 ) (296 ) — — — — — Purchases, issuances, sales and settlements Purchases — 802 — 6,250 — — — Issuances — — — — — — — Sales (5,003 ) — — (296 ) — — — Settlements (604 ) (1,824 ) (6,125 ) (1,000 ) — — — Transfers in and/or out of Level 3 — — — — — — — Balance at end of year $ 313 $ 8,141 $ 5,758 $ 62,705 $ — $ — $ (66,665 ) (1) Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities. (2) Gains or losses were included in net realized gains (losses).

Derivative Instruments (Tables)

Derivative Instruments (Tables)	12 Months Ended
	Dec. 31, 2019
Derivative Instruments and Hedging Activities Disclosure [Abstract]
Fair value and notional amount of derivatives	The following table summarizes information on the fair values and notional values of the Company’s derivative instruments: Estimated Fair Value Asset Liability Derivatives Notional Value (1) December 31, 2019 Futures contracts (2) $ 10,065 $ (13,722 ) $ 4,104,559 Foreign currency forward contracts (2) 5,352 (5,327 ) 686,878 TBAs (3) 55,010 — 53,229 Other (2) 33,529 (20,701 ) 4,356,300 Total $ 103,956 $ (39,750 ) December 31, 2018 Futures contracts (2) $ 51,800 $ (2,115 ) $ 3,153,518 Foreign currency forward contracts (2) 8,147 (7,796 ) 1,008,907 TBAs (3) 8,292 — 8,132 Other (2) 13,946 (10,753 ) 2,213,981 Total $ 82,185 $ (20,664 ) (1) Represents the absolute notional value of all outstanding contracts, consisting of long and short positions. (2) The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’ Such amounts include risk in force on GSE credit-risk sharing transactions that are accounted for as derivatives. (3) The fair value of TBAs are included in ‘fixed maturities available for sale, at fair value.’
Summary of net realized gains (losses) recorded in the consolidated statements of income	All realized and unrealized contract gains and losses on the Company’s derivative instruments are reflected in net realized gains (losses) in the consolidated statements of income, as summarized in the following table: Derivatives not designated as hedging instruments Year Ended December 31, 2019 2018 2017 Net realized gains (losses): Futures contracts $ 114,123 $ 48,443 $ 9,318 Foreign currency forward contracts (9,499 ) (21,770 ) (14,495 ) TBAs 463 (133 ) 9 Other 14,654 (10,904 ) (2,188 ) Total $ 119,741 $ 15,636 $ (7,356 )

Variable Interest Entity and _2

Variable Interest Entity and Noncontrolling Interests (Tables)	12 Months Ended
	Dec. 31, 2019
Variable Interest Entity and Noncontrolling Interest Disclosure [Abstract]
Carrying amount of assets and liabilities of consolidated VIE	The following table provides the carrying amount and balance sheet caption in which the assets and liabilities of Watford are reported: December 31, 2019 2018 Assets Investments accounted for using the fair value option $ 1,898,091 $ 2,312,003 Fixed maturities available for sale, at fair value 745,708 393,351 Equity securities, at fair value 65,338 32,206 Cash 102,437 63,529 Accrued investment income 14,025 19,461 Premiums receivable 273,657 227,301 Reinsurance recoverable on unpaid and paid losses and LAE 170,973 86,445 Ceded unearned premiums 132,577 61,587 Deferred acquisition costs, net 64,044 80,858 Receivable for securities sold 16,287 24,507 Goodwill and intangible assets 7,650 7,650 Other assets 60,070 63,959 Total assets of consolidated VIE $ 3,550,857 $ 3,372,857 Liabilities Reserves for losses and loss adjustment expenses $ 1,263,628 $ 1,032,760 Unearned premiums 438,907 390,114 Reinsurance balances payable 77,066 21,034 Revolving credit agreement borrowings 484,287 455,682 Senior notes 172,418 — Payable for securities purchased 18,180 60,142 Other liabilities 171,714 302,524 Total liabilities of consolidated VIE $ 2,626,200 $ 2,262,256 Redeemable noncontrolling interests $ 52,305 $ 220,992
Summary of VIE cash flows	The following table summarizes Watford’s cash flow from operating, investing and financing activities. Year Ended December 31, 2019 2018 2017 Total cash provided by (used for): Operating activities 239,284 229,315 286,558 Investing activities (140,620 ) (285,281 ) (467,418 ) Financing activities (61,433 ) (2,406 ) 162,152
Activity in non-redeemable noncontrolling interests	The following table sets forth activity in the non-redeemable noncontrolling interests: December 31, 2019 2018 Balance, beginning of year $ 791,560 $ 843,411 Additional paid in capital attributable to non-redeemable noncontrolling interests (2,929 ) — Repurchases attributable to non-redeemable noncontrolling interests (1) (75,056 ) — Amounts attributable to non-redeemable noncontrolling interests 40,072 (48,507 ) Other comprehensive (income) loss attributable to non-redeemable noncontrolling interests 9,130 (3,344 ) Balance, end of year $ 762,777 $ 791,560 (1) During 2019, Watford’s board of directors authorized the investment in Watford’s common shares through a share repurchase program.
Activity in redeemable noncontrolling interest	The following table sets forth activity in the redeemable noncontrolling interests: December 31, 2019 2018 2017 Balance, beginning of year $ 206,292 $ 205,922 $ 205,553 Redemption of redeemable noncontrolling interests (157,709 ) — — Accretion of preference share issuance costs 244 370 369 Other 6,577 — — Balance, end of year $ 55,404 $ 206,292 $ 205,922
Portion of income or loss attributable to noncontrolling interests	The portion of income or loss attributable to third party investors is recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests’ as summarized in the table below: December 31, 2019 2018 2017 Amounts attributable to non-redeemable noncontrolling interests $ (40,072 ) $ 48,507 $ 7,913 Dividends attributable to redeemable noncontrolling interests (16,909 ) (18,357 ) (18,344 ) Net (income) loss attributable to noncontrolling interests $ (56,981 ) $ 30,150 $ (10,431 )
Total assets and maximum loss exposure of VIE	Maximum Exposure to Loss Total VIE Assets On-Balance Sheet (Asset) Liabilities Off-Balance Sheet Total December 31, 2019 Bellemeade 2017-1 Ltd. (Oct-17) $ 216,429 $ (442 ) $ 2,794 $ 2,352 Bellemeade 2018-1 Ltd. (Apr-18) 328,482 (1,574 ) 5,757 4,183 Bellemeade 2018-2 Ltd. (Aug-18) 437,009 (877 ) 2,524 1,647 Bellemeade 2018-3 Ltd. (Oct-18) 426,806 (1,113 ) 3,937 2,824 Bellemeade 2019-1 Ltd. (Mar-19) 257,358 (226 ) 3,027 2,801 Bellemeade 2019-2 Ltd. (Apr-19) 525,959 (78 ) 2,579 2,501 Bellemeade 2019-3 Ltd. (Jul-19) 656,523 (585 ) 9,273 8,688 Bellemeade 2019-4 Ltd. (Oct-19) 577,267 (302 ) 12,193 11,891 Total $ 3,425,833 $ (5,197 ) $ 42,084 $ 36,887 December 31, 2018 Bellemeade 2015-1 Ltd. (Jul-15) $ 43,246 $ 112 $ 498 $ 610 Bellemeade 2017-1 Ltd. (Oct-17) 304,373 165 1,312 1,477 Bellemeade 2018-1 Ltd. (Apr-18) 374,460 132 3,539 3,671 Bellemeade 2018-2 Ltd. (Aug-18) 653,278 874 4,005 4,879 Bellemeade 2018-3 Ltd. (Oct-18) 506,110 469 1,836 2,305 Total $ 1,881,467 $ 1,752 $ 11,190 $ 12,942

Other Comprehensive Income (Tab

Other Comprehensive Income (Tables)	12 Months Ended
	Dec. 31, 2019
Comprehensive Income Note Disclosure [Abstract]
Schedule of changes in each component of AOCI	The following table presents the changes in each component of AOCI, net of noncontrolling interests: Unrealized Appreciation on Available-For-Sale Investments Foreign Currency Translation Adjustments Total Year Ended December 31, 2019 Beginning balance $ (114,178 ) $ (64,542 ) $ (178,720 ) Other comprehensive income (loss) before reclassifications 491,605 18,147 509,752 Amounts reclassified from accumulated other comprehensive income (118,941 ) — (118,941 ) Net current period other comprehensive income (loss) 372,664 18,147 390,811 Ending balance $ 258,486 $ (46,395 ) $ 212,091 Year Ended December 31, 2018 Beginning balance $ 157,400 $ (39,356 ) $ 118,044 Cumulative effect of an accounting change (149,794 ) — (149,794 ) Other comprehensive income (loss) before reclassifications (266,357 ) (25,186 ) (291,543 ) Amounts reclassified from accumulated other comprehensive income 144,573 — 144,573 Net current period other comprehensive income (loss) (121,784 ) (25,186 ) (146,970 ) Ending balance $ (114,178 ) $ (64,542 ) $ (178,720 ) Year Ended December 31, 2017 Beginning balance $ (27,641 ) $ (86,900 ) $ (114,541 ) Other comprehensive income (loss) before reclassifications 252,904 47,544 300,448 Amounts reclassified from accumulated other comprehensive income (67,863 ) — (67,863 ) Net current period other comprehensive income (loss) 185,041 47,544 232,585 Ending balance $ 157,400 $ (39,356 ) $ 118,044
Details about amounts reclassified from AOCI	The following tables present details about amounts reclassified from accumulated other comprehensive income and the tax effects allocated to each component of other comprehensive income (loss): Consolidated Statement of Income Amounts Reclassified from AOCI Details About Line Item That Includes Year Ended December 31, AOCI Components Reclassification 2019 2018 2017 Unrealized appreciation on available-for-sale investments Net realized gains (losses) $ 131,043 $ (153,822 ) $ 82,542 Other-than-temporary impairment losses (3,165 ) (2,829 ) (7,138 ) Total before tax 127,878 (156,651 ) 75,404 Income tax (expense) benefit (8,937 ) 12,078 (7,541 ) Net of tax $ 118,941 $ (144,573 ) $ 67,863
Schedule of tax effects allocated to each component of other comprehensive income (loss)	Following are the related tax effects allocated to each component of other comprehensive income (loss): Before Tax Tax Expense Net of Tax Amount (Benefit) Amount Year Ended December 31, 2019 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ 562,576 $ 61,805 $ 500,771 Less reclassification of net realized gains (losses) included in net income 127,878 8,937 118,941 Foreign currency translation adjustments 18,463 353 18,110 Other comprehensive income (loss) $ 453,161 $ 53,221 $ 399,940 Year Ended December 31, 2018 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (294,267 ) $ (24,210 ) $ (270,057 ) Less reclassification of net realized gains (losses) included in net income (156,651 ) (12,078 ) (144,573 ) Foreign currency translation adjustments (25,006 ) (176 ) (24,830 ) Other comprehensive income (loss) $ (162,622 ) $ (12,308 ) $ (150,314 ) Year Ended December 31, 2017 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ 266,559 $ 13,655 $ 252,904 Less reclassification of net realized gains (losses) included in net income 75,404 7,541 67,863 Foreign currency translation adjustments 47,549 535 47,014 Other comprehensive income (loss) $ 238,704 $ 6,649 $ 232,055

Earnings Per Common Share (Tabl

Earnings Per Common Share (Tables)	12 Months Ended
	Dec. 31, 2019
Earnings Per Share [Abstract]
Schedule of computation of basic and diluted earnings per common share	The following table sets forth the computation of basic and diluted earnings per common share: Year Ended December 31, 2019 2018 2017 Numerator: Net income $ 1,693,300 $ 727,821 $ 629,709 Amounts attributable to noncontrolling interests (56,981 ) 30,150 (10,431 ) Net income available to Arch 1,636,319 757,971 619,278 Preferred dividends (41,612 ) (41,645 ) (46,041 ) Loss on redemption of preferred shares — (2,710 ) (6,735 ) Net income available to Arch common shareholders $ 1,594,707 $ 713,616 $ 566,502 Denominator: Weighted average common shares outstanding 401,802,815 401,036,376 377,531,628 Series D preferred securities (1) — 3,311,245 26,606,736 Weighted average common shares outstanding – basic 401,802,815 404,347,621 404,138,364 Effect of dilutive common share equivalents: Nonvested restricted shares 1,673,770 1,474,207 3,936,594 Stock options (2) 8,132,893 7,084,650 9,710,067 Weighted average common shares and common share equivalents outstanding – diluted 411,609,478 412,906,478 417,785,025 Earnings per common share: Basic $ 3.97 $ 1.76 $ 1.40 Diluted $ 3.87 $ 1.73 $ 1.36 (1) The company has determined that, based on a review of the terms, features and rights of the Company’s non-voting common equivalent preferred shares compared to the rights of the Company’s common shareholders, the underlying common shares that the convertible securities convert to were common share equivalents at the time of their issuance. (2) Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For 2019 , 2018 and 2017 , the number of stock options excluded were 1,302,017 , 5,673,821 and 2,603,451 , respectively.

Income Taxes (Tables)

Income Taxes (Tables)	12 Months Ended
	Dec. 31, 2019
Income Tax Disclosure [Abstract]
Components of income taxes attributable to operations	The components of income taxes attributable to operations were as follows: Year Ended December 31, 2019 2018 2017 Current expense (benefit): United States $ 139,407 $ 73,078 $ (51,705 ) Non-U.S. 4,954 12,785 5,969 144,361 85,863 (45,736 ) Deferred expense (benefit): United States 11,849 19,544 169,093 Non-U.S. (400 ) 8,544 4,211 11,449 28,088 173,304 Income tax expense $ 155,810 $ 113,951 $ 127,568
Schedule of income or loss before income taxes by jurisdiction	The Company’s income or loss before income taxes was earned in the following jurisdictions: Year Ended December 31, 2019 2018 2017 Income (Loss) Before Income Taxes: Bermuda $ 1,122,952 $ 388,492 $ 406,054 United States 701,480 440,823 381,157 Other 24,678 12,457 (29,934 ) Total $ 1,849,110 $ 841,772 $ 757,277
Reconciliation of the differences between the provision for income taxes and the expected tax provision at the weighted average tax rate	A reconciliation of the difference between the provision for income taxes and the expected tax provision at the weighted average tax rate follows: Year Ended December 31, 2019 2018 2017 Expected income tax expense (benefit) computed on pre-tax income at weighted average income tax rate $ 149,799 $ 91,529 $ 126,262 Addition (reduction) in income tax expense (benefit) resulting from: Tax-exempt investment income (3,091 ) (4,790 ) (13,330 ) Meals and entertainment 1,134 1,060 1,063 State taxes, net of U.S. federal tax benefit 3,314 2,086 732 Foreign branch taxes 1,231 5,428 5,752 Prior year adjustment 632 (2,522 ) (559 ) Foreign exchange gains & losses 436 1,293 (572 ) Changes in applicable tax rate — (128 ) 7,745 Dividend withholding taxes 6,510 6,594 232 Change in valuation allowance 1,628 18,396 14,798 Contingent consideration 190 740 3,785 Share based compensation (6,592 ) (5,356 ) (18,733 ) Other 619 (379 ) 393 Income tax expense (benefit) $ 155,810 $ 113,951 $ 127,568
Significant components of deferred income tax assets and liabilities	Significant components of the Company’s deferred income tax assets and liabilities were as follows: December 31, 2019 2018 Deferred income tax assets: Net operating loss $ 30,836 $ 24,089 Uncrystallized losses 1,565 7,960 AMT credit carryforward 1,323 2,652 Discounting of net loss reserves 52,582 43,130 Net unearned premium reserve 64,269 68,305 Compensation liabilities 21,693 20,492 Foreign tax credit carryforward 9,521 9,116 Interest expense — 1,387 Goodwill and intangible assets 11,644 17,127 Bad debt reserves 5,983 5,626 Lease liability 26,438 — Net unrealized foreign exchange losses 598 949 Net unrealized decline of investments — 13,453 Other, net 206 3,418 Deferred tax assets before valuation allowance 226,658 217,704 Valuation allowance (48,219 ) (44,659 ) Deferred tax assets net of valuation allowance 178,439 173,045 Deferred income tax liabilities: Depreciation and amortization (1,215 ) (2,559 ) Deposit accounting liability (2,169 ) (2,292 ) Contingency reserve (132,831 ) (112,852 ) Deferred policy acquisition costs (29,847 ) (32,105 ) Net unrealized appreciation of investments (38,764 ) — Right-of-use asset (23,416 ) — Other, net (3,680 ) (735 ) Total deferred tax liabilities (231,922 ) (150,543 ) Net deferred income tax assets (liabilities) $ (53,483 ) $ 22,502
Summary of operating loss carryforwards	At December 31, 2019 , the Company’s net operating loss carryforwards and tax credits were as follows: Year Ended December 31, 2019 Expiration Operating Loss Carryforwards United Kingdom $ 89,000 No expiration Ireland 10,200 No expiration Australia 22,000 No expiration Hong Kong 17,600 No expiration Denmark 400 No expiration United States (1) (2) 23,100 2029 - 2038 Tax Credits U.K. foreign tax credits 9,521 No expiration U.S. refundable AMT credits 1,323 No expiration (1) Includes $0.6 million net operating loss carryforwards from Watford. (2) On January 30, 2014, the Company’s U.S. mortgage operations underwent an ownership change for U.S. federal income tax purposes as a result of the Company’s acquisition of the CMG Entities. As a result of this ownership change, a limitation has been imposed upon the utilization of approximately $8.9 million of the Company’s existing U.S. net operating loss carryforwards. Utilization is limited to approximately $0.6 million per year in accordance with Section 382 of the Internal Revenue Code of 1986 as amended (“the Code”).
Summary of tax credit carryforwards	At December 31, 2019 , the Company’s net operating loss carryforwards and tax credits were as follows: Year Ended December 31, 2019 Expiration Operating Loss Carryforwards United Kingdom $ 89,000 No expiration Ireland 10,200 No expiration Australia 22,000 No expiration Hong Kong 17,600 No expiration Denmark 400 No expiration United States (1) (2) 23,100 2029 - 2038 Tax Credits U.K. foreign tax credits 9,521 No expiration U.S. refundable AMT credits 1,323 No expiration (1) Includes $0.6 million net operating loss carryforwards from Watford. (2) On January 30, 2014, the Company’s U.S. mortgage operations underwent an ownership change for U.S. federal income tax purposes as a result of the Company’s acquisition of the CMG Entities. As a result of this ownership change, a limitation has been imposed upon the utilization of approximately $8.9 million of the Company’s existing U.S. net operating loss carryforwards. Utilization is limited to approximately $0.6 million per year in accordance with Section 382 of the Internal Revenue Code of 1986 as amended (“the Code”).
Reconciliation of the beginning and ending amount of unrecognized tax benefits	A reconciliation of the beginning and ending amount of unrecognized tax benefits is as follows: December 31, 2019 2018 Balance at beginning of year $ 2,008 $ 2,008 Additions based on tax positions related to the current year — — Additions for tax positions of prior years — — Reductions for tax positions of prior years — — Settlements — — Balance at end of year $ 2,008 $ 2,008
Summary of open tax years potentially subject to examination, by jurisdiction	The following table details open tax years that are potentially subject to examination by local tax authorities, in the following major jurisdictions: Jurisdiction Tax Years United States 2016-2019 United Kingdom 2018-2019 Ireland 2015-2019 Canada 2016-2019 Switzerland 2017-2019 Denmark 2015-2019

Leases (Tables)

Leases (Tables)	12 Months Ended
	Dec. 31, 2019
Leases [Abstract]
Additional information regarding operating leases	Additional information regarding the Company’s operating leases is as follows: December 31, 2019 Operating lease costs $ 30,478 Cash payments included in the measurement of lease liabilities reported in operating cash flows $ 27,521 Right-of-use assets obtained in exchange for new lease liabilities $ 7,445 Right-of-use assets (1) $ 131,661 Operating lease liability (1) $ 150,519 Weighted average discount rate 3.9 % Weighted average remaining lease term 6.4 years (1) The right-of-use assets are included in ‘other assets’ while the operating lease liability is included in ‘other liabilities.’
Contractual maturities of operating lease liabilities	The following table presents the contractual maturities of the Company's operating lease liabilities at December 31, 2019 : Years Ending December 31, 2020 $ 31,907 2021 30,842 2022 27,597 2023 23,027 2024 16,913 2025 and thereafter 40,167 Total undiscounted lease liability 170,453 Less: present value adjustment (19,934 ) Operating lease liability $ 150,519
Summary of future minimum lease payments	At December 31, 2018, the future minimum rental commitments, exclusive of escalation clauses and maintenance costs and net of rental income, for all of the Company’s operating leases was as follows: Years Ending December 31, 2019 $ 31,088 2020 30,491 2021 29,351 2022 26,068 2023 21,408 2024 and thereafter 54,745 Total $ 193,151

Commitments and Contingencies (

Commitments and Contingencies (Tables)	12 Months Ended
	Dec. 31, 2019
Commitments and Contingencies Disclosure [Abstract]
Broker concentration risk	The following table summarizes the percentage of the Company’s gross premiums written generated from or placed by the largest brokers: Broker Year Ended December 31, 2019 2018 2017 Aon Corporation and its subsidiaries 12.2 % 11.4 % 11.3 % Marsh & McLennan Companies and its subsidiaries 9.6 % 9.3 % 10.7 %

Debt and Financing Arrangemen_2

Debt and Financing Arrangements - (Tables)	12 Months Ended
	Dec. 31, 2019
Debt Disclosure [Abstract]
Schedule of senior notes	The Company’s senior notes payable at December 31, 2019 and 2018 were as follows: Carrying Amount at Interest Principal December 31, (Fixed) Amount 2019 2018 2034 notes (1) 7.350 % 300,000 297,254 297,150 2043 notes (2) 5.144 % 500,000 494,831 494,723 2026 notes (3) 4.011 % 500,000 496,806 496,417 2046 notes (4) 5.031 % 450,000 445,317 445,238 Watford notes (5) 6.500 % 140,000 137,418 — $ 1,890,000 $ 1,871,626 $ 1,733,528 (1) Senior notes of Arch Capital issued on May 4, 2004 and due May 1, 2034 (“2034 notes”). (2) Senior notes of Arch-U.S., a wholly-owned subsidiary of Arch Capital, issued on December 13, 2013 and due November 1, 2043 (“2043 notes”), fully and unconditionally guaranteed by Arch Capital. (3) Senior notes of Arch Capital Finance LLC (“Arch Finance”), a wholly-owned finance subsidiary of Arch Capital, issued on December 8, 2016 and due December 15, 2026 (“2026 notes”), fully and unconditionally guaranteed by Arch Capital. (4) Senior notes of Arch Finance issued on December 8, 2016 and due December 15, 2046 (“2046 notes”), fully and unconditionally guaranteed by Arch Capital (5) Senior notes of Watford issued on July 2, 2019 and due July 2, 2029, reflecting the elimination of amounts owned by Arch-U.S.
Schedule of outstanding revolving credit agreement borrowings	The Company’s outstanding revolving credit agreement borrowings were as follows: Year Ended December 31, 2019 2018 Arch Capital $ — $ — Watford 484,287 455,682 Total $ 484,287 $ 455,682

Goodwill and Intangible Assets

Goodwill and Intangible Assets (Tables)	12 Months Ended
	Dec. 31, 2019
Goodwill and Intangible Assets Disclosure [Abstract]
Analysis of goodwill and intangible assets	The following table shows an analysis of goodwill and intangible assets: Goodwill Intangible assets (indefinite life) Intangible assets (finite life) Total Net balance at Dec. 31, 2017 $ 198,236 $ 68,174 $ 386,201 $ 652,611 Acquisitions 51,476 — 43,000 94,476 Amortization — — (105,670 ) (105,670 ) Impairment (1) — (6,300 ) — (6,300 ) Foreign currency movements and other adjustments (92 ) — (105 ) (197 ) Net balance at Dec. 31, 2018 249,620 61,874 323,426 634,920 Acquisitions (2) 74,780 24,431 82,482 181,693 Amortization — — (82,104 ) (82,104 ) Impairment (1) — (1,000 ) — (1,000 ) Foreign currency movements and other adjustments 2,151 605 1,817 4,574 Net balance at Dec. 31, 2019 $ 326,551 $ 85,910 $ 325,621 $ 738,083 Gross balance at Dec. 31, 2019 $ 331,448 $ 85,305 $ 744,583 $ 1,161,336 Accumulated amortization — — (419,294 ) (419,294 ) Foreign currency movements and other adjustments (4,897 ) 605 332 (3,959 ) Net balance at Dec. 31, 2019 $ 326,551 $ 85,910 $ 325,621 $ 738,083 (1) The impairment to the indefinite-lived intangible assets during the year ended December 31, 2019 and 2018 of $1.0 million and $6.3 million
Summary of components of intangible assets	The following table presents the components of goodwill and intangible assets: Gross Balance Accumulated Foreign Currency Translation Adjustment and Other Net Balance Dec. 31, 2019 Acquired insurance contracts $ 452,470 $ (336,559 ) $ 310 $ 116,221 Operating platform 52,674 (39,571 ) (259 ) 12,844 Distribution relationships 243,838 (50,542 ) 212 193,508 Goodwill 331,448 — (4,897 ) 326,551 Insurance licenses 63,390 — — 63,390 Syndicate capacity 21,915 — 605 22,520 Unfavorable service contract (9,533 ) 8,657 — (876 ) Other 5,134 (1,279 ) 70 3,925 Total $ 1,161,336 $ (419,294 ) $ (3,959 ) $ 738,083 Dec. 31, 2018 Acquired insurance contracts $ 435,067 $ (271,981 ) $ (150 ) $ 162,936 Operating platform 47,400 (35,402 ) — 11,998 Distribution relationships 186,611 (36,718 ) (1,335 ) 148,558 Goodwill 256,668 — (7,048 ) 249,620 Insurance licenses 61,874 — — 61,874 Syndicate capacity — — — — Unfavorable service contract (9,533 ) 7,949 — (1,584 ) Other 2,556 (1,038 ) — 1,518 Total $ 980,643 $ (337,190 ) $ (8,533 ) $ 634,920
Estimated future amortization expense	The estimated remaining amortization expense for the Company’s intangible assets with finite lives is as follows: 2020 $ 65,958 2021 48,063 2022 33,972 2023 31,731 2024 27,566 2025 and thereafter 118,331 Total $ 325,621

Shareholders' Equity (Tables)

Shareholders' Equity (Tables)	12 Months Ended
	Dec. 31, 2019
Stockholders' Equity Note [Abstract]
Roll-forward of changes in issued and outstanding Common Shares	The following table presents a roll-forward of changes in Arch Capital’s issued and outstanding Common Shares: Year Ended December 31, 2019 2018 2017 Common Shares: Shares issued and outstanding, beginning of year 570,737,283 549,872,226 523,932,303 Shares issued (1) 2,835,994 2,757,506 3,388,344 Conversion of Series D preferred shares (2) — 17,022,600 21,265,860 Restricted shares issued, net of cancellations 1,043,918 1,084,951 1,285,719 Shares issued and outstanding, end of year 574,617,195 570,737,283 549,872,226 Common shares in treasury, end of year (168,997,994 ) (168,282,449 ) (156,938,409 ) Shares issued and outstanding, end of year 405,619,201 402,454,834 392,933,817 (1) Includes shares issued from the exercise of stock options and stock appreciation rights, and shares issued from the employee share purchase plan. (2) Such shares represent common shares that were issued upon conversion of the non-voting common equivalent preference shares issued in connection with the AIG acquisition.
Schedule of share repurchases	The Company’s repurchases under the share repurchase program were as follows: Year Ended December 31, 2019 2018 2017 Aggregate cost of shares repurchased $ 2,871 $ 282,762 $ — Shares repurchased 110,598 10,559,850 — Average price per share repurchased $ 25.96 $ 26.78 $ —

Share-Based Compensation (Table

Share-Based Compensation (Tables)	12 Months Ended
	Dec. 31, 2019
Share-based Payment Arrangement [Abstract]
Valuation assumptions	Year Ended December 31, 2019 2018 2017 Dividend yield — % — % — % Expected volatility 18.1 % 21.3 % 21.3 % Risk free interest rate 2.5 % 2.8 % 2.0 % Expected option life 6.0 years 6.0 years 6.0 years
Option activity	A summary of stock option and SAR activity under the Company’s Long Term Incentive and Share Award Plans during 2019 is presented below: Year Ended December 31, 2019 Number of Options / SARs Weighted Average Exercise Price Weighted Average Contractual Term Aggregate Intrinsic Value Outstanding, beginning of year 20,076,593 $ 19.37 Granted 1,228,280 $ 32.86 Exercised (2,355,216 ) $ 13.45 Forfeited or expired (96,639 ) $ 29.19 Outstanding, end of year 18,853,018 $ 20.94 5.03 $ 413,842 Exercisable, end of year 15,517,508 $ 19.05 4.28 $ 369,917
Weighted average grant date fair value	Year Ended December 31, 2019 2018 2017 Weighted average grant date fair value $ 7.90 $ 7.50 $ 8.15 Aggregate intrinsic value of Options/SARs exercised $ 51,350 $ 43,468 $ 64,173
Unvested restricted share and unit activity	A summary of restricted share and restricted unit activity under the Company’s Long Term Incentive and Share Award Plans for 2019 is presented below: Restricted Common Shares Restricted Unit Awards Unvested Shares: Unvested balance, beginning of year 1,619,285 1,254,558 Granted 384,926 810,815 Vested (931,696 ) (422,021 ) Forfeited (26,594 ) (80,340 ) Unvested balance, end of year 1,045,921 1,563,012 Weighted Average Grant Date Fair Value: Unvested balance, beginning of year $ 28.88 $ 27.58 Granted $ 33.43 $ 32.64 Vested $ 28.31 $ 27.75 Forfeited $ 30.15 $ 29.36 Unvested balance, end of year $ 31.02 $ 30.07
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Performance shares and units, valuation assumptions	Year Ended December 31, 2019 2018 2017 Expected volatility 17.1 % 16.2 % — % Risk free interest rate 2.5 % 2.6 % — %
Unvested performance share and unit activity	Performance Shares Performance Units Unvested Shares: Unvested balance, beginning of year 715,328 12,993 Granted 685,586 10,774 Vested — — Forfeited — — Unvested balance, end of year 1,400,914 23,767 Weighted Average Grant Date Fair Value: Unvested balance, beginning of year $ 24.77 $ 24.71 Granted $ 36.05 $ 35.83 Vested $ — $ — Forfeited $ — $ — Unvested balance, end of year $ 30.29 $ 29.75
Share based compensation expense	The following tables present pre-tax and after-tax share-based compensation expense recognized as well as the unrecognized compensation cost associated with unvested awards and the weighted average period over which it is expected to be recognized. Year Ended December 31, 2019 2018 2017 Pre-Tax Stock options and SARs $ 12,866 $ 16,272 $ 18,536 Restricted share and unit awards 38,988 34,025 46,884 Performance awards 8,949 4,414 — ESPP 3,045 1,224 2,443 Total $ 63,848 $ 55,935 $ 67,863 After-Tax Stock options and SARs $ 11,450 $ 14,894 $ 16,219 Restricted share and unit awards 32,999 29,044 37,708 Performance awards 8,295 4,127 — ESPP 2,758 1,114 2,171 Total $ 55,502 $ 49,179 $ 56,098
Unrecognized compensation cost	December 31, 2019 Stock Options and SARs Restricted Common Shares and Units Performance Common Shares and Units Unrecognized compensation cost related to unvested awards $ 12,823 $ 39,606 $ 8,893 Weighted average recognition period (years) 1.23 1.31 1.06
Restricted Common Shares And Restricted Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Weighted average grant date fair value of restricted stock	The following table presents the weighted average grant date fair value of restricted shares and restricted unit awards granted and the aggregate fair value of restricted shares and unit awards vesting in each year. Year Ended December 31, 2019 2018 2017 Restricted shares and restricted unit awards granted 1,195,741 1,563,287 1,747,176 Weighted average grant date fair value $ 32.89 $ 26.86 $ 32.02 Aggregate fair value of vested restricted share and unit awards $ 46,262 $ 39,898 $ 133,848
Performance Common Shares and Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Weighted average grant date fair value of restricted stock	The following table presents the weighted average grant date fair values of performance awards granted. Year Ended December 31, 2019 2018 2017 Performance awards 696,360 743,513 — Weighted average grant date fair value $ 36.05 $ 24.77 $ —

Statutory Information (Tables)

Statutory Information (Tables)	12 Months Ended
	Dec. 31, 2019
Disclosure Statutory Information [Abstract]
Summary of statutory capital, surplus and net income	The actual and required statutory capital and surplus for the Company’s principal operating subsidiaries at December 31, 2019 and 2018 : December 31, 2019 2018 Actual capital and surplus (1): Bermuda $ 13,511,729 $ 11,605,652 Ireland 721,439 653,055 United States 4,440,848 4,195,477 United Kingdom 748,276 386,892 Canada 61,351 59,096 Required capital and surplus: Bermuda $ 5,492,968 $ 4,718,345 Ireland 542,703 429,117 United States 1,697,640 1,783,268 United Kingdom 349,328 271,864 Canada 32,763 33,189 (1) Such amounts include ownership interests in affiliated insurance and reinsurance subsidiaries. There were no state-prescribed or permitted regulatory accounting practices for any of the Company’s insurance or reinsurance entities that resulted in reported statutory surplus that differed from that which would have been reported under the prescribed practices of the respective regulatory authorities, including the National Association of Insurance Commissioners. The differences between statutory financial statements and statements prepared in accordance with GAAP vary by jurisdiction, however, with the primary differences being that statutory financial statements may not reflect deferred acquisition costs, certain net deferred tax assets, goodwill and intangible assets, unrealized appreciation or depreciation on debt securities and certain unauthorized reinsurance recoverables and include contingency reserves. The statutory net income (loss) for the Company’s principal operating subsidiaries for 2019 , 2018 and 2017 was as follows: Year Ended December 31, 2019 2018 2017 Statutory net income (loss): Bermuda $ 1,876,416 $ 919,554 $ 881,665 Ireland 26,367 29,223 (14,438 ) United States 481,188 292,831 500,412 United Kingdom (17,423 ) (18,467 ) (33,257 ) Canada (1,023 ) 2,525 158

Unaudited Condensed Quarterly_2

Unaudited Condensed Quarterly Financial Information (Tables)	12 Months Ended
	Dec. 31, 2019
Quarterly Financial Information Disclosure [Abstract]
Summary of condensed quarterly financial information	The following table summarizes the 2019 and 2018 unaudited condensed quarterly financial information: Fourth Quarter Third Quarter Second Quarter First Quarter Year Ended December 31, 2019 Net premiums written $ 1,455,453 $ 1,613,457 $ 1,444,898 $ 1,525,259 Net premiums earned 1,515,882 1,438,023 1,463,727 1,368,866 Net investment income 154,263 161,488 155,038 156,949 Net realized gains (losses) 41,474 62,518 120,806 141,565 Net impairment losses recognized in earnings (644 ) (1,163 ) (49 ) (1,309 ) Underwriting income (loss) 251,421 231,262 293,134 260,148 Net income (loss) attributable to Arch 326,384 392,453 468,954 448,528 Preferred dividends (10,403 ) (10,403 ) (10,403 ) (10,403 ) Net income (loss) available to Arch common shareholders 315,981 382,050 458,551 438,125 Net income (loss) per common share -- basic $ 0.78 $ 0.95 $ 1.14 $ 1.09 Net income (loss) per common share -- diluted $ 0.76 $ 0.92 $ 1.12 $ 1.07 Year Ended December 31, 2018 Net premiums written $ 1,301,754 $ 1,333,553 $ 1,298,896 $ 1,412,544 Net premiums earned 1,369,435 1,290,878 1,336,763 1,234,899 Net investment income 157,217 144,024 135,668 126,724 Net realized gains (losses) (166,030 ) (51,705 ) (76,611 ) (110,998 ) Net impairment losses recognized in earnings (1,705 ) (492 ) (470 ) (162 ) Underwriting income (loss) 166,955 234,581 235,465 236,997 Net income (loss) attributable to Arch 136,494 227,408 243,646 150,423 Preferred dividends (10,403 ) (10,402 ) (10,403 ) (10,437 ) Net income (loss) available to Arch common shareholders 126,091 217,006 233,243 137,276 Net income (loss) per common share -- basic $ 0.31 $ 0.54 $ 0.58 $ 0.34 Net income (loss) per common share -- diluted $ 0.31 $ 0.53 $ 0.56 $ 0.33

Guarantor Financial Informati_2

Guarantor Financial Information (Tables)	12 Months Ended
	Dec. 31, 2019
Condensed Financial Information Disclosure [Abstract]
Condensed consolidating balance sheet	December 31, 2019 Condensed Consolidating Balance Sheet Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Assets Total investments $ 42 $ 692,606 $ 23,748,432 $ (38,834 ) $ 24,402,246 Cash 18,113 54,518 653,599 — 726,230 Investments in subsidiaries 11,786,861 4,347,806 — (16,134,667 ) — Due from subsidiaries and affiliates 17 200,635 1,901,865 (2,102,517 ) — Premiums receivable — — 2,547,130 (768,413 ) 1,778,717 Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses — — 9,711,773 (5,364,957 ) 4,346,816 Contractholder receivables — — 2,119,460 — 2,119,460 Ceded unearned premiums — — 2,230,164 (995,481 ) 1,234,683 Deferred acquisition costs — — 675,917 (42,517 ) 633,400 Goodwill and intangible assets — — 738,083 — 738,083 Other assets 20,461 32,187 1,981,598 (128,520 ) 1,905,726 Total assets $ 11,825,494 $ 5,327,752 $ 46,308,021 $ (25,575,906 ) $ 37,885,361 Liabilities Reserve for losses and loss adjustment expenses $ — $ — $ 19,028,538 $ (5,136,696 ) $ 13,891,842 Unearned premiums — — 5,335,030 (995,481 ) 4,339,549 Reinsurance balances payable — — 1,435,485 (768,413 ) 667,072 Contractholder payables — — 2,119,460 — 2,119,460 Collateral held for insured obligations — — 206,698 206,698 Senior notes 297,254 494,831 1,114,541 (35,000 ) 1,871,626 Revolving credit agreement borrowings — — 484,287 — 484,287 Due to subsidiaries and affiliates — 536,805 1,565,712 (2,102,517 ) — Other liabilities 30,869 33,267 2,324,793 (399,654 ) 1,989,275 Total liabilities 328,123 1,064,903 33,614,544 (9,437,761 ) 25,569,809 Redeemable noncontrolling interests — — 58,882 (3,478 ) 55,404 Shareholders' Equity Total shareholders' equity available to Arch 11,497,371 4,262,849 11,871,818 (16,134,667 ) 11,497,371 Non-redeemable noncontrolling interests — — 762,777 — 762,777 Total shareholders' equity 11,497,371 4,262,849 12,634,595 (16,134,667 ) 12,260,148 Total liabilities, noncontrolling interests and shareholders' equity $ 11,825,494 $ 5,327,752 $ 46,308,021 $ (25,575,906 ) $ 37,885,361 December 31, 2018 Condensed Consolidating Balance Sheet Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Assets Total investments $ 104 $ 452,674 $ 21,307,206 $ (14,700 ) $ 21,745,284 Cash 6,125 5,940 634,491 — 646,556 Investments in subsidiaries 9,735,256 3,999,243 — (13,734,499 ) — Due from subsidiaries and affiliates 9 2 1,802,686 (1,802,697 ) — Premiums receivable — — 1,834,389 (535,239 ) 1,299,150 Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses — — 8,618,660 (5,699,288 ) 2,919,372 Contractholder receivables — — 2,079,111 — 2,079,111 Ceded unearned premiums — — 1,730,262 (754,793 ) 975,469 Deferred acquisition costs — — 618,535 (48,961 ) 569,574 Goodwill and intangible assets — — 634,920 — 634,920 Other assets 12,588 80,949 1,466,438 (211,082 ) 1,348,893 Total assets $ 9,754,082 $ 4,538,808 $ 40,726,698 $ (22,801,259 ) $ 32,218,329 Liabilities Reserve for losses and loss adjustment expenses $ — $ — $ 17,345,142 $ (5,491,845 ) $ 11,853,297 Unearned premiums — — 4,508,429 (754,793 ) 3,753,636 Reinsurance balances payable — — 928,346 (535,239 ) 393,107 Contractholder payables — — 2,079,111 — 2,079,111 Collateral held for insured obligations — — 236,630 — 236,630 Senior notes 297,150 494,723 941,655 — 1,733,528 Revolving credit agreement borrowings — — 455,682 — 455,682 Due to subsidiaries and affiliates — 536,805 1,265,892 (1,802,697 ) — Other liabilities 17,105 26,270 1,699,768 (467,484 ) 1,275,659 Total liabilities 314,255 1,057,798 29,460,655 (9,052,058 ) 21,780,650 Redeemable noncontrolling interests — — 220,992 (14,700 ) 206,292 Shareholders' Equity Total shareholders' equity available to Arch 9,439,827 3,481,010 10,253,491 (13,734,501 ) 9,439,827 Non-redeemable noncontrolling interests — — 791,560 — 791,560 Total shareholders' equity 9,439,827 3,481,010 11,045,051 (13,734,501 ) 10,231,387 Total liabilities, noncontrolling interests and shareholders' equity $ 9,754,082 $ 4,538,808 $ 40,726,698 $ (22,801,259 ) $ 32,218,329
Condensed consolidating statement of income and comprehensive income	Year Ended December 31, 2019 Condensed Consolidating Statement of Income and Comprehensive Income Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Revenues Net premiums earned $ — $ — $ 5,786,498 $ — $ 5,786,498 Net investment income 212 14,270 706,038 (92,782 ) 627,738 Net realized gains (losses) — 25,313 352,771 (11,721 ) 366,363 Net impairment losses recognized in earnings — — (3,165 ) — (3,165 ) Other underwriting income — — 24,861 — 24,861 Equity in net income (loss) of investments accounted for using the equity method — 779 122,893 — 123,672 Other income (loss) (762 ) — 2,995 — 2,233 Total revenues (550 ) 40,362 6,992,891 (104,503 ) 6,928,200 Expenses Losses and loss adjustment expenses — — 3,133,452 — 3,133,452 Acquisition expenses — — 840,945 — 840,945 Other operating expenses — — 800,997 — 800,997 Corporate expenses 62,701 7,221 10,189 — 80,111 Amortization of intangible assets — — 82,104 — 82,104 Interest expense 22,154 47,951 142,662 (91,895 ) 120,872 Net foreign exchange (gains) losses 1 — 22,188 (1,580 ) 20,609 Total expenses 84,856 55,172 5,032,537 (93,475 ) 5,079,090 Income (loss) before income taxes (85,406 ) (14,810 ) 1,960,354 (11,028 ) 1,849,110 Income tax (expense) benefit — 3,696 (159,506 ) — (155,810 ) Income (loss) before equity in net income of subsidiaries (85,406 ) (11,114 ) 1,800,848 (11,028 ) 1,693,300 Equity in net income of subsidiaries 1,721,725 564,657 — (2,286,382 ) — Net income 1,636,319 553,543 1,800,848 (2,297,410 ) 1,693,300 Net (income) loss attributable to noncontrolling interests — — (57,868 ) 887 (56,981 ) Net income available to Arch 1,636,319 553,543 1,742,980 (2,296,523 ) 1,636,319 Preferred dividends (41,612 ) — — — (41,612 ) Net income available to Arch common shareholders $ 1,594,707 $ 553,543 $ 1,742,980 $ (2,296,523 ) $ 1,594,707 Comprehensive income (loss) available to Arch $ 2,027,129 $ 751,210 $ 2,124,455 $ (2,875,665 ) $ 2,027,129 Year Ended December 31, 2018 Condensed Consolidating Statement of Income and Comprehensive Income Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Revenues Net premiums earned $ — $ — $ 5,231,975 $ — $ 5,231,975 Net investment income 49 3,902 649,394 (89,712 ) 563,633 Net realized gains (losses) 29 (2,676 ) (410,014 ) 7,317 (405,344 ) Net impairment losses recognized in earnings — — (2,829 ) — (2,829 ) Other underwriting income — — 15,073 — 15,073 Equity in net income (loss) of investments accounted for using the equity method — — 45,641 — 45,641 Other income (loss) 1,918 — 501 — 2,419 Total revenues 1,996 1,226 5,529,741 (82,395 ) 5,450,568 Expenses Losses and loss adjustment expenses — — 2,890,106 — 2,890,106 Acquisition expenses — — 805,135 — 805,135 Other operating expenses — — 677,809 — 677,809 Corporate expenses 64,279 2,422 12,293 — 78,994 Amortization of intangible assets — — 105,670 — 105,670 Interest expense 22,147 48,103 138,672 (88,438 ) 120,484 Net foreign exchange (gains) losses 30 — (59,607 ) (9,825 ) (69,402 ) Total expenses 86,456 50,525 4,570,078 (98,263 ) 4,608,796 Income (loss) before income taxes (84,460 ) (49,299 ) 959,663 15,868 841,772 Income tax (expense) benefit — 13,314 (127,265 ) — (113,951 ) Income (loss) before equity in net income of subsidiaries (84,460 ) (35,985 ) 832,398 15,868 727,821 Equity in net income of subsidiaries 842,431 388,260 — (1,230,691 ) — Net income 757,971 352,275 832,398 (1,214,823 ) 727,821 Net (income) loss attributable to noncontrolling interests — — 28,875 1,275 30,150 Net income available to Arch 757,971 352,275 861,273 (1,213,548 ) 757,971 Preferred dividends (41,645 ) — — — (41,645 ) Loss on repurchase of preferred shares (2,710 ) — — — (2,710 ) Net income available to Arch common shareholders $ 713,616 $ 352,275 $ 861,273 $ (1,213,548 ) $ 713,616 Comprehensive income (loss) available to Arch $ 611,003 $ 292,973 $ 730,828 $ (1,023,801 ) $ 611,003 Year Ended December 31, 2017 Condensed Consolidating Statement of Income and Comprehensive Income Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Revenues Net premiums earned $ — $ — $ 4,844,532 $ — $ 4,844,532 Net investment income 243 1,420 559,963 (90,754 ) 470,872 Net realized gains (losses) — — 149,141 — 149,141 Net impairment losses recognized in earnings — — (7,138 ) — (7,138 ) Other underwriting income — — 30,253 — 30,253 Equity in net income (loss) of investments accounted for using the equity method — — 142,286 — 142,286 Other income (loss) (482 ) — (2,089 ) — (2,571 ) Total revenues (239 ) 1,420 5,716,948 (90,754 ) 5,627,375 Expenses Losses and loss adjustment expenses — — 2,967,446 — 2,967,446 Acquisition expenses — — 775,458 — 775,458 Other operating expenses — — 684,451 — 684,451 Corporate expenses 67,450 4,152 12,150 — 83,752 Amortization of intangible assets — — 125,778 — 125,778 Interest expense 23,560 47,993 135,342 (89,464 ) 117,431 Net foreign exchange (gains) losses 2 — 68,900 46,880 115,782 Total expenses 91,012 52,145 4,769,525 (42,584 ) 4,870,098 Income (loss) before income taxes (91,251 ) (50,725 ) 947,423 (48,170 ) 757,277 Income tax (expense) benefit — 10,333 (137,901 ) — (127,568 ) Income (loss) before equity in net income of subsidiaries (91,251 ) (40,392 ) 809,522 (48,170 ) 629,709 Equity in net income of subsidiaries 710,529 303,991 — (1,014,520 ) — Net income 619,278 263,599 809,522 (1,062,690 ) 629,709 Net (income) loss attributable to noncontrolling interests — — (11,721 ) 1,290 (10,431 ) Net income available to Arch 619,278 263,599 797,801 (1,061,400 ) 619,278 Preferred dividends (46,041 ) — — — (46,041 ) Loss on repurchase of preferred shares (6,735 ) — — — (6,735 ) Net income available to Arch common shareholders $ 566,502 $ 263,599 $ 797,801 $ (1,061,400 ) $ 566,502 Comprehensive income (loss) available to Arch $ 851,863 $ 288,752 $ 983,475 $ (1,272,227 ) $ 851,863
Condensed consolidating statement of cash flows	Year Ended December 31, 2019 Condensed Consolidating Statement of Cash Flows Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Operating Activities Net Cash Provided By (Used For) Operating Activities $ 52,487 $ 486,252 $ 2,138,195 $ (628,475 ) $ 2,048,459 Investing Activities Purchases of fixed maturity investments — (878,577 ) (29,347,333 ) 172,133 (30,053,777 ) Purchases of equity securities — (155,890 ) (726,820 ) 70,743 (811,967 ) Purchases of other investments — (28,490 ) (1,442,055 ) — (1,470,545 ) Proceeds from the sales of fixed maturity investments — 806,603 27,937,616 (148,354 ) 28,595,865 Proceeds from the sales of equity securities — 7,441 493,120 (70,743 ) 429,818 Proceeds from the sales, redemptions and maturities of other investments — 1,634 1,207,925 — 1,209,559 Proceeds from redemptions and maturities of fixed maturity investments — — 643,265 — 643,265 Net settlements of derivative instruments — — 59,982 — 59,982 Net (purchases) sales of short-term investments 61 34,372 5,400 — 39,833 Change in cash collateral related to securities lending — — (62,193 ) — (62,193 ) Contributions to subsidiaries (2,121 ) (6,000 ) (57,039 ) 65,160 — Issuance of intercompany loans — (200,000 ) (87,783 ) 287,783 — Purchases of fixed assets (162 ) — (37,675 ) — (37,837 ) Other — (18,767 ) (329,719 ) — (348,486 ) Net Cash Provided By (Used For) Investing Activities (2,222 ) (437,674 ) (1,743,309 ) 376,722 (1,806,483 ) Financing Activities Purchases of common shares under share repurchase program (2,871 ) — — — (2,871 ) Proceeds from common shares issued, net 6,203 — 65,160 (65,160 ) 6,203 Proceeds from intercompany borrowings — — 287,783 (287,783 ) — Proceeds from borrowings — — 235,083 (35,000 ) 200,083 Repayments of borrowings — — (49,182 ) — (49,182 ) Change in cash collateral related to securities lending — — 62,193 — 62,193 Change in third party investment in non-redeemable noncontrolling interests — — (75,056 ) — (75,056 ) Change in third party investment in redeemable noncontrolling interests — — (173,103 ) 11,221 (161,882 ) Dividends paid to redeemable noncontrolling interests — — (13,402 ) 887 (12,515 ) Dividends paid to parent (1) — — (627,588 ) 627,588 — Other — — (6,023 ) — (6,023 ) Preferred dividends paid (41,612 ) — — — (41,612 ) Net Cash Provided By (Used For) Financing Activities (38,280 ) — (294,135 ) 251,753 (80,662 ) Effects of exchange rate changes on foreign currency cash and restricted cash — — 17,741 — 17,741 Increase (decrease) in cash and restricted cash 11,985 48,578 118,492 — 179,055 Cash and restricted cash, beginning of year 6,159 5,940 712,544 — 724,643 Cash and restricted cash, end of period $ 18,144 $ 54,518 $ 831,036 $ — $ 903,698 (1) Included in net cash provided by (used for) operating activities in the Arch Capital (Parent Guarantor) and/or Arch-U.S. (Subsidiary Issuer) columns. Year Ended December 31, 2018 Condensed Consolidating Statement of Cash Flows Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Operating Activities Net Cash Provided By (Used For) Operating Activities $ 324,319 $ 481,751 $ 1,703,181 $ (949,929 ) $ 1,559,322 Investing Activities Purchases of fixed maturity investments — (906,482 ) (33,662,541 ) 1,241,363 (33,327,660 ) Purchases of equity securities — (44,830 ) (956,319 ) — (1,001,149 ) Purchases of other investments — — (2,014,622 ) — (2,014,622 ) Proceeds from the sales of fixed maturity investments — 535,947 32,218,687 (1,241,363 ) 31,513,271 Proceeds from the sales of equity securities — — 1,118,445 — 1,118,445 Proceeds from the sales, redemptions and maturities of other investments — — 1,561,958 — 1,561,958 Proceeds from redemptions and maturities of fixed maturity investments — — 892,755 — 892,755 Net settlements of derivative instruments — — 44,699 — 44,699 Net (purchases) sales of short-term investments 96,476 7,674 381,323 — 485,473 Change in cash collateral related to securities lending — — 180,883 — 180,883 Contributions to subsidiaries — (98,500 ) 98,500 — — Purchases of fixed assets (110 ) — (29,699 ) — (29,809 ) Other (4 ) — 21,740 — 21,736 Net Cash Provided By (Used For) Investing Activities 96,362 (506,191 ) (144,191 ) — (554,020 ) Financing Activities Redemption of preferred shares (92,555 ) — — — (92,555 ) Purchases of common shares under share repurchase program (282,762 ) — — — (282,762 ) Proceeds from common shares issued, net (7,608 ) — — — (7,608 ) Proceeds from borrowings — — 218,259 — 218,259 Repayments of borrowings — — (576,401 ) — (576,401 ) Change in cash collateral related to securities lending — — (180,883 ) — (180,883 ) Dividends paid to redeemable noncontrolling interests — — (19,264 ) 1,275 (17,989 ) Dividends paid to parent (1) — — (948,654 ) 948,654 — Other — — (7,226 ) — (7,226 ) Preferred dividends paid (41,645 ) — — — (41,645 ) Net Cash Provided By (Used For) Financing Activities (424,570 ) — (1,514,169 ) 949,929 (988,810 ) Effects of exchange rate changes on foreign currency cash and restricted cash — — (19,133 ) — (19,133 ) Increase (decrease) in cash and restricted cash (3,889 ) (24,440 ) 25,688 — (2,641 ) Cash and restricted cash, beginning of year 10,048 30,380 686,856 — 727,284 Cash and restricted cash, end of period $ 6,159 $ 5,940 $ 712,544 $ — $ 724,643 (1) Included in net cash provided by (used for) operating activities in the Arch Capital (Parent Guarantor) and/or Arch-U.S. (Subsidiary Issuer) columns. Year Ended December 31, 2017 Condensed Consolidating Statement of Cash Flows Arch Capital (Parent Guarantor) Arch-U.S. (Subsidiary Issuer) Other Arch Capital Subsidiaries Consolidating Adjustments and Eliminations Arch Capital Consolidated Operating Activities Net Cash Provided By (Used For) Operating Activities $ 159,130 $ (10,289 ) $ 1,649,751 $ (703,714 ) $ 1,094,878 Investing Activities Purchases of fixed maturity investments — — (36,806,913 ) — (36,806,913 ) Purchases of equity securities — — (1,021,016 ) — (1,021,016 ) Purchases of other investments — — (2,020,624 ) — (2,020,624 ) Proceeds from the sales of fixed maturity investments — — 35,686,779 — 35,686,779 Proceeds from the sales of equity securities — — 1,056,401 — 1,056,401 Proceeds from the sales, redemptions and maturities of other investments — — 1,528,617 — 1,528,617 Proceeds from redemptions and maturities of fixed maturity investments — — 907,417 — 907,417 Net settlements of derivative instruments — — (28,563 ) — (28,563 ) Proceeds from investment in joint venture — — — — — Net (purchases) sales of short-term investments (93,864 ) (4,586 ) (636,104 ) — (734,554 ) Change in cash collateral related to securities lending — — 12,540 — 12,540 Contributions to subsidiaries 20,457 (73,700 ) (423,998 ) 477,241 — Issuance of intercompany loans — — (47,000 ) 47,000 — Repayment of intercompany loans — 47,000 80,840 (127,840 ) — Purchases of fixed assets (18 ) — (22,823 ) — (22,841 ) Other — — 111,516 (20,641 ) 90,875 Net Cash Provided By (Used For) Investing Activities (73,425 ) (31,286 ) (1,622,931 ) 375,760 (1,351,882 ) Financing Activities Proceeds from issuance of Series C preferred shares issued, net 319,694 — — — 319,694 Redemption of preferred shares (230,000 ) — — — (230,000 ) Purchases of common shares under share repurchase program — — — — — Proceeds from common shares issued, net (21,048 ) — 477,244 (477,244 ) (21,048 ) Proceeds from intercompany borrowings — — 47,000 (47,000 ) — Proceeds from borrowings — — 253,415 — 253,415 Repayments of intercompany borrowings — — (127,840 ) 127,840 — Repayments of borrowings (100,000 ) — (97,000 ) — (197,000 ) Change in cash collateral relating to securities lending — — (12,540 ) — (12,540 ) Dividends paid to redeemable noncontrolling — — (19,264 ) 1,275 (17,989 ) Dividends paid to parent (1) — — (702,442 ) 702,442 — Other — — (72,537 ) 20,641 (51,896 ) Preferred dividends paid (46,041 ) — — — (46,041 ) Net Cash Provided By (Used For) Financing Activities (77,395 ) — (253,964 ) 327,954 (3,405 ) Effects of exchange rate changes on foreign currency cash and restricted cash — — 18,124 — 18,124 Increase (decrease) in cash and restricted cash 8,310 (41,575 ) (209,020 ) — (242,285 ) Cash and restricted cash, beginning of year 1,738 71,955 895,876 — 969,569 Cash and restricted cash, end of period $ 10,048 $ 30,380 $ 686,856 $ — $ 727,284 (1) Included in net cash provided by (used for) operating activities in the Arch Capital (Parent Guarantor) and/or Arch-U.S. (Subsidiary Issuer) columns.

Business Acquired (Details)

Business Acquired (Details) $ in Millions	Jul. 01, 2017USD ($)
AIG United Guaranty Insurance (Asia) Limited
Business Acquisition [Line Items]
Total purchase price	$ 40

Significant Accounting Polici_3

Significant Accounting Policies (Details) $ in Thousands	1 Months Ended	12 Months Ended
	May 31, 2018	Dec. 31, 2019USD ($)	Dec. 31, 2018	Jan. 01, 2019USD ($)
Significant Accounting Policies [Line Items]
Share split conversion ratio	3		3
Premium revenue recognition period		12 months
Securities lending rate of collateral required (percentage)		102.00%
Equity method investments, time lag for reporting - low end of range		1 month
Equity method investments, time lag for reporting - high end of range		3 months
Vesting period, share-based awards		3 years
Requisite service period, share-based awards		3 years
Operating lease liability		$ 150,519
Losses occurring
Significant Accounting Policies [Line Items]
Premium revenue recognition period		12 months
Risks attaching
Significant Accounting Policies [Line Items]
Premium revenue recognition period		24 months
Other assets
Significant Accounting Policies [Line Items]
Right-of-use assets		$ 131,661
Other liabilities
Significant Accounting Policies [Line Items]
Operating lease liability		$ 150,519
ASU 2016-02 | Other assets
Significant Accounting Policies [Line Items]
Right-of-use assets				$ 147,900
ASU 2016-02 | Other liabilities
Significant Accounting Policies [Line Items]
Operating lease liability				$ 163,600

Segment Information - Analysis

Segment Information - Analysis of underwriting income by segment and reconciliation to net income available to common shareholders (Details) $ in Thousands		3 Months Ended								12 Months Ended
		Dec. 31, 2019USD ($)	Sep. 30, 2019USD ($)	Jun. 30, 2019USD ($)	Mar. 31, 2019USD ($)	Dec. 31, 2018USD ($)	Sep. 30, 2018USD ($)	Jun. 30, 2018USD ($)	Mar. 31, 2018USD ($)	Dec. 31, 2019USD ($)segment	Dec. 31, 2018USD ($)	Dec. 31, 2017USD ($)
Segment Reporting Information [Line Items]
Gross premiums written										$ 8,138,960	$ 6,961,004	$ 6,368,425
Premiums ceded										(2,099,893)	(1,614,257)	(1,407,052)
Net premiums written		$ 1,455,453	$ 1,613,457	$ 1,444,898	$ 1,525,259	$ 1,301,754	$ 1,333,553	$ 1,298,896	$ 1,412,544	6,039,067	5,346,747	4,961,373
Change in unearned premiums										(252,569)	(114,772)	(116,841)
Net premiums earned		1,515,882	1,438,023	1,463,727	1,368,866	1,369,435	1,290,878	1,336,763	1,234,899	5,786,498	5,231,975	4,844,532
Other underwriting income										24,861	15,073	30,253
Losses and loss adjustment expenses										(3,133,452)	(2,890,106)	(2,967,446)
Acquisition expenses, net										(840,945)	(805,135)	(775,458)
Other operating expenses										(800,997)	(677,809)	(684,451)
Underwriting income (loss)		251,421	231,262	293,134	260,148	166,955	234,581	235,465	236,997	1,035,965	873,998	447,430
Net investment income		154,263	161,488	155,038	156,949	157,217	144,024	135,668	126,724	627,738	563,633	470,872
Net realized gains (losses)		41,474	62,518	120,806	141,565	(166,030)	(51,705)	(76,611)	(110,998)	366,363	(405,344)	149,141
Net impairment losses recognized in earnings		(644)	(1,163)	(49)	(1,309)	(1,705)	(492)	(470)	(162)	(3,165)	(2,829)	(7,138)
Equity in net income (loss) of investment funds accounted for using the equity method										123,672	45,641	142,286
Other income (loss)										2,233	2,419	(2,571)
Corporate expenses										(65,667)	(58,608)	(61,602)
Transaction costs and other										(14,444)	(20,386)	(22,150)
Amortization of intangible assets										(82,104)	(105,670)	(125,778)
Interest expense										(120,872)	(120,484)	(117,431)
Net foreign exchange gains (losses)										(20,609)	69,402	(115,782)
Income (loss) before income taxes										1,849,110	841,772	757,277
Income tax (expense) benefit										(155,810)	(113,951)	(127,568)
Net income		326,384	392,453	468,954	448,528	136,494	227,408	243,646	150,423	1,693,300	727,821	629,709
Dividends attributable to redeemable noncontrolling interests										(16,909)	(18,357)	(18,344)
Amounts attributable to nonredeemable noncontrolling interests										(40,072)	48,507	7,913
Net income available to Arch										1,636,319	757,971	619,278
Preferred dividends		(10,403)	(10,403)	(10,403)	(10,403)	(10,403)	(10,402)	(10,403)	(10,437)	(41,612)	(41,645)	(46,041)
Loss on redemption of preferred shares										0	(2,710)	(6,735)
Net income (loss) available to Arch common shareholders		315,981	$ 382,050	$ 458,551	$ 438,125	126,091	$ 217,006	$ 233,243	$ 137,276	$ 1,594,707	$ 713,616	$ 566,502
Underwriting Ratios
Loss ratio										54.20%	55.20%	61.30%
Acquisition expense ratio										14.50%	15.40%	16.00%
Other operating expense ratio										13.80%	13.00%	14.10%
Combined ratio										82.50%	83.60%	91.40%
Goodwill and intangible assets		738,083				634,920				$ 738,083	$ 634,920	$ 652,611
Total investable assets		24,990,265				22,324,524				24,990,265	22,324,524	22,156,488
Total assets		37,885,361				32,218,329				37,885,361	32,218,329	32,051,658
Total liabilities		25,569,809				21,780,650				$ 25,569,809	21,780,650	21,805,723
Other
Segment Reporting Information [Line Items]
Number of segments | segment										2
Gross premiums written	[1]									$ 754,881	735,015	600,304
Premiums ceded	[2]									(222,019)	(130,840)	(47,187)
Net premiums written										532,862	604,175	553,117
Change in unearned premiums										23,827	(25,313)	(21,390)
Net premiums earned										556,689	578,862	531,727
Other underwriting income										2,412	2,722	3,180
Losses and loss adjustment expenses										(453,135)	(441,255)	(436,402)
Acquisition expenses, net										(105,980)	(125,558)	(129,971)
Other operating expenses										(51,651)	(37,889)	(31,928)
Underwriting income (loss)										(51,665)	(23,118)	(63,394)
Net investment income										136,671	125,675	88,800
Net realized gains (losses)										15,161	(120,915)	343
Net impairment losses recognized in earnings										0	0	0
Equity in net income (loss) of investment funds accounted for using the equity method										0	0	0
Other income (loss)										0	0	0
Corporate expenses										0	0	0
Transaction costs and other										0	(9,000)	0
Amortization of intangible assets										0	0	0
Interest expense										(27,137)	(19,465)	(13,839)
Net foreign exchange gains (losses)										(11,357)	10,691	(2,437)
Income (loss) before income taxes										61,673	(36,132)	9,473
Income tax (expense) benefit										(20)	(27)	(21)
Net income										61,653	(36,159)	9,452
Dividends attributable to redeemable noncontrolling interests										(16,909)	(18,357)	(18,344)
Amounts attributable to nonredeemable noncontrolling interests										(40,072)	48,507	7,913
Net income available to Arch										4,672	(6,009)	(979)
Preferred dividends										0	0	0
Loss on redemption of preferred shares										0	0	0
Net income (loss) available to Arch common shareholders										$ 4,672	$ (6,009)	$ (979)
Underwriting Ratios
Loss ratio										81.40%	76.20%	82.10%
Acquisition expense ratio										19.00%	21.70%	24.40%
Other operating expense ratio										9.30%	6.50%	6.00%
Combined ratio										109.70%	104.40%	112.50%
Goodwill and intangible assets		7,650				7,650				$ 7,650	$ 7,650	$ 7,650
Total investable assets		2,704,589				2,757,663				2,704,589	2,757,663	2,440,067
Total assets		3,510,893				3,372,856				3,510,893	3,372,856	3,014,654
Total liabilities		2,592,173				2,262,255				$ 2,592,173	2,262,255	1,846,149
Underwriting segments
Segment Reporting Information [Line Items]
Number of segments | segment										3
Gross premiums written	[1]									$ 7,695,645	6,534,423	6,088,254
Premiums ceded										(2,189,440)	(1,791,851)	(1,679,998)
Net premiums written										5,506,205	4,742,572	4,408,256
Change in unearned premiums										(276,396)	(89,459)	(95,451)
Net premiums earned										5,229,809	4,653,113	4,312,805
Other underwriting income										22,449	12,351	27,073
Losses and loss adjustment expenses										(2,680,317)	(2,448,851)	(2,531,044)
Acquisition expenses, net										(734,965)	(679,577)	(645,487)
Other operating expenses										(749,346)	(639,920)	(652,523)
Underwriting income (loss)										1,087,630	897,116	510,824
Net investment income										491,067	437,958	382,072
Net realized gains (losses)										351,202	(284,429)	148,798
Net impairment losses recognized in earnings										(3,165)	(2,829)	(7,138)
Equity in net income (loss) of investment funds accounted for using the equity method										123,672	45,641	142,286
Other income (loss)										2,233	2,419	(2,571)
Corporate expenses										(65,667)	(58,608)	(61,602)
Transaction costs and other										(14,444)	(11,386)	(22,150)
Amortization of intangible assets										(82,104)	(105,670)	(125,778)
Interest expense										(93,735)	(101,019)	(103,592)
Net foreign exchange gains (losses)										(9,252)	58,711	(113,345)
Income (loss) before income taxes										1,787,437	877,904	747,804
Income tax (expense) benefit										(155,790)	(113,924)	(127,547)
Net income										1,631,647	763,980	620,257
Dividends attributable to redeemable noncontrolling interests										0	0	0
Amounts attributable to nonredeemable noncontrolling interests										0	0	0
Net income available to Arch										1,631,647	763,980	620,257
Preferred dividends										(41,612)	(41,645)	(46,041)
Loss on redemption of preferred shares										0	(2,710)	(6,735)
Net income (loss) available to Arch common shareholders										$ 1,590,035	$ 719,625	$ 567,481
Underwriting Ratios
Loss ratio										51.30%	52.60%	58.70%
Acquisition expense ratio										14.10%	14.60%	15.00%
Other operating expense ratio										14.30%	13.80%	15.10%
Combined ratio										79.70%	81.00%	88.80%
Goodwill and intangible assets		730,433				627,270				$ 730,433	$ 627,270	$ 644,961
Total investable assets		22,285,676				19,566,861				22,285,676	19,566,861	19,716,421
Total assets		34,374,468				28,845,473				34,374,468	28,845,473	29,037,004
Total liabilities		22,977,636				19,518,395				22,977,636	19,518,395	19,959,574
Underwriting segments | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]									3,907,993	3,262,332	3,081,086
Premiums ceded	[2]									(1,266,267)	(1,050,207)	(958,646)
Net premiums written										2,641,726	2,212,125	2,122,440
Change in unearned premiums										(244,646)	(6,464)	(9,422)
Net premiums earned										2,397,080	2,205,661	2,113,018
Other underwriting income										0	0	0
Losses and loss adjustment expenses										(1,615,475)	(1,520,680)	(1,622,444)
Acquisition expenses, net										(361,614)	(349,702)	(323,639)
Other operating expenses										(454,770)	(364,138)	(359,524)
Underwriting income (loss)										$ (34,779)	$ (28,859)	$ (192,589)
Underwriting Ratios
Loss ratio										67.40%	68.90%	76.80%
Acquisition expense ratio										15.10%	15.90%	15.30%
Other operating expense ratio										19.00%	16.50%	17.00%
Combined ratio										101.50%	101.30%	109.10%
Goodwill and intangible assets		289,021				114,012				$ 289,021	$ 114,012	$ 22,310
Underwriting segments | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]									2,323,223	1,912,522	1,640,399
Premiums ceded	[2]									(720,500)	(539,950)	(465,925)
Net premiums written										1,602,723	1,372,572	1,174,474
Change in unearned premiums										(136,334)	(111,356)	(31,853)
Net premiums earned										1,466,389	1,261,216	1,142,621
Other underwriting income										6,444	(682)	11,336
Losses and loss adjustment expenses										(1,011,329)	(846,882)	(773,923)
Acquisition expenses, net										(239,032)	(211,280)	(221,250)
Other operating expenses										(141,484)	(133,350)	(146,663)
Underwriting income (loss)										$ 80,988	$ 69,022	$ 12,121
Underwriting Ratios
Loss ratio										69.00%	67.10%	67.70%
Acquisition expense ratio										16.30%	16.80%	19.40%
Other operating expense ratio										9.60%	10.60%	12.80%
Combined ratio										94.90%	94.50%	99.90%
Goodwill and intangible assets		2,516				0				$ 2,516	$ 0	$ 211
Underwriting segments | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[1]									1,466,265	1,360,708	1,368,138
Premiums ceded	[2]									(204,509)	(202,833)	(256,796)
Net premiums written										1,261,756	1,157,875	1,111,342
Change in unearned premiums										104,584	28,361	(54,176)
Net premiums earned										1,366,340	1,186,236	1,057,166
Other underwriting income										16,005	13,033	15,737
Losses and loss adjustment expenses										(53,513)	(81,289)	(134,677)
Acquisition expenses, net										(134,319)	(118,595)	(100,598)
Other operating expenses										(153,092)	(142,432)	(146,336)
Underwriting income (loss)										$ 1,041,421	$ 856,953	$ 691,292
Underwriting Ratios
Loss ratio										3.90%	6.90%	12.70%
Acquisition expense ratio										9.80%	10.00%	9.50%
Other operating expense ratio										11.20%	12.00%	13.80%
Combined ratio										24.90%	28.90%	36.00%
Goodwill and intangible assets		$ 438,896				$ 513,258				$ 438,896	$ 513,258	$ 622,440
[1]	Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.
[2]	Certain amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

Segment Information - Summary o

Segment Information - Summary of net premiums written and earned by major line of business and net premiums written by location (Details) - USD ($) $ in Thousands		3 Months Ended								12 Months Ended
		Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Segment Reporting Information [Line Items]
Net premiums earned		$ 1,515,882	$ 1,438,023	$ 1,463,727	$ 1,368,866	$ 1,369,435	$ 1,290,878	$ 1,336,763	$ 1,234,899	$ 5,786,498	$ 5,231,975	$ 4,844,532
Net premiums written		$ 1,455,453	$ 1,613,457	$ 1,444,898	$ 1,525,259	$ 1,301,754	$ 1,333,553	$ 1,298,896	$ 1,412,544	6,039,067	5,346,747	4,961,373
Other
Segment Reporting Information [Line Items]
Net premiums earned										556,689	578,862	531,727
Net premiums written										532,862	604,175	553,117
Other | United States
Segment Reporting Information [Line Items]
Net premiums written										127,176	49,800	11,750
Other | Europe
Segment Reporting Information [Line Items]
Net premiums written										52,065	91,635	91,463
Other | Bermuda
Segment Reporting Information [Line Items]
Net premiums written										353,621	462,740	449,904
Other | Other specialty
Segment Reporting Information [Line Items]
Net premiums earned	[1],[2]									185,547	204,485	135,855
Other | Casualty
Segment Reporting Information [Line Items]
Net premiums earned	[2],[3]									246,894	277,589	333,275
Other | Property excluding property catastrophe
Segment Reporting Information [Line Items]
Net premiums earned	[2]									3,503	2,802	1,392
Other | Property catastrophe
Segment Reporting Information [Line Items]
Net premiums earned	[2]									13,399	10,998	12,690
Other | Other
Segment Reporting Information [Line Items]
Net premiums earned	[2],[4]									107,346	82,988	48,515
Underwriting segments
Segment Reporting Information [Line Items]
Net premiums earned										5,229,809	4,653,113	4,312,805
Net premiums written										5,506,205	4,742,572	4,408,256
Underwriting segments | Insurance
Segment Reporting Information [Line Items]
Net premiums earned										2,397,080	2,205,661	2,113,018
Net premiums written										2,641,726	2,212,125	2,122,440
Underwriting segments | Insurance | United States
Segment Reporting Information [Line Items]
Net premiums written	[5]									1,983,476	1,736,651	1,715,467
Underwriting segments | Insurance | Europe
Segment Reporting Information [Line Items]
Net premiums written	[5]									559,214	401,974	344,836
Underwriting segments | Insurance | Other geographic location
Segment Reporting Information [Line Items]
Net premiums written	[5]									99,036	73,500	62,137
Underwriting segments | Insurance | Professional lines
Segment Reporting Information [Line Items]
Net premiums earned	[6]									499,224	458,425	444,137
Underwriting segments | Insurance | Programs
Segment Reporting Information [Line Items]
Net premiums earned	[5]									414,103	389,186	364,639
Underwriting segments | Insurance | Property, energy, marine and aviation
Segment Reporting Information [Line Items]
Net premiums earned	[5]									298,966	205,069	173,779
Underwriting segments | Insurance | Construction and national accounts
Segment Reporting Information [Line Items]
Net premiums earned	[5],[7]									325,687	322,440	324,517
Underwriting segments | Insurance | Travel, accident and health
Segment Reporting Information [Line Items]
Net premiums earned	[5]									305,085	297,147	257,358
Underwriting segments | Insurance | Excess and surplus casualty
Segment Reporting Information [Line Items]
Net premiums earned	[5]									200,615	172,424	195,154
Underwriting segments | Insurance | Lenders products
Segment Reporting Information [Line Items]
Net premiums earned	[5]									66,079	94,248	97,043
Underwriting segments | Insurance | Other
Segment Reporting Information [Line Items]
Net premiums earned	[5],[8]									287,321	266,722	256,391
Underwriting segments | Reinsurance
Segment Reporting Information [Line Items]
Net premiums earned										1,466,389	1,261,216	1,142,621
Net premiums written										1,602,723	1,372,572	1,174,474
Underwriting segments | Reinsurance | United States
Segment Reporting Information [Line Items]
Net premiums written	[9]									529,943	413,550	399,379
Underwriting segments | Reinsurance | Bermuda
Segment Reporting Information [Line Items]
Net premiums written	[9]									578,618	487,523	350,681
Underwriting segments | Reinsurance | Europe and other
Segment Reporting Information [Line Items]
Net premiums written										494,162	471,499	424,414
Underwriting segments | Reinsurance | Other specialty
Segment Reporting Information [Line Items]
Net premiums earned	[9],[10]									478,517	474,568	408,566
Underwriting segments | Reinsurance | Casualty
Segment Reporting Information [Line Items]
Net premiums earned	[9],[11]									429,288	347,034	341,122
Underwriting segments | Reinsurance | Property excluding property catastrophe
Segment Reporting Information [Line Items]
Net premiums earned	[9],[12]									362,841	287,788	255,453
Underwriting segments | Reinsurance | Property catastrophe
Segment Reporting Information [Line Items]
Net premiums earned	[9]									90,934	75,249	73,300
Underwriting segments | Reinsurance | Marine and aviation
Segment Reporting Information [Line Items]
Net premiums earned	[9]									48,274	39,238	36,214
Underwriting segments | Reinsurance | Other
Segment Reporting Information [Line Items]
Net premiums earned	[9],[13]									56,535	37,339	27,966
Underwriting segments | Mortgage
Segment Reporting Information [Line Items]
Net premiums earned										1,366,340	1,186,236	1,057,166
Net premiums written										1,261,756	1,157,875	1,111,342
Underwriting segments | Mortgage | United States
Segment Reporting Information [Line Items]
Net premiums earned										1,134,849	1,009,765	901,858
Net premiums written										1,032,868	948,323	903,329
Underwriting segments | Mortgage | Other geographic location
Segment Reporting Information [Line Items]
Net premiums earned										231,491	176,471	155,308
Net premiums written										$ 228,888	$ 209,552	$ 208,013
[1]	Includes proportional motor and other.
[2]	Other segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.
[3]	Includes professional liability, excess motor, programs and other.
[4]	Includes mortgage and other.
[5]	Insurance segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.
[6]	Includes professional liability, executive assurance and healthcare business.
[7]	Includes casualty and contract binding business.
[8]	Includes alternative markets, excess workers' compensation and surety business.
[9]	Reinsurance segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.
[10]	Includes proportional motor, surety, accident and health, workers’ compensation catastrophe, agriculture, trade credit and other.
[11]	Includes executive assurance, professional liability, workers’ compensation, excess motor, healthcare and other.
[12]	Includes life, casualty clash and other.
[13]	Includes life, casualty clash and other.

Reserve for Losses and Loss A_3

Reserve for Losses and Loss Adjustment Expenses - Reconciliation of beginning and ending balances of losses and loss adjustment reserves (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]
Reserve for losses and loss adjustment expenses at beginning of year		$ 11,853,297	$ 11,383,792	$ 10,200,960
Unpaid losses and loss adjustment expenses recoverable		2,814,291	2,464,910	2,083,575
Net reserve for losses and loss adjustment expenses at beginning of year		9,039,006	8,918,882	8,117,385
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year		3,297,037	3,162,818	3,205,428
Prior years		(163,585)	(272,712)	(237,982)
Total net incurred losses and loss adjustment expenses		3,133,452	2,890,106	2,967,446
Net losses and loss adjustment expense reserves of acquired business	[1]	209,486	0	0
Retroactive reinsurance transaction	[2]	(225,500)	(420,404)	0
Foreign exchange (gains) losses		36,003	(143,414)	186,963
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year		(621,202)	(524,048)	(505,424)
Prior years		(1,762,053)	(1,682,116)	(1,847,488)
Total net paid losses and loss adjustment expenses		(2,383,255)	(2,206,164)	(2,352,912)
Net reserve for losses and loss adjustment expenses at end of year		9,809,192	9,039,006	8,918,882
Unpaid losses and loss adjustment expenses recoverable		4,082,650	2,814,291	2,464,910
Reserve for losses and loss adjustment expenses at end of year		$ 13,891,842	$ 11,853,297	$ 11,383,792
[1]	The 2019 amount primarily related to the acquisition of Barbican.
[2]	During the 2019 first quarter and 2018 second quarter, a subsidiary of the Company entered into two separate retroactive reinsurance transactions with third party reinsurers to reinsure run-off liabilities associated with certain U.S. insurance exposures.

Reserve for Losses and Loss A_4

Reserve for Losses and Loss Adjustment Expenses - Prior years reserve development (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	$ (163,585)	$ (272,712)	$ (237,982)
Other
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	23,800	(2,200)	31,000
Underwriting segments | Reinsurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	$ (46,400)	$ (138,500)	$ (165,400)
Prior year reserve development (points)	3.20%	11.00%	14.50%
Underwriting segments | Reinsurance | Short-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	$ (70,500)	$ (110,400)	$ (101,000)
Underwriting segments | Reinsurance | Short-tailed lines | Property catastrophe and property other than property catastrophe
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	(33,700)	(80,800)	(82,600)
Underwriting segments | Reinsurance | Short-tailed lines | Other specialty lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	(40,800)
Underwriting segments | Reinsurance | Medium-tailed and long-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)		(28,100)	(64,400)
Underwriting segments | Reinsurance | Medium-tailed and long-tailed lines | Casualty
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)		(12,500)	(43,700)
Underwriting segments | Reinsurance | Medium-tailed and long-tailed lines | Marine and aviation
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)		(15,600)	(19,600)
Underwriting segments | Reinsurance | Long-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	40,100
Underwriting segments | Reinsurance | Long-tailed lines | Casualty
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	44,500
Underwriting segments | Reinsurance | Medium-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	(16,000)
Underwriting segments | Insurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	$ (15,800)	$ (24,400)	$ (8,600)
Prior year reserve development (points)	7.00%	1.10%	4.00%
Underwriting segments | Insurance | Short-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	$ (54,900)	$ (48,400)	$ (14,900)
Underwriting segments | Insurance | Short-tailed lines | Property
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)		(50,100)	(22,800)
Underwriting segments | Insurance | Short-tailed lines | Travel, accident and health
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)		5,000	11,800
Underwriting segments | Insurance | Medium-tailed and long-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	39,100
Underwriting segments | Insurance | Medium-tailed and long-tailed lines | Programs
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	30,100
Underwriting segments | Insurance | Medium-tailed and long-tailed lines | Professional liability
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	(19,300)
Underwriting segments | Insurance | Medium-tailed and long-tailed lines | Surety
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	(15,800)
Underwriting segments | Insurance | Medium-tailed and long-tailed lines | Contract binding
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	33,600
Underwriting segments | Insurance | Long-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)		(26,300)	(11,800)
Underwriting segments | Insurance | Long-tailed lines | Casualty
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)		(1,400)	(8,300)
Underwriting segments | Insurance | Long-tailed lines | Executive assurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)		(19,700)	(10,000)
Underwriting segments | Insurance | Long-tailed lines | Professional liability
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)			(36,200)
Underwriting segments | Insurance | Medium-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)		50,300	18,100
Underwriting segments | Insurance | Medium-tailed lines | Programs
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)			56,300
Underwriting segments | Insurance | Medium-tailed lines | Contract binding
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)		50,300
Underwriting segments | Mortgage
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	$ (125,200)	$ (107,600)	$ (95,000)
Prior year reserve development (points)	9.20%	9.10%	9.00%
Underwriting segments | Mortgage | Primary mortgage business
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year reserve development favorable (unfavorable)	$ (117,100)	$ (103,400)	$ (89,300)

Short Duration Contracts - Clai

Short Duration Contracts - Claims development - Insurance (Details) $ in Thousands	Dec. 31, 2019USD ($)claims	Dec. 31, 2018USD ($)	Dec. 31, 2017USD ($)	Dec. 31, 2015USD ($)	Dec. 31, 2014USD ($)	Dec. 31, 2013USD ($)	Dec. 31, 2012USD ($)	Dec. 31, 2011USD ($)	Dec. 31, 2010USD ($)	Dec. 31, 2009USD ($)
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance	$ 9,536,526
Insurance | Property, energy, marine and aviation
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	1,527,721
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,219,882
All outstanding liabilities before 2008, net of reinsurance	32,875
Liabilities for losses and loss adjustment expenses, net of reinsurance	340,714
Insurance | Property, energy, marine and aviation | 2010
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	118,570	$ 120,813	$ 124,974	$ 127,530	$ 128,799	$ 128,475	$ 139,757	$ 151,937	$ 187,305	$ 197,399
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	116,822	119,276	118,437	119,953	117,737	110,892	105,887	87,476	65,846	28,433
Total of IBNR liabilities plus expected development on reported claims	$ 1,310
Cumulative number of reported claims | claims	3,676
Insurance | Property, energy, marine and aviation | 2011
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 198,370	198,956	198,763	205,344	208,494	217,753	229,244	269,790	266,725
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	196,056	196,272	195,613	199,943	198,128	165,950	140,555	98,616	34,002
Total of IBNR liabilities plus expected development on reported claims	$ 868
Cumulative number of reported claims | claims	4,219
Insurance | Property, energy, marine and aviation | 2012
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 178,394	188,649	190,930	194,746	197,187	203,408	229,820	230,399
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	173,058	179,138	177,945	165,488	159,862	137,179	92,034	20,301
Total of IBNR liabilities plus expected development on reported claims	$ 2,487
Cumulative number of reported claims | claims	4,266
Insurance | Property, energy, marine and aviation | 2013
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 128,247	132,211	132,839	140,967	146,777	154,313	156,936
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	123,696	123,392	120,385	118,131	109,088	83,689	31,874
Total of IBNR liabilities plus expected development on reported claims	$ 752
Cumulative number of reported claims | claims	4,279
Insurance | Property, energy, marine and aviation | 2014
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 129,973	133,482	134,055	145,065	143,825	146,391
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	99,041	86,518	83,080	76,774	53,060	25,620
Total of IBNR liabilities plus expected development on reported claims	$ 6,769
Cumulative number of reported claims | claims	3,930
Insurance | Property, energy, marine and aviation | 2015
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 97,361	102,221	102,535	108,260	110,867
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	88,433	84,964	75,340	63,990	23,271
Total of IBNR liabilities plus expected development on reported claims	$ 5,669
Cumulative number of reported claims | claims	4,613
Insurance | Property, energy, marine and aviation | 2016
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 100,542	104,246	99,899	102,910
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	97,674	97,147	82,357	24,442
Total of IBNR liabilities plus expected development on reported claims	$ 560
Cumulative number of reported claims | claims	6,388
Insurance | Property, energy, marine and aviation | 2017
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 235,152	247,072	278,549
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	196,290	138,525	29,915
Total of IBNR liabilities plus expected development on reported claims	$ 14,830
Cumulative number of reported claims | claims	6,744
Insurance | Property, energy, marine and aviation | 2018
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 179,262	185,486
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	102,798	29,641
Total of IBNR liabilities plus expected development on reported claims	$ 29,117
Cumulative number of reported claims | claims	5,333
Insurance | Property, energy, marine and aviation | 2019
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 161,850
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	26,014
Total of IBNR liabilities plus expected development on reported claims	$ 59,863
Cumulative number of reported claims | claims	5,688
Insurance | Third party occurrence business
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 3,413,519
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,330,399
All outstanding liabilities before 2008, net of reinsurance	181,719
Liabilities for losses and loss adjustment expenses, net of reinsurance	2,264,839
Insurance | Third party occurrence business | 2010
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	211,046	218,374	215,332	223,618	229,534	233,204	230,859	230,710	235,241	217,431
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	158,370	148,140	142,380	132,818	117,250	102,391	72,696	45,550	25,511	6,753
Total of IBNR liabilities plus expected development on reported claims	$ 33,176
Cumulative number of reported claims | claims	62,757
Insurance | Third party occurrence business | 2011
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 233,563	239,395	246,721	253,598	252,227	258,348	253,691	240,406	233,958
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	171,744	160,326	152,472	134,342	113,283	73,268	43,309	25,142	7,006
Total of IBNR liabilities plus expected development on reported claims	$ 44,601
Cumulative number of reported claims | claims	71,101
Insurance | Third party occurrence business | 2012
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 242,454	242,648	252,497	257,059	270,603	267,980	262,373	240,917
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	153,263	142,932	129,369	108,087	83,193	58,387	30,799	6,962
Total of IBNR liabilities plus expected development on reported claims	$ 60,258
Cumulative number of reported claims | claims	65,806
Insurance | Third party occurrence business | 2013
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 271,116	275,101	281,437	301,403	306,358	296,492	282,629
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	162,910	148,951	122,043	101,148	71,328	29,214	6,842
Total of IBNR liabilities plus expected development on reported claims	$ 74,749
Cumulative number of reported claims | claims	66,990
Insurance | Third party occurrence business | 2014
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 341,595	340,408	342,455	338,194	335,281	329,448
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	188,871	161,780	112,434	71,397	40,232	9,204
Total of IBNR liabilities plus expected development on reported claims	$ 98,049
Cumulative number of reported claims | claims	75,526
Insurance | Third party occurrence business | 2015
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 388,744	394,268	398,185	391,198	358,478
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	179,435	139,283	88,383	44,522	11,112
Total of IBNR liabilities plus expected development on reported claims	$ 146,656
Cumulative number of reported claims | claims	77,727
Insurance | Third party occurrence business | 2016
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 397,914	406,785	393,991	389,333
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	135,617	87,424	41,893	11,684
Total of IBNR liabilities plus expected development on reported claims	$ 193,182
Cumulative number of reported claims | claims	77,100
Insurance | Third party occurrence business | 2017
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 421,414	419,456	416,856
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	99,225	52,283	13,392
Total of IBNR liabilities plus expected development on reported claims	$ 254,057
Cumulative number of reported claims | claims	82,458
Insurance | Third party occurrence business | 2018
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 450,950	434,854
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	62,762	16,994
Total of IBNR liabilities plus expected development on reported claims	$ 315,814
Cumulative number of reported claims | claims	74,221
Insurance | Third party occurrence business | 2019
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 454,723
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	18,202
Total of IBNR liabilities plus expected development on reported claims	$ 390,054
Cumulative number of reported claims | claims	62,988
Insurance | Third party claims-made business
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 2,820,289
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,721,336
All outstanding liabilities before 2008, net of reinsurance	126,168
Liabilities for losses and loss adjustment expenses, net of reinsurance	1,225,121
Insurance | Third party claims-made business | 2010
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	284,427	283,530	280,497	298,444	314,388	331,006	338,238	332,779	311,709	286,202
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	252,119	241,887	233,085	229,824	213,530	197,142	162,490	127,531	70,583	13,811
Total of IBNR liabilities plus expected development on reported claims	$ 8,775
Cumulative number of reported claims | claims	12,335
Insurance | Third party claims-made business | 2011
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 279,909	284,242	281,487	294,367	315,118	309,684	314,961	323,369	281,448
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	259,416	248,524	235,181	223,458	204,215	171,354	128,011	71,038	13,510
Total of IBNR liabilities plus expected development on reported claims	$ 14,003
Cumulative number of reported claims | claims	11,762
Insurance | Third party claims-made business | 2012
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 272,826	271,663	268,765	283,903	305,362	310,359	312,143	309,654
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	240,281	221,391	204,240	185,656	160,480	117,891	67,314	17,307
Total of IBNR liabilities plus expected development on reported claims	$ 17,820
Cumulative number of reported claims | claims	14,759
Insurance | Third party claims-made business | 2013
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 271,290	286,280	288,506	313,738	317,165	313,601	295,759
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	230,377	212,488	193,704	175,328	134,509	85,442	18,557
Total of IBNR liabilities plus expected development on reported claims	$ 29,604
Cumulative number of reported claims | claims	14,542
Insurance | Third party claims-made business | 2014
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 287,424	278,182	273,876	293,467	275,172	260,698
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	223,907	204,330	170,331	127,683	62,308	13,572
Total of IBNR liabilities plus expected development on reported claims	$ 42,805
Cumulative number of reported claims | claims	13,935
Insurance | Third party claims-made business | 2015
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 246,366	257,902	271,343	272,413	254,540
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	168,664	124,381	98,371	51,064	8,845
Total of IBNR liabilities plus expected development on reported claims	$ 43,026
Cumulative number of reported claims | claims	13,815
Insurance | Third party claims-made business | 2016
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 304,266	306,837	286,677	270,537
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	156,030	125,740	67,446	10,371
Total of IBNR liabilities plus expected development on reported claims	$ 81,707
Cumulative number of reported claims | claims	15,716
Insurance | Third party claims-made business | 2017
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 300,710	284,875	266,526
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	111,532	66,582	9,180
Total of IBNR liabilities plus expected development on reported claims	$ 131,795
Cumulative number of reported claims | claims	15,904
Insurance | Third party claims-made business | 2018
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 301,247	272,655
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	67,567	12,123
Total of IBNR liabilities plus expected development on reported claims	$ 177,552
Cumulative number of reported claims | claims	14,934
Insurance | Third party claims-made business | 2019
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 271,824
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	11,443
Total of IBNR liabilities plus expected development on reported claims	$ 224,119
Cumulative number of reported claims | claims	9,698
Insurance | Multi-line and other specialty
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 3,606,029
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	2,742,139
All outstanding liabilities before 2008, net of reinsurance	23,337
Liabilities for losses and loss adjustment expenses, net of reinsurance	887,227
Insurance | Multi-line and other specialty | 2010
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	150,342	151,951	153,598	153,526	154,716	158,092	166,892	169,307	176,796	173,984
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	146,413	146,482	146,357	143,459	140,372	135,981	125,897	111,143	91,265	$ 49,906
Total of IBNR liabilities plus expected development on reported claims	$ 2,508
Cumulative number of reported claims | claims	37,891
Insurance | Multi-line and other specialty | 2011
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 169,467	169,851	168,243	171,691	171,923	175,794	182,213	187,924	182,372
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	161,887	158,902	156,619	151,126	147,466	136,078	117,372	102,910	$ 51,145
Total of IBNR liabilities plus expected development on reported claims	$ 3,097
Cumulative number of reported claims | claims	44,881
Insurance | Multi-line and other specialty | 2012
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 243,042	246,482	246,077	254,155	255,055	257,420	263,326	252,699
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	235,461	232,064	230,929	222,024	208,372	189,330	165,305	$ 78,178
Total of IBNR liabilities plus expected development on reported claims	$ 4,255
Cumulative number of reported claims | claims	55,403
Insurance | Multi-line and other specialty | 2013
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 247,659	252,713	251,187	263,097	262,837	271,603	263,349
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	235,784	233,572	224,665	212,713	179,785	150,432	$ 86,403
Total of IBNR liabilities plus expected development on reported claims	$ 7,096
Cumulative number of reported claims | claims	71,701
Insurance | Multi-line and other specialty | 2014
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 312,400	316,047	317,161	317,210	324,736	300,962
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	290,702	279,950	265,927	232,950	196,081	$ 107,529
Total of IBNR liabilities plus expected development on reported claims	$ 11,578
Cumulative number of reported claims | claims	109,295
Insurance | Multi-line and other specialty | 2015
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 355,095	363,627	355,484	356,543	333,519
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	319,788	304,464	276,608	235,193	$ 137,561
Total of IBNR liabilities plus expected development on reported claims	$ 17,097
Cumulative number of reported claims | claims	147,950
Insurance | Multi-line and other specialty | 2016
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 413,668	425,281	428,530	406,309
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	360,602	339,125	302,470	$ 174,366
Total of IBNR liabilities plus expected development on reported claims	$ 25,881
Cumulative number of reported claims | claims	173,735
Insurance | Multi-line and other specialty | 2017
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 488,276	498,860	479,694
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	378,500	339,753	$ 179,777
Total of IBNR liabilities plus expected development on reported claims	$ 46,435
Cumulative number of reported claims | claims	217,360
Insurance | Multi-line and other specialty | 2018
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 621,724	573,827
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	399,443	$ 213,065
Total of IBNR liabilities plus expected development on reported claims	$ 123,652
Cumulative number of reported claims | claims	243,725
Insurance | Multi-line and other specialty | 2019
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 604,356
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	213,559
Total of IBNR liabilities plus expected development on reported claims	$ 299,028
Cumulative number of reported claims | claims	169,915

Short Duration Contracts - Cl_2

Short Duration Contracts - Claims development - Reinsurance (Details) - USD ($) $ in Thousands	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2015	Dec. 31, 2014	Dec. 31, 2013	Dec. 31, 2012	Dec. 31, 2011	Dec. 31, 2010	Dec. 31, 2009
Claims Development [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance	$ 9,536,526
Reinsurance | Casualty
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	2,152,541
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	735,064
All outstanding liabilities before 2008, net of reinsurance	290,219
Liabilities for losses and loss adjustment expenses, net of reinsurance	1,707,696
Reinsurance | Casualty | 2010
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	145,012	$ 149,360	$ 154,969	$ 158,797	$ 164,530	$ 175,107	$ 185,429	$ 193,935	$ 190,639	$ 189,406
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	108,584	106,944	98,414	90,611	79,732	69,362	51,467	37,608	20,781	2,135
Total of IBNR liabilities plus expected development on reported claims	22,988
Reinsurance | Casualty | 2011
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	127,056	125,712	128,535	134,486	137,580	141,854	146,786	152,793	149,186
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	81,596	75,747	70,578	63,712	54,298	38,315	21,541	11,403	2,300
Total of IBNR liabilities plus expected development on reported claims	23,269
Reinsurance | Casualty | 2012
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	121,306	118,026	109,376	114,660	124,626	136,540	140,694	142,523
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	69,776	59,423	47,732	36,497	25,468	14,648	8,458	1,294
Total of IBNR liabilities plus expected development on reported claims	32,311
Reinsurance | Casualty | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	130,954	134,615	136,163	148,223	154,478	158,693	165,465
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	70,674	63,035	54,496	43,009	22,998	9,902	2,466
Total of IBNR liabilities plus expected development on reported claims	39,769
Reinsurance | Casualty | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	238,510	228,802	232,303	218,392	221,252	216,073
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	114,226	90,965	63,376	40,763	16,038	3,912
Total of IBNR liabilities plus expected development on reported claims	52,506
Reinsurance | Casualty | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	240,762	236,743	229,481	220,835	222,008
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	96,592	70,956	47,198	20,254	4,457
Total of IBNR liabilities plus expected development on reported claims	65,978
Reinsurance | Casualty | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	264,406	249,540	226,214	213,803
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	86,681	51,641	25,643	5,735
Total of IBNR liabilities plus expected development on reported claims	73,050
Reinsurance | Casualty | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	265,751	250,550	264,219
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	59,262	29,376	6,425
Total of IBNR liabilities plus expected development on reported claims	78,119
Reinsurance | Casualty | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	292,526	278,129
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	31,572	7,579
Total of IBNR liabilities plus expected development on reported claims	167,212
Reinsurance | Casualty | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	326,258
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	16,101
Total of IBNR liabilities plus expected development on reported claims	254,304
Reinsurance | Property catastrophe
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	486,160
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	373,437
All outstanding liabilities before 2008, net of reinsurance	330
Liabilities for losses and loss adjustment expenses, net of reinsurance	113,053
Reinsurance | Property catastrophe | 2010
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	43,500	42,544	42,738	42,535	42,732	42,333	38,823	38,916	47,218	92,632
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	41,901	41,593	41,411	41,357	40,092	38,527	37,332	31,371	23,406	8,464
Total of IBNR liabilities plus expected development on reported claims	0
Reinsurance | Property catastrophe | 2011
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	140,905	141,950	146,028	148,230	148,956	152,784	165,402	183,897	203,903
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	138,911	138,355	137,967	135,928	133,439	127,960	113,275	82,065	59,545
Total of IBNR liabilities plus expected development on reported claims	0
Reinsurance | Property catastrophe | 2012
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	97,192	97,084	99,118	99,931	102,158	108,624	122,948	149,918
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	95,359	94,672	94,062	92,933	90,774	83,869	70,836	25,850
Total of IBNR liabilities plus expected development on reported claims	164
Reinsurance | Property catastrophe | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	27,532	28,400	29,119	31,664	36,133	47,409	66,695
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	27,694	27,690	27,450	25,704	23,872	19,095	12,126
Total of IBNR liabilities plus expected development on reported claims	(125)
Reinsurance | Property catastrophe | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	19,822	20,527	22,263	25,114	30,625	44,896
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	18,892	18,699	19,108	18,280	19,823	13,657
Total of IBNR liabilities plus expected development on reported claims	(10)
Reinsurance | Property catastrophe | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	2,715	4,546	10,497	16,787	32,159
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	569	1,044	784	(3,422)	(3,689)
Total of IBNR liabilities plus expected development on reported claims	184
Reinsurance | Property catastrophe | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	9,370	13,044	16,786	23,411
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	2,778	1,593	1,331	(7,324)
Total of IBNR liabilities plus expected development on reported claims	639
Reinsurance | Property catastrophe | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	42,594	45,467	78,418
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	31,558	27,463	28,735
Total of IBNR liabilities plus expected development on reported claims	(3,620)
Reinsurance | Property catastrophe | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	59,033	72,769
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	11,872	25,481
Total of IBNR liabilities plus expected development on reported claims	4,671
Reinsurance | Property catastrophe | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	43,497
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	3,903
Total of IBNR liabilities plus expected development on reported claims	15,329
Reinsurance | Property excluding property catastrophe
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	1,511,074
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,057,795
All outstanding liabilities before 2008, net of reinsurance	5,302
Liabilities for losses and loss adjustment expenses, net of reinsurance	458,581
Reinsurance | Property excluding property catastrophe | 2010
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	99,299	100,442	101,224	104,403	108,188	110,319	112,249	117,919	128,147	142,466
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	97,842	97,733	97,793	97,363	96,718	95,571	93,354	88,196	76,429	37,776
Total of IBNR liabilities plus expected development on reported claims	821
Reinsurance | Property excluding property catastrophe | 2011
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	153,198	154,519	155,539	157,811	159,117	163,262	166,987	179,479	206,803
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	150,305	149,291	149,019	148,777	147,675	145,621	141,120	121,234	47,605
Total of IBNR liabilities plus expected development on reported claims	1,531
Reinsurance | Property excluding property catastrophe | 2012
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	108,374	110,927	112,398	114,617	119,040	123,613	121,698	156,087
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	102,552	102,612	103,435	102,801	101,831	93,165	77,957	26,109
Total of IBNR liabilities plus expected development on reported claims	850
Reinsurance | Property excluding property catastrophe | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	62,423	63,616	64,397	66,121	70,499	76,856	115,375
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	61,118	55,609	53,730	52,931	49,753	42,669	25,955
Total of IBNR liabilities plus expected development on reported claims	787
Reinsurance | Property excluding property catastrophe | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	84,134	88,436	90,708	99,198	117,304	143,307
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	78,659	78,271	76,632	71,691	62,790	23,500
Total of IBNR liabilities plus expected development on reported claims	3,430
Reinsurance | Property excluding property catastrophe | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	187,493	188,219	183,977	188,293	213,740
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	165,186	160,029	149,122	118,655	75,325
Total of IBNR liabilities plus expected development on reported claims	13,082
Reinsurance | Property excluding property catastrophe | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	136,298	137,493	145,251	176,017
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	104,085	98,708	94,875	33,282
Total of IBNR liabilities plus expected development on reported claims	19,522
Reinsurance | Property excluding property catastrophe | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	226,555	239,608	256,757
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	145,172	116,304	25,258
Total of IBNR liabilities plus expected development on reported claims	21,691
Reinsurance | Property excluding property catastrophe | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	240,094	222,345
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	107,496	29,478
Total of IBNR liabilities plus expected development on reported claims	31,217
Reinsurance | Property excluding property catastrophe | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	213,206
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	45,380
Total of IBNR liabilities plus expected development on reported claims	94,880
Reinsurance | Marine and aviation
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	292,398
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	177,613
All outstanding liabilities before 2008, net of reinsurance	17,110
Liabilities for losses and loss adjustment expenses, net of reinsurance	131,895
Reinsurance | Marine and aviation | 2010
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	28,347	28,521	30,331	31,160	31,910	33,524	35,428	38,520	42,297	40,973
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	27,118	27,119	27,544	27,182	26,535	20,220	18,478	16,752	13,402	8,523
Total of IBNR liabilities plus expected development on reported claims	32
Reinsurance | Marine and aviation | 2011
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	23,783	24,863	27,253	27,188	28,785	32,405	35,848	32,910	39,323
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	21,965	21,903	21,979	16,626	15,952	19,231	16,529	12,121	4,420
Total of IBNR liabilities plus expected development on reported claims	1,541
Reinsurance | Marine and aviation | 2012
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	43,000	46,019	49,697	51,053	52,261	55,027	58,857	59,013
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	38,010	37,719	36,232	35,033	33,294	27,518	11,434	2,657
Total of IBNR liabilities plus expected development on reported claims	4,052
Reinsurance | Marine and aviation | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	34,084	34,528	35,265	35,364	36,796	37,841	39,025
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	24,155	23,778	22,510	21,500	18,511	13,845	4,932
Total of IBNR liabilities plus expected development on reported claims	8,204
Reinsurance | Marine and aviation | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	23,270	23,635	25,633	27,334	29,140	30,949
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	15,016	14,583	12,410	11,538	7,946	4,151
Total of IBNR liabilities plus expected development on reported claims	6,819
Reinsurance | Marine and aviation | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	30,822	31,770	31,831	37,614	33,831
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	22,663	20,888	19,052	13,436	5
Total of IBNR liabilities plus expected development on reported claims	5,769
Reinsurance | Marine and aviation | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	19,279	23,569	22,752	27,366
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	3,258	523	(1,676)	(7,317)
Total of IBNR liabilities plus expected development on reported claims	10,917
Reinsurance | Marine and aviation | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	23,806	26,342	28,796
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	9,339	6,516	1,657
Total of IBNR liabilities plus expected development on reported claims	10,283
Reinsurance | Marine and aviation | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	26,206	28,164
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	7,015	2,001
Total of IBNR liabilities plus expected development on reported claims	13,754
Reinsurance | Marine and aviation | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	39,801
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	9,074
Total of IBNR liabilities plus expected development on reported claims	23,090
Reinsurance | Other specialty
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	2,118,981
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,490,454
All outstanding liabilities before 2008, net of reinsurance	9,262
Liabilities for losses and loss adjustment expenses, net of reinsurance	637,789
Reinsurance | Other specialty | 2010
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	21,171	21,382	21,990	22,222	22,461	22,821	23,827	26,070	32,881	43,160
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	19,818	19,802	19,783	19,165	18,943	18,366	17,584	16,559	13,424	$ 4,049
Total of IBNR liabilities plus expected development on reported claims	670
Reinsurance | Other specialty | 2011
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	86,232	85,812	87,708	88,313	89,670	91,553	93,206	97,229	112,256
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	82,787	83,080	81,984	79,803	78,073	74,604	69,981	57,832	$ 28,875
Total of IBNR liabilities plus expected development on reported claims	2,679
Reinsurance | Other specialty | 2012
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	188,044	193,811	195,632	192,692	194,895	200,482	210,448	221,101
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	172,137	170,374	166,066	161,902	154,202	143,106	120,600	$ 45,128
Total of IBNR liabilities plus expected development on reported claims	12,317
Reinsurance | Other specialty | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	210,201	210,698	213,089	212,088	215,711	225,620	251,978
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	182,911	175,474	170,279	160,651	144,491	118,642	$ 56,857
Total of IBNR liabilities plus expected development on reported claims	15,212
Reinsurance | Other specialty | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	248,573	246,896	251,960	258,738	256,819	275,419
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	213,450	202,401	195,903	182,625	146,900	$ 68,948
Total of IBNR liabilities plus expected development on reported claims	19,791
Reinsurance | Other specialty | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	197,337	196,972	199,726	201,558	210,183
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	154,816	145,820	138,794	114,768	$ 54,762
Total of IBNR liabilities plus expected development on reported claims	24,609
Reinsurance | Other specialty | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	210,053	215,354	221,177	223,625
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	174,625	162,836	138,782	$ 64,928
Total of IBNR liabilities plus expected development on reported claims	26,895
Reinsurance | Other specialty | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	255,873	265,098	275,721
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	197,699	167,782	$ 74,926
Total of IBNR liabilities plus expected development on reported claims	44,453
Reinsurance | Other specialty | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	328,750	333,228
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	208,755	$ 74,550
Total of IBNR liabilities plus expected development on reported claims	80,916
Reinsurance | Other specialty | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	372,747
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	83,456
Total of IBNR liabilities plus expected development on reported claims	$ 170,179

Short Duration Contracts - Cl_3

Short Duration Contracts - Claims development - Mortgage (Details)	12 Months Ended
	Dec. 31, 2019USD ($)claims	Dec. 31, 2018USD ($)	Dec. 31, 2017USD ($)	Dec. 31, 2016USD ($)	Dec. 31, 2015USD ($)	Dec. 31, 2014USD ($)	Dec. 31, 2013USD ($)	Dec. 31, 2012USD ($)
Claims Development [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance	$ 9,536,526,000
Mortgage
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	1,750,243,000
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,514,010,000
All outstanding liabilities before 2012, net of reinsurance	19,005,000
Liabilities for losses and loss adjustment expenses, net of reinsurance	255,238,000
Large claim size threshold	250,000
Mortgage | 2012
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	456,286,000	$ 458,065,000	$ 459,467,000	$ 467,296,000	$ 469,238,000	$ 475,317,000	$ 480,592,000	$ 520,835,000
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	452,348,000	448,151,000	441,577,000	426,024,000	395,695,000	327,605,000	186,605,000	$ (106,065,000)
Total of IBNR liabilities plus expected development on reported claims	$ 46,000
Cumulative number of paid claims | claims	15,052
Mortgage | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 390,987,000	393,149,000	395,693,000	405,809,000	411,793,000	419,668,000	469,311,000
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	386,853,000	382,200,000	373,909,000	353,189,000	308,956,000	203,957,000	$ 41,447,000
Total of IBNR liabilities plus expected development on reported claims	$ 38,000
Cumulative number of paid claims | claims	9,445
Mortgage | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 261,091,000	265,992,000	266,027,000	279,434,000	297,151,000	316,095,000
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	254,175,000	247,038,000	233,879,000	201,925,000	129,159,000	$ 20,099,000
Total of IBNR liabilities plus expected development on reported claims	$ 68,000
Cumulative number of paid claims | claims	6,250
Mortgage | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 189,235,000	194,677,000	198,001,000	197,238,000	222,790,000
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	180,321,000	171,337,000	151,222,000	92,431,000	$ 16,159,000
Total of IBNR liabilities plus expected development on reported claims	$ 67,000
Cumulative number of paid claims | claims	4,490
Mortgage | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 140,608,000	148,715,000	170,532,000	183,556,000
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	127,286,000	113,357,000	72,201,000	$ 11,462,000
Total of IBNR liabilities plus expected development on reported claims	$ 111,000
Cumulative number of paid claims | claims	3,334
Mortgage | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 107,255,000	132,220,000	179,376,000
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	78,650,000	48,112,000	$ 8,622,000
Total of IBNR liabilities plus expected development on reported claims	$ 212,000
Cumulative number of paid claims | claims	2,241
Mortgage | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 96,357,000	132,318,000
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	31,478,000	$ 3,966,000
Total of IBNR liabilities plus expected development on reported claims	$ 616,000
Cumulative number of paid claims | claims	1,006
Mortgage | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 108,424,000
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	2,899,000
Total of IBNR liabilities plus expected development on reported claims	$ 11,315,000
Cumulative number of paid claims | claims	87

Short Duration Contracts - Perc

Short Duration Contracts - Percentage annual payout - all segments (Details)	Dec. 31, 2019
Insurance | Property, energy, marine and aviation
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	19.10%
Year Two	39.10%
Year Three	19.20%
Year Four	9.10%
Year Five	5.30%
Year Six	5.10%
Year Seven	0.10%
Year Eight	(1.50%)
Year Nine	0.30%
Year Ten	(2.10%)
Insurance | Third party occurrence business
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	3.10%
Year Two	8.80%
Year Three	10.90%
Year Four	12.00%
Year Five	12.30%
Year Six	8.50%
Year Seven	6.50%
Year Eight	4.10%
Year Nine	3.80%
Year Ten	4.80%
Insurance | Third party claims-made business
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	4.60%
Year Two	19.30%
Year Three	19.10%
Year Four	13.40%
Year Five	11.60%
Year Six	6.60%
Year Seven	5.70%
Year Eight	4.30%
Year Nine	3.50%
Year Ten	3.60%
Insurance | Multi-line and other specialty
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	35.20%
Year Two	29.90%
Year Three	10.50%
Year Four	9.40%
Year Five	5.40%
Year Six	3.20%
Year Seven	1.70%
Year Eight	1.60%
Year Nine	0.90%
Year Ten	0.00%
Reinsurance | Casualty
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	2.20%
Year Two	7.50%
Year Three	9.70%
Year Four	11.40%
Year Five	10.80%
Year Six	8.00%
Year Seven	7.10%
Year Eight	6.00%
Year Nine	5.20%
Year Ten	1.10%
Reinsurance | Property catastrophe
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	10.70%
Year Two	25.50%
Year Three	28.80%
Year Four	9.20%
Year Five	(0.70%)
Year Six	1.70%
Year Seven	1.20%
Year Eight	0.40%
Year Nine	0.40%
Year Ten	0.70%
Reinsurance | Property catastrophe and property other than property catastrophe
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	27.20%
Year Two	38.80%
Year Three	11.60%
Year Four	5.30%
Year Five	1.70%
Year Six	1.20%
Year Seven	2.20%
Year Eight	0.20%
Year Nine	0.30%
Year Ten	0.10%
Reinsurance | Marine and aviation
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	8.70%
Year Two	25.00%
Year Three	17.30%
Year Four	9.10%
Year Five	2.40%
Year Six	6.70%
Year Seven	7.30%
Year Eight	0.50%
Year Nine	(0.60%)
Year Ten	0.00%
Reinsurance | Other specialty
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	26.40%
Year Two	35.70%
Year Three	12.90%
Year Four	5.50%
Year Five	3.90%
Year Six	2.80%
Year Seven	2.40%
Year Eight	1.70%
Year Nine	(0.10%)
Year Ten	0.10%
Mortgage
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	3.30%
Year Two	42.30%
Year Three	29.10%
Year Four	11.80%
Year Five	5.40%
Year Six	2.80%
Year Seven	1.30%
Year Eight	0.90%

Short Duration Contracts - Reco

Short Duration Contracts - Reconciliation of claims development to liability (Details) - USD ($) $ in Thousands		Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		$ 9,536,526
Unpaid losses and loss adjustment expenses recoverable		4,082,650	$ 2,814,291	$ 2,464,910	$ 2,083,575
Lines other than short duration		55,989
Discounting		(22,012)
Unallocated claims adjustment expenses		188,055
Total reconciling items		222,032
Reserve for losses and loss adjustment expenses		13,891,842	$ 11,853,297	$ 11,383,792	$ 10,200,960
Other short duration lines not included
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance	[1]	1,514,373
Unpaid losses and loss adjustment expenses recoverable	[2],[3]	1,472,777
Other short duration lines not included | Loss portfolio transfer
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Unpaid losses and loss adjustment expenses recoverable	[2],[3]	319,300
Total for short duration lines
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Unpaid losses and loss adjustment expenses recoverable		4,133,284
Insurance | Property, energy, marine and aviation
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		340,714
Unpaid losses and loss adjustment expenses recoverable		213,004
Insurance | Third party occurrence business
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		2,264,839
Unpaid losses and loss adjustment expenses recoverable		1,105,669
Insurance | Third party claims-made business
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		1,225,121
Unpaid losses and loss adjustment expenses recoverable		728,511
Insurance | Multi-line and other specialty
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		887,227
Unpaid losses and loss adjustment expenses recoverable		189,613
Reinsurance | Casualty
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		1,707,696
Unpaid losses and loss adjustment expenses recoverable		532,387
Reinsurance | Property catastrophe
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		113,053
Unpaid losses and loss adjustment expenses recoverable		282,910
Reinsurance | Property excluding property catastrophe
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		458,581
Unpaid losses and loss adjustment expenses recoverable		48,554
Reinsurance | Marine and aviation
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		131,895
Unpaid losses and loss adjustment expenses recoverable		28,893
Reinsurance | Other specialty
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		637,789
Unpaid losses and loss adjustment expenses recoverable		206,022
Mortgage
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		255,238
Unpaid losses and loss adjustment expenses recoverable		21,875
Consolidating adjustments and eliminations
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Unpaid losses and loss adjustment expenses recoverable		(696,931)
Other | Other short duration lines not included
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance	[1]	$ 1,100,000
[1]	Includes net outstanding liabilities of $1.1 billion
[2]	$319.3 million related to the loss portfolio transfer reinsurance agreement.
[3]	Includes unpaid loss and loss adjustment expenses recoverable

Reinsurance - Effects of reinsu

Reinsurance - Effects of reinsurance (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Premiums Written
Direct									$ 5,681,523	$ 4,838,902	$ 4,447,457
Assumed									2,457,437	2,122,102	1,920,968
Ceded									(2,099,893)	(1,614,257)	(1,407,052)
Net premiums written	$ 1,455,453	$ 1,613,457	$ 1,444,898	$ 1,525,259	$ 1,301,754	$ 1,333,553	$ 1,298,896	$ 1,412,544	6,039,067	5,346,747	4,961,373
Premiums Earned
Direct									5,447,829	4,799,842	4,379,131
Assumed									2,337,950	1,988,038	1,856,573
Ceded									(1,999,281)	(1,555,905)	(1,391,172)
Net premiums earned	$ 1,515,882	$ 1,438,023	$ 1,463,727	$ 1,368,866	$ 1,369,435	$ 1,290,878	$ 1,336,763	$ 1,234,899	5,786,498	5,231,975	4,844,532
Losses and Loss Adjustment Expenses
Direct									2,953,072	2,472,133	2,568,327
Assumed									1,602,528	1,307,317	1,442,077
Ceded									(1,422,148)	(889,344)	(1,042,958)
Net									$ 3,133,452	$ 2,890,106	$ 2,967,446

Reinsurance - Ceded credit risk

Reinsurance - Ceded credit risk (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2019	Dec. 31, 2018
Concentration Risk [Line Items]
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses		$ 4,346,816	$ 2,919,372
Concentration risk percentage		10.00%
Credit concentration risk | Reinsurance recoverable | Unrated fully collateralized reinsurers
Concentration Risk [Line Items]
Concentration risk percentage	[1]	13.50%	12.90%
Reinsurer concentration risk | Stockholders' equity
Concentration Risk [Line Items]
Concentration risk percentage		1.70%	2.70%
AM Best A minus Or Better Rating | Credit concentration risk | Reinsurance recoverable
Concentration Risk [Line Items]
Concentration risk percentage		61.20%	63.00%
Not Rated | Credit concentration risk | Reinsurance recoverable
Concentration Risk [Line Items]
Concentration risk percentage	[2]	25.30%	24.10%
Reinsurance trusts or letters of credit | Not Rated | Credit concentration risk | Reinsurance recoverable
Concentration Risk [Line Items]
Concentration risk percentage		90.00%
[1]	Such amount is fully collateralized through reinsurance trusts
[2]	Over 90% of such amount is collateralized through reinsurance trusts or letters of credit.

Reinsurance - Coverage and rete

Reinsurance - Coverage and retention (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2019		Dec. 31, 2018
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Amortization period		10 years
Variable Interest Entity, Not Primary Beneficiary
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Coverage		$ 3,425,833		$ 1,881,467
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2017-1 Ltd. (Oct-17)
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Aggregate reinsurance agreement	[1]	368,114
Coverage		216,429	[1]	304,373
First layer retention	[1]	165,652
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-1 Ltd. (Apr-18)
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Aggregate reinsurance agreement	[2]	374,460
Coverage		328,482	[2]	374,460
First layer retention	[2]	168,510
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-2 Ltd. (Aug-18)
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Aggregate reinsurance agreement	[3]	653,278
Coverage	[3]	437,009
First layer retention	[3]	352,258
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-3 Ltd. (Oct-18)
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Aggregate reinsurance agreement	[4]	506,110
Coverage		426,806	[4]	$ 506,110
First layer retention	[4]	179,331
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-1 Ltd. (Mar-19)
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Aggregate reinsurance agreement	[5]	341,790
Coverage	[5]	257,358
First layer retention	[5]	208,046
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-2 Ltd. (Apr-19)
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Aggregate reinsurance agreement	[6]	621,022
Coverage	[6]	525,959
First layer retention	[6]	221,794
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-3 Ltd. (Jul-19)
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Aggregate reinsurance agreement	[7]	700,920
Coverage	[7]	656,523
First layer retention	[7]	232,093
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-4 Ltd. (Oct-19)
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Aggregate reinsurance agreement	[8]	577,267
Coverage	[8]	577,267
First layer retention	[8]	$ 162,357
[1]	Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017.
[2]	Issued in April 2018, covering in-force policies issued between July 1, 2017 and December 31, 2017.
[3]	Issued in August 2018, covering in-force policies issued between April 1, 2013 and December 31, 2015.
[4]	Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018.
[5]	Issued in March 2019, covering in-force policies primarily issued between 2005 to 2008 under United Guaranty Residential Insurance Company (“UGRIC”); as well as policies issued through 2015 under both UGRIC and Arch Mortgage Insurance Company.
[6]	Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018.
[7]	Issued in July 2019, covering in-force policies issued in 2016.
[8]	Issued in October 2019, covering in-force policies issued between January 1, 2019 and June 30, 2019.

Investment Information - Summar

Investment Information - Summary of Available for Sale Securities (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2019	Dec. 31, 2018
Available for sale securities:
Estimated Fair Value		$ 18,219,582	$ 15,908,390
Gross Unrealized Gains		351,114	76,259
Gross Unrealized Losses		(55,003)	(205,900)
Cost or Amortized Cost		17,923,471	16,038,031
OTTI Unrealized Losses		(6)	(75)
Fixed maturities and fixed maturities pledged under securities lending agreements
Available for sale securities:
Estimated Fair Value		17,263,036	14,952,510
Gross Unrealized Gains		350,303	76,223
Gross Unrealized Losses		(53,455)	(205,506)
Cost or Amortized Cost		16,966,188	15,081,793
OTTI Unrealized Losses	[1]	(6)	(75)
Fixed maturities and fixed maturities pledged under securities lending agreements | Corporate bonds
Available for sale securities:
Estimated Fair Value		6,406,591	5,537,548
Gross Unrealized Gains	[2]	191,889	14,476
Gross Unrealized Losses	[2]	(12,793)	(105,428)
Cost or Amortized Cost		6,227,495	5,628,500
OTTI Unrealized Losses	[1]	0	(69)
Fixed maturities and fixed maturities pledged under securities lending agreements | Mortgage backed securities
Available for sale securities:
Estimated Fair Value		562,309	541,193
Gross Unrealized Gains	[2]	9,669	3,991
Gross Unrealized Losses	[2]	(931)	(3,216)
Cost or Amortized Cost		553,571	540,418
OTTI Unrealized Losses	[1]	(6)	(6)
Fixed maturities and fixed maturities pledged under securities lending agreements | Municipal bonds
Available for sale securities:
Estimated Fair Value		881,926	1,013,395
Gross Unrealized Gains	[2]	24,628	5,380
Gross Unrealized Losses	[2]	(2,213)	(11,891)
Cost or Amortized Cost		859,511	1,019,906
OTTI Unrealized Losses	[1]	0	0
Fixed maturities and fixed maturities pledged under securities lending agreements | Commercial mortgage backed securities
Available for sale securities:
Estimated Fair Value		733,108	729,442
Gross Unrealized Gains	[2]	14,951	2,650
Gross Unrealized Losses	[2]	(2,330)	(10,751)
Cost or Amortized Cost		720,487	737,543
OTTI Unrealized Losses	[1]	0	0
Fixed maturities and fixed maturities pledged under securities lending agreements | US government and government agencies
Available for sale securities:
Estimated Fair Value		4,916,592	3,758,698
Gross Unrealized Gains	[2]	36,600	27,189
Gross Unrealized Losses	[2]	(10,134)	(8,474)
Cost or Amortized Cost		4,890,126	3,739,983
OTTI Unrealized Losses	[1]	0	0
Fixed maturities and fixed maturities pledged under securities lending agreements | Non-US government securities
Available for sale securities:
Estimated Fair Value		2,078,757	1,771,338
Gross Unrealized Gains	[2]	48,549	14,477
Gross Unrealized Losses	[2]	(20,330)	(50,948)
Cost or Amortized Cost		2,050,538	1,807,809
OTTI Unrealized Losses	[1]	0	0
Fixed maturities and fixed maturities pledged under securities lending agreements | Asset backed securities
Available for sale securities:
Estimated Fair Value		1,683,753	1,600,896
Gross Unrealized Gains	[2]	24,017	8,060
Gross Unrealized Losses	[2]	(4,724)	(14,798)
Cost or Amortized Cost		1,664,460	1,607,634
OTTI Unrealized Losses	[1]	0	0
Short-term investments
Available for sale securities:
Estimated Fair Value		956,546	955,880
Gross Unrealized Gains		811	36
Gross Unrealized Losses		(1,548)	(394)
Cost or Amortized Cost		957,283	956,238
OTTI Unrealized Losses		$ 0	$ 0
[1]	Represents the total OTTI recognized in accumulated other comprehensive income (“AOCI”). It does not include the change in fair value subsequent to the impairment measurement date. At December 31, 2019 and 2018, the net unrealized gain related to securities for which a non-credit OTTI was recognized in AOCI was nil
[2]	In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

Investment Information - Aging

Investment Information - Aging of Available For Sale Securities in an Unrealized Loss Position (Details) - USD ($) $ in Thousands		Dec. 31, 2019		Dec. 31, 2018
Available for sale securities:
Estimated Fair Value - Less than 12 Months		$ 4,280,273		$ 5,843,772
Gross Unrealized Losses - Less than 12 Months		(52,926)		(120,614)
Estimated Fair Value - 12 Months or More		158,538		3,094,853
Gross Unrealized Losses - 12 Months or More		(2,077)		(85,286)
Estimated Fair Value - Total		4,438,811		8,938,625
Gross Unrealized Losses - Total		(55,003)		(205,900)
Fixed maturities and fixed maturities pledged under securities lending agreements
Available for sale securities:
Estimated Fair Value - Less than 12 Months		4,184,496	[1]	5,720,894
Gross Unrealized Losses - Less than 12 Months		(51,378)	[1]	(120,220)
Estimated Fair Value - 12 Months or More		158,538	[1]	3,094,853
Gross Unrealized Losses - 12 Months or More		(2,077)	[1]	(85,286)
Estimated Fair Value - Total		4,343,034	[1]	8,815,747
Gross Unrealized Losses - Total		(53,455)	[1]	(205,506)
Fixed maturities and fixed maturities pledged under securities lending agreements | Corporate bonds
Available for sale securities:
Estimated Fair Value - Less than 12 Months	[1]	675,131		2,983,195
Gross Unrealized Losses - Less than 12 Months	[1]	(12,350)		(68,910)
Estimated Fair Value - 12 Months or More	[1]	37,671		1,234,865
Gross Unrealized Losses - 12 Months or More	[1]	(443)		(36,518)
Estimated Fair Value - Total	[1]	712,802		4,218,060
Gross Unrealized Losses - Total	[1]	(12,793)		(105,428)
Fixed maturities and fixed maturities pledged under securities lending agreements | Mortgage backed securities
Available for sale securities:
Estimated Fair Value - Less than 12 Months	[1]	102,887		84,296
Gross Unrealized Losses - Less than 12 Months	[1]	(927)		(695)
Estimated Fair Value - 12 Months or More	[1]	203		109,009
Gross Unrealized Losses - 12 Months or More	[1]	(4)		(2,521)
Estimated Fair Value - Total	[1]	103,090		193,305
Gross Unrealized Losses - Total	[1]	(931)		(3,216)
Fixed maturities and fixed maturities pledged under securities lending agreements | Municipal bonds
Available for sale securities:
Estimated Fair Value - Less than 12 Months	[1]	220,296		233,081
Gross Unrealized Losses - Less than 12 Months	[1]	(2,213)		(2,074)
Estimated Fair Value - 12 Months or More	[1]	0		408,155
Gross Unrealized Losses - 12 Months or More	[1]	0		(9,817)
Estimated Fair Value - Total	[1]	220,296		641,236
Gross Unrealized Losses - Total	[1]	(2,213)		(11,891)
Fixed maturities and fixed maturities pledged under securities lending agreements | Commercial mortgage backed securities
Available for sale securities:
Estimated Fair Value - Less than 12 Months	[1]	147,290		223,341
Gross Unrealized Losses - Less than 12 Months	[1]	(2,302)		(2,831)
Estimated Fair Value - 12 Months or More	[1]	2,683		193,956
Gross Unrealized Losses - 12 Months or More	[1]	(28)		(7,920)
Estimated Fair Value - Total	[1]	149,973		417,297
Gross Unrealized Losses - Total	[1]	(2,330)		(10,751)
Fixed maturities and fixed maturities pledged under securities lending agreements | US government and government agencies
Available for sale securities:
Estimated Fair Value - Less than 12 Months	[1]	1,373,127		635,049
Gross Unrealized Losses - Less than 12 Months	[1]	(10,089)		(1,354)
Estimated Fair Value - 12 Months or More	[1]	32,058		391,102
Gross Unrealized Losses - 12 Months or More	[1]	(45)		(7,120)
Estimated Fair Value - Total	[1]	1,405,185		1,026,151
Gross Unrealized Losses - Total	[1]	(10,134)		(8,474)
Fixed maturities and fixed maturities pledged under securities lending agreements | Non-US government securities
Available for sale securities:
Estimated Fair Value - Less than 12 Months	[1]	1,224,243		1,028,340
Gross Unrealized Losses - Less than 12 Months	[1]	(20,163)		(35,524)
Estimated Fair Value - 12 Months or More	[1]	37,610		389,671
Gross Unrealized Losses - 12 Months or More	[1]	(167)		(15,424)
Estimated Fair Value - Total	[1]	1,261,853		1,418,011
Gross Unrealized Losses - Total	[1]	(20,330)		(50,948)
Fixed maturities and fixed maturities pledged under securities lending agreements | Asset backed securities
Available for sale securities:
Estimated Fair Value - Less than 12 Months	[1]	441,522		533,592
Gross Unrealized Losses - Less than 12 Months	[1]	(3,334)		(8,832)
Estimated Fair Value - 12 Months or More	[1]	48,313		368,095
Gross Unrealized Losses - 12 Months or More	[1]	(1,390)		(5,966)
Estimated Fair Value - Total	[1]	489,835		901,687
Gross Unrealized Losses - Total	[1]	(4,724)		(14,798)
Short-term investments
Available for sale securities:
Estimated Fair Value - Less than 12 Months		95,777		122,878
Gross Unrealized Losses - Less than 12 Months		(1,548)		(394)
Estimated Fair Value - 12 Months or More		0		0
Gross Unrealized Losses - 12 Months or More		0		0
Estimated Fair Value - Total		95,777		122,878
Gross Unrealized Losses - Total		$ (1,548)		$ (394)
[1]	In securities lending transactions, the Company receives collateral in excess of the fair value of the fixed maturities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See “—Securities Lending Agreements.”

Investment Information - Maturi

Investment Information - Maturity Profile of Available For Sale Securities (Details) - USD ($) $ in Thousands	Dec. 31, 2019	Dec. 31, 2018
Estimated Fair Value:
Estimated fair value	$ 16,894,526	$ 14,699,010
Amortized Cost:
Amortized cost	16,598,808	14,829,902
Fixed maturities and fixed maturities pledged under securities lending agreements
Estimated Fair Value:
Due in one year or less	428,659	276,682
Due after one year through five years	10,126,403	8,666,297
Due after five years through 10 years	3,317,535	2,919,232
Due after 10 years	411,269	218,768
Single maturity date	14,283,866	12,080,979
Estimated fair value	17,263,036	14,952,510
Amortized Cost:
Due in one year or less	423,617	279,135
Due after one year through five years	9,996,206	8,738,944
Due after five years through 10 years	3,219,567	2,951,582
Due after 10 years	388,280	226,537
Single maturity date	14,027,670	12,196,198
Amortized cost	16,966,188	15,081,793
Fixed maturities and fixed maturities pledged under securities lending agreements | Mortgage backed securities
Estimated Fair Value:
Securities without single maturity date	562,309	541,193
Amortized Cost:
Securities without single maturity date	553,571	540,418
Fixed maturities and fixed maturities pledged under securities lending agreements | Commercial mortgage backed securities
Estimated Fair Value:
Securities without single maturity date	733,108	729,442
Amortized Cost:
Securities without single maturity date	720,487	737,543
Fixed maturities and fixed maturities pledged under securities lending agreements | Asset backed securities
Estimated Fair Value:
Securities without single maturity date	1,683,753	1,600,896
Amortized Cost:
Securities without single maturity date	$ 1,664,460	$ 1,607,634

Investment Information - Securi

Investment Information - Securities lending arrangements (Details) - USD ($) $ in Thousands	Dec. 31, 2019	Dec. 31, 2018
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Equity securities, at fair value	$ 838,925	$ 338,899
Securities lending payable	388,366	274,125
Gross amount of recognized liabilities for securities lending in offsetting disclosure in Note 10	0	0
Amounts related to securities lending not included in offsetting disclosure in Note 10	388,366	274,125
Collateral received under securities lending, at fair value	388,376	274,133
Cash and Cash Equivalents
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Collateral received under securities lending, at fair value	81,200	19,000
Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Collateral received under securities lending, at fair value	307,200	255,100
US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	356,305	251,859
Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	2,570	7,129
Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	29,491	15,137
Overnight and Continuous
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	272,393	241,542
Overnight and Continuous | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	240,332	219,276
Overnight and Continuous | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	2,570	7,129
Overnight and Continuous | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	29,491	15,137
Less than 30 Days
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
Less than 30 Days | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
Less than 30 Days | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
Less than 30 Days | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
30-90 Days
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	115,973	32,583
30-90 Days | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	115,973	32,583
30-90 Days | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
30-90 Days | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 Days or More
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 Days or More | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 Days or More | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	0	0
90 Days or More | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	$ 0	$ 0

Investment Information - Other

Investment Information - Other Investments (Details) - USD ($) $ in Thousands	Dec. 31, 2019	Dec. 31, 2018
Schedule Of Other Investments [Line Items]
Other investments and fair value option investments	$ 2,429,316	$ 2,311,939
Fair value option | Term loan investments
Schedule Of Other Investments [Line Items]
Other investments and fair value option investments	1,326,018	1,282,287
Other investments par	1,453,574	1,369,216
Fair value option | Lending
Schedule Of Other Investments [Line Items]
Other investments and fair value option investments	602,841	524,112
Fair value option | Credit related funds
Schedule Of Other Investments [Line Items]
Other investments and fair value option investments	123,020	202,123
Fair value option | Energy
Schedule Of Other Investments [Line Items]
Other investments and fair value option investments	97,402	117,509
Fair value option | Investment grade fixed income
Schedule Of Other Investments [Line Items]
Other investments and fair value option investments	151,594	101,902
Fair value option | Infrastructure
Schedule Of Other Investments [Line Items]
Other investments and fair value option investments	61,786	45,371
Fair value option | Private equity
Schedule Of Other Investments [Line Items]
Other investments and fair value option investments	49,376	24,383
Fair value option | Real estate
Schedule Of Other Investments [Line Items]
Other investments and fair value option investments	$ 17,279	$ 14,252

Investment Information - Equity

Investment Information - Equity Method Investments (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 1,660,396	$ 1,493,791
Balance sheet:
Invested assets	26,383,370	28,299,386
Total assets	28,039,181	29,833,681
Total liabilities	3,595,695	3,406,612
Net assets	24,443,486	26,427,069
Income statement:
Total revenues	164,669	4,565,354	$ 3,867,874
Total expenses	528,762	1,135,602	782,773
Net income (loss)	(364,093)	3,429,752	$ 3,085,101
Credit related funds
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	428,437	429,402
Equities
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	293,686	375,273
Real estate
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	246,851	232,647
Lending
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	202,690	125,041
Private equity
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	144,983	114,019
Infrastructure
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	235,033	113,748
Energy
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 108,716	$ 103,661

Investment Information - Fair V

Investment Information - Fair Value Option (Details) - USD ($) $ in Thousands	Dec. 31, 2019	Dec. 31, 2018
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option	$ 3,663,477	$ 3,983,571
Fixed maturities
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option	754,452	1,245,562
Other investments
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option	2,429,316	2,311,939
Short-term investments
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option	377,014	322,177
Equity securities
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option	$ 102,695	$ 103,893

Investment Information - Limite

Investment Information - Limited partnership interests (Details) - USD ($) $ in Thousands		Dec. 31, 2019	Dec. 31, 2018
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss		$ 1,848,679	$ 1,656,189
Aggregate commitments		1,690,000	1,770,000
Equity method investments
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss	[1]	1,660,396	1,493,791
Aggregate commitments		1,360,000	1,220,000
Fair value option
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss	[2]	188,283	162,398
Aggregate commitments		$ 41,700	$ 117,500
[1]	Aggregate unfunded commitments were $1.36 billion at December 31, 2019 , compared to $1.22 billion at December 31, 2018 .
[2]	Aggregate unfunded commitments were $41.7 million at December 31, 2019 , compared to $117.5 million at December 31, 2018 .

Investment Information - Net In

Investment Information - Net Investment Income (Details) - USD ($) $ in Thousands		3 Months Ended								12 Months Ended
		Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Net investment income:
Gross investment income										$ 716,643	$ 655,727	$ 562,901
Investment expenses										(88,905)	(92,094)	(92,029)
Net investment income		$ 154,263	$ 161,488	$ 155,038	$ 156,949	$ 157,217	$ 144,024	$ 135,668	$ 126,724	627,738	563,633	470,872
Fixed maturities
Net investment income:
Gross investment income										505,399	470,912	385,919
Term loan investments
Net investment income:
Gross investment income										98,949	87,926	86,017
Equity securities
Net investment income:
Gross investment income										15,857	13,154	11,752
Short-term investments
Net investment income:
Gross investment income										15,820	18,793	10,964
Other
Net investment income:
Gross investment income	[1]									$ 80,618	$ 64,942	$ 68,249
[1]	Includes income distributions from investment funds and other items.

Investment Information - Net Re

Investment Information - Net Realized Gains and Losses (Details) - USD ($) $ in Thousands		3 Months Ended								12 Months Ended
		Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Net realized gains and losses:
Available for sale securities, gross gains on investment sales										$ 235,655	$ 69,299	$ 286,415
Available for sale securities, gross losses on investment sales										(104,612)	(223,123)	(203,873)
Equity securities at fair value, net realized gains (losses) on sales during the period	[1]									11,313	(40,117)	0
Equity securities at fair value, net unrealized gains (losses) on equity securities still held at reporting date	[1]									97,768	(22,828)	0
Derivative instruments	[2]									119,741	15,636	(7,356)
Other	[3]									(19,348)	(16,090)	(25,599)
Net realized gains (losses)		$ 41,474	$ 62,518	$ 120,806	$ 141,565	$ (166,030)	$ (51,705)	$ (76,611)	$ (110,998)	366,363	(405,344)	149,141
Fixed maturities
Net realized gains and losses:
Change in fair value of assets and liabilities accounted for using the fair value option										41,910	(90,898)	29,451
Equity securities
Net realized gains and losses:
Change in fair value of assets and liabilities accounted for using the fair value option										15,869	(5,984)	18,707
Other investments
Net realized gains and losses:
Change in fair value of assets and liabilities accounted for using the fair value option										(35,734)	(90,778)	51,124
Short-term investments
Net realized gains and losses:
Change in fair value of assets and liabilities accounted for using the fair value option										$ 3,801	$ (461)	$ 272
[1]	hanges in fair value on equity securities are recorded through net income.
[2]	See Note 10 for information on the Company’s derivative instruments.
[3]	Includes the re-measurement of contingent consideration liability amounts.

Investment Information - Othe_2

Investment Information - Other Than Temporary Impairments Recognized in Earnings (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Other than Temporary Impairment, Credit Losses Recognized in Earnings [Line Items]
Net impairment losses recognized in earnings	$ (644)	$ (1,163)	$ (49)	$ (1,309)	$ (1,705)	$ (492)	$ (470)	$ (162)	$ (3,165)	$ (2,829)	$ (7,138)
Fixed maturities
Other than Temporary Impairment, Credit Losses Recognized in Earnings [Line Items]
Net impairment losses recognized in earnings									(3,165)	(2,770)	(5,549)
Fixed maturities | Mortgage backed securities
Other than Temporary Impairment, Credit Losses Recognized in Earnings [Line Items]
Net impairment losses recognized in earnings									(915)	(437)	(1,488)
Fixed maturities | Corporate bonds
Other than Temporary Impairment, Credit Losses Recognized in Earnings [Line Items]
Net impairment losses recognized in earnings									(1,256)	(1,232)	(2,884)
Fixed maturities | Non-US government securities
Other than Temporary Impairment, Credit Losses Recognized in Earnings [Line Items]
Net impairment losses recognized in earnings									0	(290)	(376)
Fixed maturities | Asset backed securities
Other than Temporary Impairment, Credit Losses Recognized in Earnings [Line Items]
Net impairment losses recognized in earnings									(994)	(811)	0
Fixed maturities | US government and government agencies
Other than Temporary Impairment, Credit Losses Recognized in Earnings [Line Items]
Net impairment losses recognized in earnings									0	0	(426)
Fixed maturities | Municipal bonds
Other than Temporary Impairment, Credit Losses Recognized in Earnings [Line Items]
Net impairment losses recognized in earnings									0	0	(375)
Short-term investments
Other than Temporary Impairment, Credit Losses Recognized in Earnings [Line Items]
Net impairment losses recognized in earnings									0	(59)	0
Equity securities
Other than Temporary Impairment, Credit Losses Recognized in Earnings [Line Items]
Net impairment losses recognized in earnings									0	0	(1,422)
Other investments
Other than Temporary Impairment, Credit Losses Recognized in Earnings [Line Items]
Net impairment losses recognized in earnings									$ 0	$ 0	$ (167)

Investment Information - Othe_3

Investment Information - Other Than Temporary Impairments Rollforward (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Rollforward:
Balance at start of year	$ 637	$ 767	$ 13,138
Credit loss impairments recognized on securities not previously impaired	0	0	31
Credit loss impairments recognized on securities previously impaired	0	0	210
Reductions for increases in cash flows expected to be collected that are recognized over the remaining life of the security	0	0	0
Reductions for securities sold during the period	(291)	(130)	(12,612)
Balance at end of year	$ 346	$ 637	$ 767

Investment Information - Restri

Investment Information - Restricted Assets (Details) - USD ($) $ in Thousands	Dec. 31, 2019	Dec. 31, 2018
Restricted Assets [Line Items]
Restricted assets	$ 7,721,618	$ 7,553,903
Collateral or guarantees - affiliated transactions
Restricted Assets [Line Items]
Restricted assets	4,526,761	4,623,483
Collateral or guarantees - third party agreements
Restricted Assets [Line Items]
Restricted assets	2,278,248	2,181,682
Deposits with US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	797,371	689,114
Deposits with non-US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	119,238	59,624
Watford Holdings Ltd
Restricted Assets [Line Items]
Assets pledged as collateral	$ 1,000,000	$ 1,300,000

Investment Information - Cash a

Investment Information - Cash and restricted cash (Details) - USD ($) $ in Thousands	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016
Disclosure Investment Information [Abstract]
Cash	$ 726,230	$ 646,556	$ 606,199
Restricted cash (included in ‘other assets’)	177,468	78,087	121,085
Cash and restricted cash	$ 903,698	$ 724,643	$ 727,284	$ 969,569

Investment Information - Narrat

Investment Information - Narrative (Details) $ in Thousands	12 Months Ended
	Dec. 31, 2019USD ($)lots	Dec. 31, 2018USD ($)lots	Dec. 31, 2017USD ($)
Segment Reporting Information [Line Items]
Investable assets	$ 24,990,265	$ 22,324,524	$ 22,156,488
OTTI unrealized losses at current fair value	$ 0	$ 0
Continuous unrealized loss, qualitative disclosures:
Number of positions in an unrealized loss position (lots) | lots	2,230	5,870
Total number of positions (lots) | lots	9,590	8,450
Largest single loss	$ 900	$ 2,600
OTTI Unrealized Losses	6	75
Equity securities, at fair value	838,925	338,899
Equity Method Investment, Financial Statement, Reported Amounts [Abstract]
Equity in net income (loss) of investment funds accounted for using the equity method	$ 123,672	$ 45,641	$ 142,286
Equity method investments, time lag for reporting - low end of range	1 month
Equity method investments, time lag for reporting - high end of range	3 months
Watford Holdings Ltd
Segment Reporting Information [Line Items]
Investable assets	$ 2,700,000
ACGL
Segment Reporting Information [Line Items]
Investable assets	$ 22,290,000

Fair Value - Fair Value Hierarc

Fair Value - Fair Value Hierarchy (Details) - Recurring - USD ($) $ in Thousands		Dec. 31, 2019	Dec. 31, 2018
Quoted Prices in Active Markets for Identical Assets (Level 1)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		$ 6,932,402	$ 5,332,640
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[2]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities and fixed maturities pledged under securities lending agreements
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		4,805,581	3,657,181
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities and fixed maturities pledged under securities lending agreements | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities and fixed maturities pledged under securities lending agreements | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities and fixed maturities pledged under securities lending agreements | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities and fixed maturities pledged under securities lending agreements | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities and fixed maturities pledged under securities lending agreements | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	4,805,581	3,657,181
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities and fixed maturities pledged under securities lending agreements | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities and fixed maturities pledged under securities lending agreements | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		789,596	321,927
Quoted Prices in Active Markets for Identical Assets (Level 1) | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		904,804	875,881
Quoted Prices in Active Markets for Identical Assets (Level 1) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		432,421	477,651
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,852	111,138
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		333,320	278,579
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		43,962	48,827
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		53,287	39,107
Significant Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		14,641,044	13,852,372
Liabilities measured at fair value		(106,007)	(28,454)
Significant Other Observable Inputs (Level 2) | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		0	0
Significant Other Observable Inputs (Level 2) | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	(66,257)	(7,790)
Significant Other Observable Inputs (Level 2) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[2]	(39,750)	(20,664)
Significant Other Observable Inputs (Level 2) | Fixed maturities and fixed maturities pledged under securities lending agreements
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		12,443,388	11,286,875
Significant Other Observable Inputs (Level 2) | Fixed maturities and fixed maturities pledged under securities lending agreements | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	6,397,740	5,529,407
Significant Other Observable Inputs (Level 2) | Fixed maturities and fixed maturities pledged under securities lending agreements | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	562,055	540,884
Significant Other Observable Inputs (Level 2) | Fixed maturities and fixed maturities pledged under securities lending agreements | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	881,926	1,013,395
Significant Other Observable Inputs (Level 2) | Fixed maturities and fixed maturities pledged under securities lending agreements | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	733,108	729,438
Significant Other Observable Inputs (Level 2) | Fixed maturities and fixed maturities pledged under securities lending agreements | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	111,011	101,517
Significant Other Observable Inputs (Level 2) | Fixed maturities and fixed maturities pledged under securities lending agreements | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	2,078,757	1,771,338
Significant Other Observable Inputs (Level 2) | Fixed maturities and fixed maturities pledged under securities lending agreements | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	1,678,791	1,600,896
Significant Other Observable Inputs (Level 2) | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		4,798	31,867
Significant Other Observable Inputs (Level 2) | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		51,742	79,999
Significant Other Observable Inputs (Level 2) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	48,946	73,893
Significant Other Observable Inputs (Level 2) | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,092,170	2,379,738
Significant Other Observable Inputs (Level 2) | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		487,470	846,827
Significant Other Observable Inputs (Level 2) | Fair value option | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		11,947	16,731
Significant Other Observable Inputs (Level 2) | Fair value option | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		377	7,144
Significant Other Observable Inputs (Level 2) | Fair value option | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,134	0
Significant Other Observable Inputs (Level 2) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		110	108
Significant Other Observable Inputs (Level 2) | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		50,465	79,066
Significant Other Observable Inputs (Level 2) | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		200,163	178,790
Significant Other Observable Inputs (Level 2) | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		43,694	43,598
Significant Other Observable Inputs (Level 2) | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		641	55,066
Significant Other Observable Inputs (Level 2) | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,296,169	1,152,408
Significant Unobservable Inputs (Level 3)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		197,799	76,917
Liabilities measured at fair value		(7,998)	(66,665)
Significant Unobservable Inputs (Level 3) | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(7,998)	(66,665)
Significant Unobservable Inputs (Level 3) | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	0	0
Significant Unobservable Inputs (Level 3) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[2]	0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities and fixed maturities pledged under securities lending agreements
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		14,067	8,454
Significant Unobservable Inputs (Level 3) | Fixed maturities and fixed maturities pledged under securities lending agreements | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	8,851	8,141
Significant Unobservable Inputs (Level 3) | Fixed maturities and fixed maturities pledged under securities lending agreements | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	254	309
Significant Unobservable Inputs (Level 3) | Fixed maturities and fixed maturities pledged under securities lending agreements | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities and fixed maturities pledged under securities lending agreements | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	0	4
Significant Unobservable Inputs (Level 3) | Fixed maturities and fixed maturities pledged under securities lending agreements | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities and fixed maturities pledged under securities lending agreements | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities and fixed maturities pledged under securities lending agreements | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	4,962	0
Significant Unobservable Inputs (Level 3) | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		55,889	0
Significant Unobservable Inputs (Level 3) | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	0	0
Significant Unobservable Inputs (Level 3) | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		127,843	68,463
Significant Unobservable Inputs (Level 3) | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		932	5,758
Significant Unobservable Inputs (Level 3) | Fair value option | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		58,094	0
Significant Unobservable Inputs (Level 3) | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		68,817	62,705
Estimated Fair Value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		22,782,288	20,319,648
Liabilities measured at fair value		(114,005)	(95,119)
Estimated Fair Value | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(7,998)	(66,665)
Estimated Fair Value | Securities sold but not yet purchased
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[1]	(66,257)	(7,790)
Estimated Fair Value | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value	[2]	(39,750)	(20,664)
Estimated Fair Value | Fixed maturities and fixed maturities pledged under securities lending agreements
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		17,263,036	14,952,510
Estimated Fair Value | Fixed maturities and fixed maturities pledged under securities lending agreements | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	6,406,591	5,537,548
Estimated Fair Value | Fixed maturities and fixed maturities pledged under securities lending agreements | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	562,309	541,193
Estimated Fair Value | Fixed maturities and fixed maturities pledged under securities lending agreements | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	881,926	1,013,395
Estimated Fair Value | Fixed maturities and fixed maturities pledged under securities lending agreements | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	733,108	729,442
Estimated Fair Value | Fixed maturities and fixed maturities pledged under securities lending agreements | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	4,916,592	3,758,698
Estimated Fair Value | Fixed maturities and fixed maturities pledged under securities lending agreements | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	2,078,757	1,771,338
Estimated Fair Value | Fixed maturities and fixed maturities pledged under securities lending agreements | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[3]	1,683,753	1,600,896
Estimated Fair Value | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		850,283	353,794
Estimated Fair Value | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		956,546	955,880
Estimated Fair Value | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[2]	48,946	73,893
Estimated Fair Value | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		3,663,477	3,983,571
Estimated Fair Value | Fair value option | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		488,402	852,585
Estimated Fair Value | Fair value option | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		11,947	16,731
Estimated Fair Value | Fair value option | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		377	7,144
Estimated Fair Value | Fair value option | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,134	0
Estimated Fair Value | Fair value option | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,962	111,246
Estimated Fair Value | Fair value option | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		50,465	79,066
Estimated Fair Value | Fair value option | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		200,163	178,790
Estimated Fair Value | Fair value option | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		377,014	322,177
Estimated Fair Value | Fair value option | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		102,697	103,893
Estimated Fair Value | Fair value option | Other investments fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,418,273	1,254,220
Estimated Fair Value | Fair value option | Other investments at net asset value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[4]	$ 1,011,043	$ 1,057,719
[1]	Represents the Company’s obligations to deliver securities that it did not own at the time of sale. Such amounts are included in “other liabilities” on the Company’s consolidated balance sheets.
[2]	See Note 10
[3]	In securities lending transactions, the Company receives collateral in excess of the fair value of the securities pledged. For purposes of this table, the Company has excluded the collateral received under securities lending, at fair value and included the securities pledged under securities lending, at fair value. See Note 8
[4]	In accordance with applicable accounting guidance, certain investments that are measured at fair value using the net asset value per share (or its equivalent) practical expedient have not been classified in the fair value hierarchy. The fair value amounts presented in this table are intended to permit reconciliation of the fair value hierarchy to the amounts presented in the consolidated balance sheets.

Fair Value - Rollforward of Lev

Fair Value - Rollforward of Level 3 assets and liabilities (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2019	Dec. 31, 2018
Contingent consideration liability
Level 3 liabilities rollforward
Balance at beginning of year		$ (66,665)	$ (60,996)
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(1,478)	(5,669)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0
Purchases, issuances, sales and settlements
Purchases		0	0
Issuances		(548)	0
Sales		0	0
Settlements		60,693	0
Transfers in and/or out of Level 3		0	0
Balance at end of year		(7,998)	(66,665)
Equity securities
Level 3 assets rollforward
Balance at beginning of year		0	0
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(3,418)	0
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0
Purchases, issuances, sales and settlements
Purchases		36,077	0
Issuances		0	0
Sales		(27,982)	0
Settlements		0	0
Transfers in and/or out of Level 3		51,212	0
Balance at end of year		55,889	0
Available for sale | Asset backed securities
Level 3 assets rollforward
Balance at beginning of year		313	5,927
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	1,760	4
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		3	(11)
Purchases, issuances, sales and settlements
Purchases		0	0
Issuances		0	0
Sales		(1,757)	(5,003)
Settlements		(552)	(604)
Transfers in and/or out of Level 3		5,449	0
Balance at end of year		5,216	313
Available for sale | Corporate bonds
Level 3 assets rollforward
Balance at beginning of year		8,141	9,460
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	2	(1)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		(267)	(296)
Purchases, issuances, sales and settlements
Purchases		881	802
Issuances		0	0
Sales		0	0
Settlements		(1,766)	(1,824)
Transfers in and/or out of Level 3		1,860	0
Balance at end of year		8,851	8,141
Fair value option | Corporate bonds
Level 3 assets rollforward
Balance at beginning of year		5,758	12,217
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(162)	(334)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0
Purchases, issuances, sales and settlements
Purchases		0	0
Issuances		0	0
Sales		(28,583)	0
Settlements		0	(6,125)
Transfers in and/or out of Level 3		23,919	0
Balance at end of year		932	5,758
Fair value option | Other investments
Level 3 assets rollforward
Balance at beginning of year		62,705	59,167
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(8,119)	(1,416)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0
Purchases, issuances, sales and settlements
Purchases		3,746	6,250
Issuances		0	0
Sales		(20,495)	(296)
Settlements		(600)	(1,000)
Transfers in and/or out of Level 3		31,580	0
Balance at end of year		68,817	62,705
Fair value option | Equity securities
Level 3 assets rollforward
Balance at beginning of year		0	0
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	1,949	0
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0
Purchases, issuances, sales and settlements
Purchases		0	0
Issuances		0	0
Sales		0	0
Settlements		0	0
Transfers in and/or out of Level 3		56,145	0
Balance at end of year		$ 58,094	$ 0
[1]	Gains or losses were included in net realized gains (losses).

Fair Value - Narrative (Details

Fair Value - Narrative (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Senior notes	$ 1,871,626	$ 1,733,528
Total assets and liabilities measured at fair value	22,900,000	20,400,000
Total assets and liabilities measured at fair value priced using non-binding broker quotes	$ 179,600	$ 217,900
Total assets and liabilities measured at fair value priced using non-binding broker quotes (percentage)	0.80%	1.10%
Unsecured debt | Senior Notes
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Senior notes	$ 1,870,000	$ 1,730,000
Estimated fair value of senior notes	2,340,000	$ 1,880,000
Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Asset Transfers Into Level 3	107,400
Other investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Asset Transfers Into Level 3	31,600
Corporate bonds | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Asset Transfers Into Level 3	$ 25,800

Derivative Instruments (Details

Derivative Instruments (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Derivative offsetting [Abstract]
Derivative assets subject to master netting agreements		$ 97,800	$ 80,400
Derivative liabilities subject to master netting agreements		37,800	18,900
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments	[1]	119,741	15,636	$ (7,356)
Not Designated as Hedging Instrument
Derivative [Line Items]
Asset derivatives - fair value		103,956	82,185
Liability derivatives - fair value		(39,750)	(20,664)
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		119,741	15,636	(7,356)
Not Designated as Hedging Instrument | Futures contracts
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		114,123	48,443	9,318
Not Designated as Hedging Instrument | Futures contracts | Other investments available for sale, at fair value
Derivative [Line Items]
Asset derivatives - fair value	[2]	10,065	51,800
Liability derivatives - fair value	[2]	(13,722)	(2,115)
Net derivatives - notional value	[2],[3]	4,104,559	3,153,518
Not Designated as Hedging Instrument | Foreign currency forward contracts
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(9,499)	(21,770)	(14,495)
Not Designated as Hedging Instrument | Foreign currency forward contracts | Other investments available for sale, at fair value
Derivative [Line Items]
Asset derivatives - fair value	[2]	5,352	8,147
Liability derivatives - fair value	[2]	(5,327)	(7,796)
Net derivatives - notional value	[2],[3]	686,878	1,008,907
Not Designated as Hedging Instrument | TBAs
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		463	(133)	9
Not Designated as Hedging Instrument | TBAs | Fixed maturities available for sale, at fair value
Derivative [Line Items]
Asset derivatives - fair value	[4]	55,010	8,292
Liability derivatives - fair value	[4]	0	0
Net derivatives - notional value	[3],[4]	53,229	8,132
Not Designated as Hedging Instrument | Other
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		14,654	(10,904)	$ (2,188)
Not Designated as Hedging Instrument | Other | Other investments available for sale, at fair value
Derivative [Line Items]
Asset derivatives - fair value	[2]	33,529	13,946
Liability derivatives - fair value	[2]	(20,701)	(10,753)
Net derivatives - notional value	[2],[3]	$ 4,356,300	$ 2,213,981
[1]	See Note 10 for information on the Company’s derivative instruments.
[2]	The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’ Such amounts include risk in force on GSE credit-risk sharing transactions that are accounted for as derivatives.
[3]	Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.
[4]	The fair value of TBAs are included in ‘fixed maturities available for sale, at fair value.’

Variable Interest Entity and _3

Variable Interest Entity and Noncontrolling Interests - Variable interest entity (Details) - USD ($) $ in Thousands	1 Months Ended	3 Months Ended	12 Months Ended
	Mar. 31, 2014	Mar. 31, 2014	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Variable Interest Entity [Line Items]
Proceeds on issuance of preference shares			$ 0	$ 0	$ 319,694
Watford Holdings Ltd | Variable Interest Entity, Primary Beneficiary
Variable Interest Entity [Line Items]
Initial capitalization amount		$ 1,100,000
Proceeds from from common shares issued, net	$ 895,600
Proceeds on issuance of preference shares	219,200
Initial investment contribution amount	$ 100,000
Number of shares acquired	2,500,000	2,500,000
Number of shares called by warrants	975,503	975,503
Ownership percentage			13.00%
Watford Holdings Ltd | Variable Interest Entity, Primary Beneficiary | Common shares
Variable Interest Entity [Line Items]
Initial capitalization amount		$ 907,300
Watford Holdings Ltd | Variable Interest Entity, Primary Beneficiary | Preference equity
Variable Interest Entity [Line Items]
Initial capitalization amount		$ 226,600

Variable Interest Entity and _4

Variable Interest Entity and Noncontrolling Interests - Carrying amount of assets and liabilities of variable interest entity (Details) - USD ($) $ in Thousands	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016
Assets
Investments accounted for using the fair value option	$ 3,663,477	$ 3,983,571
Fixed maturities available for sale, at fair value	16,894,526	14,699,010
Equity securities, at fair value	838,925	338,899
Cash	726,230	646,556	$ 606,199
Accrued investment income	117,937	114,641
Premiums receivable	1,778,717	1,299,150
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	4,346,816	2,919,372
Ceded unearned premiums	1,234,683	975,469
Deferred acquisition costs	633,400	569,574
Receivable for securities sold	24,133	36,246
Goodwill and intangible assets	738,083	634,920	652,611
Other assets	1,383,788	929,611
Total assets of consolidated VIE	37,885,361	32,218,329	32,051,658
Liabilities
Reserve for losses and loss adjustment expenses	13,891,842	11,853,297	11,383,792	$ 10,200,960
Unearned premiums	4,339,549	3,753,636
Reinsurance balances payable	667,072	393,107
Revolving credit agreement borrowings	484,287	455,682
Senior notes	1,871,626	1,733,528
Payable for securities purchased	87,579	90,034
Other liabilities	1,513,330	911,500
Total liabilities of consolidated VIE	25,569,809	21,780,650	$ 21,805,723
Watford Holdings Ltd | Variable Interest Entity, Primary Beneficiary
Assets
Investments accounted for using the fair value option	1,898,091	2,312,003
Fixed maturities available for sale, at fair value	745,708	393,351
Equity securities, at fair value	65,338	32,206
Cash	102,437	63,529
Accrued investment income	14,025	19,461
Premiums receivable	273,657	227,301
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	170,973	86,445
Ceded unearned premiums	132,577	61,587
Deferred acquisition costs	64,044	80,858
Receivable for securities sold	16,287	24,507
Goodwill and intangible assets	7,650	7,650
Other assets	60,070	63,959
Total assets of consolidated VIE	3,550,857	3,372,857
Liabilities
Reserve for losses and loss adjustment expenses	1,263,628	1,032,760
Unearned premiums	438,907	390,114
Reinsurance balances payable	77,066	21,034
Revolving credit agreement borrowings	484,287	455,682
Senior notes	172,418	0
Payable for securities purchased	18,180	60,142
Other liabilities	171,714	302,524
Total liabilities of consolidated VIE	2,626,200	2,262,256
Redeemable noncontrolling interests	$ 52,305	$ 220,992

Variable Interest Entity and _5

Variable Interest Entity and Noncontrolling Interests - Cash flows of variable interest entity (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Variable Interest Entity [Line Items]
Net Cash Provided by (Used in) Operating Activities	$ 2,048,459	$ 1,559,322	$ 1,094,878
Net cash provided by (used for) investing activities	(1,806,483)	(554,020)	(1,351,882)
Net cash provided by (used for) financing activities	(80,662)	(988,810)	(3,405)
Watford Holdings Ltd | Variable Interest Entity, Primary Beneficiary
Variable Interest Entity [Line Items]
Net Cash Provided by (Used in) Operating Activities	239,284	229,315	286,558
Net cash provided by (used for) investing activities	(140,620)	(285,281)	(467,418)
Net cash provided by (used for) financing activities	$ (61,433)	$ (2,406)	$ 162,152

Variable Interest Entity and _6

Variable Interest Entity and Noncontrolling Interests - Non-redeemable noncontrolling interest (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interest, beginning of year	$ 791,560	$ 843,411
Amounts attributable to nonredeemable noncontrolling interests	(40,072)	48,507	$ 7,913
Non-redeemable noncontrolling interest, end of year	762,777	791,560	843,411
Watford Holdings Ltd | Noncontrolling Interest
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interest, beginning of year	791,560	843,411
Additional paid in capital attributable to non-redeemable noncontrolling interests	(2,929)	0
Repurchases attributable to non-redeemable noncontrolling interests (1)	(75,056)	0
Amounts attributable to nonredeemable noncontrolling interests	40,072	(48,507)
Other comprehensive (income) loss attributable to non-redeemable noncontrolling interests	9,130	(3,344)
Non-redeemable noncontrolling interest, end of year	$ 762,777	$ 791,560	$ 843,411
Common shares | Watford Holdings Ltd | Noncontrolling Interest
Noncontrolling Interest [Line Items]
Noncontrolling interest, ownership percentage by noncontrolling owners	87.00%

Variable Interest Entity and _7

Variable Interest Entity and Noncontrolling Interests - Redeemable noncontrolling interest (Details) - USD ($) $ / shares in Units, $ in Thousands	Aug. 01, 2019	Mar. 31, 2014	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017	Jul. 31, 2019
Redeemable Noncontrolling Interest [Line Items]
Balance, beginning of year			$ 206,292	$ 205,922	$ 205,553
Redemption of redeemable noncontrolling interests			(157,709)	0	0
Accretion of preference share issuance costs			244	370	369
Other			6,577	0	0
Balance, end of year			$ 55,404	206,292	205,922
Preferred shares, par value per share			$ 0.01
Watford Holdings Ltd
Redeemable Noncontrolling Interest [Line Items]
Preferred dividends including accretion of discount and issuance costs			$ 17,800	$ 19,600	$ 19,600
Redeemable Preferred Stock [Member] | Watford Holdings Ltd
Redeemable Noncontrolling Interest [Line Items]
Preferred shares, par value per share		$ 0.01
Liquidation preference per share		25
Shares Issued, Price Per Share		$ 24.50
Preferred shares, dividend rate (as a percent)		8.50%
Redeemable Preferred Stock [Member] | Watford Holdings Ltd | 3 month US dollar LIBOR
Redeemable Noncontrolling Interest [Line Items]
Preferred shares, dividend rate (as a percent)		1.00%
Variable Interest Entity, Primary Beneficiary | Watford Holdings Ltd
Redeemable Noncontrolling Interest [Line Items]
Preference shares, number of shares issued						9,065,200
Stock Redeemed or Called During Period, Shares	6,919,998
Preferred shares, redemption price per share	$ 25.19748
Proceeds from Redemption Of Preferred Shares By Variable Interest Entity	$ 11,500

Variable Interest Entity and _8

Variable Interest Entity and Noncontrolling Interests - Income or loss attributable to third party investors (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Noncontrolling Interest [Line Items]
Amounts attributable to non-redeemable noncontrolling interests	$ (40,072)	$ 48,507	$ 7,913
Dividends attributable to redeemable noncontrolling interests	(16,909)	(18,357)	(18,344)
Net (income) loss attributable to noncontrolling interests	(56,981)	30,150	(10,431)
Other
Noncontrolling Interest [Line Items]
Amounts attributable to non-redeemable noncontrolling interests	(40,072)	48,507	7,913
Dividends attributable to redeemable noncontrolling interests	(16,909)	(18,357)	(18,344)
Net (income) loss attributable to noncontrolling interests	$ (56,981)	$ 30,150	$ (10,431)

Variable Interest Entity and _9

Variable Interest Entity and Noncontrolling Interests - Other variable interest entity disclosures (Details) - USD ($) $ in Thousands		Dec. 31, 2019		Dec. 31, 2018
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		$ 1,848,679		$ 1,656,189
Variable Interest Entity, Not Primary Beneficiary
Variable Interest Entity [Line Items]
Total VIE Assets		3,425,833		1,881,467
Maximum Exposure to Loss		36,887		12,942
Variable Interest Entity, Not Primary Beneficiary | On Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		(5,197)		1,752
Variable Interest Entity, Not Primary Beneficiary | Off Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		42,084		11,190
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2015-1 Ltd. (Jul-15)
Variable Interest Entity [Line Items]
Total VIE Assets				43,246
Maximum Exposure to Loss				610
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2015-1 Ltd. (Jul-15) | On Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss				112
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2015-1 Ltd. (Jul-15) | Off Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss				498
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2017-1 Ltd. (Oct-17)
Variable Interest Entity [Line Items]
Total VIE Assets		216,429	[1]	304,373
Maximum Exposure to Loss		2,352		1,477
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2017-1 Ltd. (Oct-17) | On Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		(442)		165
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2017-1 Ltd. (Oct-17) | Off Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		2,794		1,312
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-1 Ltd. (Apr-18)
Variable Interest Entity [Line Items]
Total VIE Assets		328,482	[2]	374,460
Maximum Exposure to Loss		4,183		3,671
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-1 Ltd. (Apr-18) | On Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		(1,574)		132
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-1 Ltd. (Apr-18) | Off Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		5,757		3,539
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-2 Ltd. (Aug-18)
Variable Interest Entity [Line Items]
Total VIE Assets		437,009		653,278
Maximum Exposure to Loss		1,647		4,879
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-2 Ltd. (Aug-18) | On Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		(877)		874
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-2 Ltd. (Aug-18) | Off Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		2,524		4,005
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-3 Ltd. (Oct-18)
Variable Interest Entity [Line Items]
Total VIE Assets		426,806	[3]	506,110
Maximum Exposure to Loss		2,824		2,305
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-3 Ltd. (Oct-18) | On Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		(1,113)		469
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-3 Ltd. (Oct-18) | Off Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		3,937		$ 1,836
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-1 Ltd. (Mar-19)
Variable Interest Entity [Line Items]
Total VIE Assets	[4]	257,358
Maximum Exposure to Loss		2,801
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-1 Ltd. (Mar-19) | On Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		(226)
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-1 Ltd. (Mar-19) | Off Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		3,027
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-2 Ltd. (Apr-19)
Variable Interest Entity [Line Items]
Total VIE Assets	[5]	525,959
Maximum Exposure to Loss		2,501
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-2 Ltd. (Apr-19) | On Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		(78)
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-2 Ltd. (Apr-19) | Off Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		2,579
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-3 Ltd. (Jul-19)
Variable Interest Entity [Line Items]
Total VIE Assets	[6]	656,523
Maximum Exposure to Loss		8,688
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-3 Ltd. (Jul-19) | On Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		(585)
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-3 Ltd. (Jul-19) | Off Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		9,273
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-4 Ltd. (Oct-19)
Variable Interest Entity [Line Items]
Total VIE Assets	[7]	577,267
Maximum Exposure to Loss		11,891
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-4 Ltd. (Oct-19) | On Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		(302)
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-4 Ltd. (Oct-19) | Off Balance Sheet
Variable Interest Entity [Line Items]
Maximum Exposure to Loss		$ 12,193
[1]	Issued in October 2017, covering in-force policies issued between January 1, 2017 and June 30, 2017.
[2]	Issued in April 2018, covering in-force policies issued between July 1, 2017 and December 31, 2017.
[3]	Issued in October 2018, covering in-force policies issued between January 1, 2018 and June 30, 2018.
[4]	Issued in March 2019, covering in-force policies primarily issued between 2005 to 2008 under United Guaranty Residential Insurance Company (“UGRIC”); as well as policies issued through 2015 under both UGRIC and Arch Mortgage Insurance Company.
[5]	Issued in April 2019, covering in-force policies issued between July 1, 2018 and December 31, 2018.
[6]	Issued in July 2019, covering in-force policies issued in 2016.
[7]	Issued in October 2019, covering in-force policies issued between January 1, 2019 and June 30, 2019.

Other Comprehensive Income - C

Other Comprehensive Income - Components of accumulated other comprehensive income (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	$ (178,720)	$ 118,044	$ (114,541)
Cumulative effect of an accounting change		(149,794)
Other comprehensive income (loss) before reclassifications	509,752	(291,543)	300,448
Amounts reclassified from accumulated other comprehensive income	(118,941)	144,573	(67,863)
Net current period other comprehensive income (loss)	390,811	(146,970)	232,585
Ending balance	212,091	(178,720)	118,044
Unrealized Appreciation on Available-For-Sale Investments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(114,178)	157,400	(27,641)
Cumulative effect of an accounting change	0	(149,794)	0
Other comprehensive income (loss) before reclassifications	491,605	(266,357)	252,904
Amounts reclassified from accumulated other comprehensive income	(118,941)	144,573	(67,863)
Net current period other comprehensive income (loss)	372,664	(121,784)	185,041
Ending balance	258,486	(114,178)	157,400
Foreign Currency Translation Adjustments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(64,542)	(39,356)	(86,900)
Cumulative effect of an accounting change		0
Other comprehensive income (loss) before reclassifications	18,147	(25,186)	47,544
Amounts reclassified from accumulated other comprehensive income	0	0	0
Net current period other comprehensive income (loss)	18,147	(25,186)	47,544
Ending balance	$ (46,395)	$ (64,542)	$ (39,356)

Other Comprehensive Income - A

Other Comprehensive Income - Amounts reclassified from accumulated other comprehensive income (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Reclassification out of Accumulated Other Comprehensive Income [Line Items]
Other-than-temporary impairment losses	$ (644)	$ (1,163)	$ (49)	$ (1,309)	$ (1,705)	$ (492)	$ (470)	$ (162)	$ (3,165)	$ (2,829)	$ (7,138)
Income (loss) before income taxes									1,849,110	841,772	757,277
Income tax (expense) benefit									(155,810)	(113,951)	(127,568)
Net of tax									1,636,319	757,971	619,278
Reclassification out of accumulated other comprehensive income | Unrealized Appreciation on Available-For-Sale Investments
Reclassification out of Accumulated Other Comprehensive Income [Line Items]
Net realized gains									131,043	(153,822)	82,542
Other-than-temporary impairment losses									(3,165)	(2,829)	(7,138)
Income (loss) before income taxes									127,878	(156,651)	75,404
Income tax (expense) benefit									(8,937)	12,078	(7,541)
Net of tax									$ 118,941	$ (144,573)	$ 67,863

Other Comprehensive Income -_2

Other Comprehensive Income - Components of other comprehensive income (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Before tax amount:
Unrealized holding gains (losses) arising during period, before tax	$ 562,576	$ (294,267)	$ 266,559
Less reclassification of net realized gains (losses) included in net income, before tax	127,878	(156,651)	75,404
Foreign currency translation adjustments, before tax	18,463	(25,006)	47,549
Other comprehensive income (loss), before tax	453,161	(162,622)	238,704
Tax expense (benefit):
Unrealized holding gains (losses) arising during period, tax	61,805	(24,210)	13,655
Less reclassification of net realized gains (losses) included in net income, tax	8,937	(12,078)	7,541
Foreign currency translation adjustments, tax	353	(176)	535
Other comprehensive income (loss), tax	53,221	(12,308)	6,649
Net of tax amount:
Unrealized holding gains (losses) arising during period, net of tax	500,771	(270,057)	252,904
Less reclassification of net realized gains (losses) included in net income, net of tax	118,941	(144,573)	67,863
Foreign currency translation adjustments, net of tax	18,110	(24,830)	47,014
Net current period other comprehensive income (loss)	$ 399,940	$ (150,314)	$ 232,055

Earnings Per Common Share (Deta

Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended								12 Months Ended
		Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Numerator:
Net income		$ 326,384	$ 392,453	$ 468,954	$ 448,528	$ 136,494	$ 227,408	$ 243,646	$ 150,423	$ 1,693,300	$ 727,821	$ 629,709
Net (income) loss attributable to noncontrolling interests										(56,981)	30,150	(10,431)
Net income available to Arch										1,636,319	757,971	619,278
Preferred dividends		(10,403)	(10,403)	(10,403)	(10,403)	(10,403)	(10,402)	(10,403)	(10,437)	(41,612)	(41,645)	(46,041)
Loss on redemption of preferred shares										0	(2,710)	(6,735)
Net income available to Arch common shareholders		$ 315,981	$ 382,050	$ 458,551	$ 438,125	$ 126,091	$ 217,006	$ 233,243	$ 137,276	$ 1,594,707	$ 713,616	$ 566,502
Denominator:
Weighted average common shares outstanding										401,802,815	401,036,376	377,531,628
Series D preferred securities	[1]									0	3,311,245	26,606,736
Weighted average common shares outstanding — basic										401,802,815	404,347,621	404,138,364
Effect of dilutive common share equivalents:
Nonvested restricted shares										1,673,770	1,474,207	3,936,594
Stock options	[2]									8,132,893	7,084,650	9,710,067
Weighted average common shares and common share equivalents outstanding — diluted										411,609,478	412,906,478	417,785,025
Earnings per common share:
Basic (per share)		$ 0.78	$ 0.95	$ 1.14	$ 1.09	$ 0.31	$ 0.54	$ 0.58	$ 0.34	$ 3.97	$ 1.76	$ 1.40
Diluted (per share)		$ 0.76	$ 0.92	$ 1.12	$ 1.07	$ 0.31	$ 0.53	$ 0.56	$ 0.33	$ 3.87	$ 1.73	$ 1.36
Stock Options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)										1,302,017	5,673,821	2,603,451
[1]	The company has determined that, based on a review of the terms, features and rights of the Company’s non-voting common equivalent preferred shares compared to the rights of the Company’s common shareholders, the underlying common shares that the convertible securities convert to were common share equivalents at the time of their issuance.
[2]	Certain stock options were not included in the computation of diluted earnings per share where the exercise price of the stock options exceeded the average market price and would have been anti-dilutive or where, when applying the treasury stock method to in-the-money options, the sum of the proceeds, including unrecognized compensation, exceeded the average market price and would have been anti-dilutive. For 2019 , 2018 and 2017 , the number of stock options excluded were 1,302,017 , 5,673,821 and 2,603,451 , respectively.

Income Taxes - Components of in

Income Taxes - Components of income tax (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Current expense (benefit):
United States	$ 139,407	$ 73,078	$ (51,705)
Non-U.S.	4,954	12,785	5,969
Current Income Tax Expense (Benefit)	144,361	85,863	(45,736)
Deferred expense (benefit):
United States	11,849	19,544	169,093
Non-U.S.	(400)	8,544	4,211
Deferred Income Tax Expense (Benefit)	11,449	28,088	173,304
Income tax expense (benefit)	$ 155,810	$ 113,951	$ 127,568

Income Taxes - Income before ta

Income Taxes - Income before taxes by jurisdiction (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Income Tax Disclosure [Line Items]
Income (loss) before income taxes	$ 1,849,110	$ 841,772	$ 757,277
Bermuda
Income Tax Disclosure [Line Items]
Income (loss) before income taxes	1,122,952	388,492	406,054
United States
Income Tax Disclosure [Line Items]
Income (loss) before income taxes	701,480	440,823	381,157
Other
Income Tax Disclosure [Line Items]
Income (loss) before income taxes	$ 24,678	$ 12,457	$ (29,934)

Income Taxes - Statutory tax ra

Income Taxes - Statutory tax rate by jurisdiction (Details)	Jan. 01, 2018	Dec. 31, 2019	Dec. 31, 2017
Bermuda
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)		0.00%
United States
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)	21.00%	21.00%	35.00%
United Kingdom
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)		19.00%
Ireland
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)		12.50%
Denmark
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)		22.00%
Canada
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)		26.50%
Gibraltar
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)		10.00%
Australia
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)		30.00%
Hong Kong
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)		16.50%
Netherlands
Income Tax Disclosure [Line Items]
Statutory tax rate (percentage)		19.00%

Income Taxes - Reconciliation o

Income Taxes - Reconciliation of effective tax rate (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Income Tax Disclosure [Abstract]
Expected income tax expense (benefit) computed on pre-tax income at weighted average income tax rate	$ 149,799	$ 91,529	$ 126,262
Addition (reduction) in income tax expense (benefit) resulting from:
Tax-exempt investment income	(3,091)	(4,790)	(13,330)
Meals and entertainment	1,134	1,060	1,063
State taxes, net of U.S. federal tax benefit	3,314	2,086	732
Foreign branch taxes	1,231	5,428	5,752
Prior year adjustment	632	(2,522)	(559)
Foreign exchange gains & losses	436	1,293	(572)
Changes in applicable tax rate	0	(128)	7,745
Dividend withholding taxes	6,510	6,594	232
Change in valuation allowance	1,628	18,396	14,798
Contingent consideration	190	740	3,785
Share based compensation	(6,592)	(5,356)	(18,733)
Other	619	(379)	393
Income tax expense	$ 155,810	$ 113,951	$ 127,568

Income Taxes - Components of de

Income Taxes - Components of deferred tax assets and liabilities (Details) - USD ($) $ in Thousands	Dec. 31, 2019	Dec. 31, 2018
Deferred income tax assets:
Net operating loss	$ 30,836	$ 24,089
Uncrystallized losses	1,565	7,960
AMT credit carryforward	1,323	2,652
Discounting of net loss reserves	52,582	43,130
Net unearned premium reserve	64,269	68,305
Compensation liabilities	21,693	20,492
Foreign tax credit carryforward	9,521	9,116
Interest expense	0	1,387
Goodwill and intangible assets	11,644	17,127
Bad debt reserves	5,983	5,626
Lease liability	26,438	0
Net unrealized foreign exchange losses	598	949
Net unrealized decline of investments	0	13,453
Other, net	206	3,418
Deferred tax assets before valuation allowance	226,658	217,704
Valuation allowance	(48,219)	(44,659)
Deferred tax assets net of valuation allowance	178,439	173,045
Deferred income tax liabilities:
Depreciation and amortization	(1,215)	(2,559)
Deposit accounting liability	(2,169)	(2,292)
Contingency reserve	(132,831)	(112,852)
Deferred policy acquisition costs	(29,847)	(32,105)
Net unrealized appreciation of investments	(38,764)	0
Right-of-use asset	(23,416)	0
Other, net	(3,680)	(735)
Total deferred tax liabilities	(231,922)	(150,543)
Net deferred income tax liabilities	$ (53,483)
Net deferred income tax assets (liabilities)		$ 22,502

Income Taxes - Operating loss c

Income Taxes - Operating loss carryfowards and tax credits (Details) - USD ($) $ in Thousands		Dec. 31, 2019	Dec. 31, 2018
Operating Loss Carryforwards [Line Items]
U.K. foreign tax credits		$ 9,521	$ 9,116
U.S. refundable AMT credits		1,323	$ 2,652
United Kingdom
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		89,000
U.K. foreign tax credits		9,521
Ireland
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		10,200
Australia
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		22,000
Hong Kong
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		17,600
Denmark
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		400
United States
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards	[1],[2]	23,100
U.S. refundable AMT credits		1,323
Operating loss carryforward, portion subject to utilization limits		8,900
Operating loss carryforward, annual utilization limit		600
Watford Holdings Ltd | United States
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		$ 600
[1]	Includes $0.6 million net operating loss carryforwards from Watford.
[2]	On January 30, 2014, the Company’s U.S. mortgage operations underwent an ownership change for U.S. federal income tax purposes as a result of the Company’s acquisition of the CMG Entities. As a result of this ownership change, a limitation has been imposed upon the utilization of approximately $8.9 million of the Company’s existing U.S. net operating loss carryforwards. Utilization is limited to approximately $0.6 million per year in accordance with Section 382 of the Internal Revenue Code of 1986 as amended (“the Code”).

Income Taxes - Unrecognized tax

Income Taxes - Unrecognized tax benefits (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018
Reconciliation of beginning and ending amount of unrecognized tax benefits
Balance at beginning of year	$ 2,008	$ 2,008
Additions based on tax positions related to the current year	0	0
Additions for tax positions of prior years	0	0
Reductions for tax positions of prior years	0	0
Settlements	0	0
Balance at end of year	$ 2,008	$ 2,008

Income Taxes - Summary of open

Income Taxes - Summary of open tax years by major jurisdiction (Details)	12 Months Ended
	Dec. 31, 2019
United States | Minimum
Income Tax Contingency [Line Items]
Open tax year	2016
United States | Maximum
Income Tax Contingency [Line Items]
Open tax year	2019
United Kingdom | Minimum
Income Tax Contingency [Line Items]
Open tax year	2018
United Kingdom | Maximum
Income Tax Contingency [Line Items]
Open tax year	2019
Ireland | Minimum
Income Tax Contingency [Line Items]
Open tax year	2015
Ireland | Maximum
Income Tax Contingency [Line Items]
Open tax year	2019
Canada | Minimum
Income Tax Contingency [Line Items]
Open tax year	2016
Canada | Maximum
Income Tax Contingency [Line Items]
Open tax year	2019
Switzerland | Minimum
Income Tax Contingency [Line Items]
Open tax year	2017
Switzerland | Maximum
Income Tax Contingency [Line Items]
Open tax year	2019
Denmark | Minimum
Income Tax Contingency [Line Items]
Open tax year	2015
Denmark | Maximum
Income Tax Contingency [Line Items]
Open tax year	2019

Income Taxes - Narrative (Detai

Income Taxes - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018
Operating Loss Carryforwards [Line Items]
Current income taxes payable	$ (13.5)
United States
Operating Loss Carryforwards [Line Items]
Tax Cuts and Jobs Act, Income Tax Expense (Benefit)	1.2
Other assets | T&L Bonds
Operating Loss Carryforwards [Line Items]
US mortgage guaranty tax and loss bonds	$ 207	$ 183

Transactions with Related Par_2

Transactions with Related Parties (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Related Party Transaction [Line Items]
Purchases of other investments	$ 1,470,545	$ 2,014,622	$ 2,020,624
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	4,346,816	2,919,372
Premia Holdings Ltd.
Related Party Transaction [Line Items]
Percentage ownership			25.00%
Purchases of other investments			$ 100,000
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	$ 177,700
Funds held liability		$ 180,000

Leases - Additional information

Leases - Additional information regarding leases (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Lessee, Lease, Description [Line Items]
Operating lease costs	$ 30,478	$ 27,600	$ 31,100
Cash payments included in the measurement of lease liabilities reported in operating cash flows	27,521
Right-of-use assets obtained in exchange for new lease liabilities	7,445
Operating lease liability	$ 150,519
Weighted average discount rate	3.90%
Weighted average remaining lease term	6 years 4 months 24 days
Other assets
Lessee, Lease, Description [Line Items]
Right-of-use assets	$ 131,661
Other liabilities
Lessee, Lease, Description [Line Items]
Operating lease liability	$ 150,519
Maximum
Lessee, Lease, Description [Line Items]
Operating lease term	11 years

Leases - Contractual maturities

Leases - Contractual maturities (Details) $ in Thousands	Dec. 31, 2019USD ($)
Contractual maturities of operating lease liabilities
2020	$ 31,907
2021	30,842
2023	27,597
2024	23,027
2025	16,913
2025 and thereafter	40,167
Total undiscounted lease liability	170,453
Less: present value adjustment	(19,934)
Operating lease liability	150,519
Future lease payments on capital leases
2021	4,800
2022	$ 2,100

Leases - Future minimum rental

Leases - Future minimum rental payments (Details) $ in Thousands	Dec. 31, 2019USD ($)
Leases [Abstract]
2019	$ 31,088
2020	30,491
2021	29,351
2022	26,068
2023	21,408
2024 and thereafter	54,745
Total future minimum lease payments	$ 193,151

Commitments and Contingencies -

Commitments and Contingencies - Concentrations of credit risk (Details)	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Concentration Risk [Line Items]
Concentration risk percentage	10.00%
Customer Concentration Risk | Gross Written Premiums | Aon Corporation
Concentration Risk [Line Items]
Concentration risk percentage	12.20%	11.40%	11.30%
Customer Concentration Risk | Gross Written Premiums | Marsh And McLennan Companies
Concentration Risk [Line Items]
Concentration risk percentage	9.60%	9.30%	10.70%

Commitments and Contingencies_2

Commitments and Contingencies - Other commitments (Details) - USD ($) $ in Millions	Dec. 31, 2019	Apr. 30, 2019	Dec. 31, 2018	Apr. 30, 2017
Line of Credit Facility [Line Items]
Investment commitments	$ 1,690		$ 1,770
Estimated purchase commitments, primarily related to software and computerized systems	55.6		$ 39.5
CMG Mortgage Insurance Company
Line of Credit Facility [Line Items]
Contingent consideration liability	$ 6.7	$ 61.5		$ 71.7

Debt and Financing Arrangemen_3

Debt and Financing Arrangements - Schedule of senior notes outstanding (Details) - USD ($) $ in Thousands		Jul. 02, 2019	Dec. 31, 2019	Dec. 31, 2018
Debt Instrument [Line Items]
Carrying amount			$ 1,871,626	$ 1,733,528
Senior Notes
Debt Instrument [Line Items]
Principal amount			1,890,000
Carrying amount			$ 1,871,626	1,733,528
Senior Notes | 7.350% senior notes due 2034
Debt Instrument [Line Items]
Stated interest rate (percentage)	[1]		7.35%
Principal amount	[1]		$ 300,000
Carrying amount			$ 297,254	297,150
Senior Notes | 5.144% senior notes due 2043
Debt Instrument [Line Items]
Stated interest rate (percentage)	[2]		5.144%
Principal amount	[2]		$ 500,000
Carrying amount			$ 494,831	494,723
Senior Notes | 4.011% senior notes due 2026
Debt Instrument [Line Items]
Stated interest rate (percentage)	[3]		4.011%
Principal amount	[3]		$ 500,000
Carrying amount			$ 496,806	496,417
Senior Notes | 5.031% senior notes due 2046
Debt Instrument [Line Items]
Stated interest rate (percentage)	[4]		5.031%
Principal amount	[4]		$ 450,000
Carrying amount			$ 445,317	445,238
Senior Notes | Watford notes
Debt Instrument [Line Items]
Stated interest rate (percentage)	[5]		6.50%
Principal amount	[5]		$ 140,000
Carrying amount			$ 137,418	0
Variable Interest Entity, Primary Beneficiary | Senior Notes
Debt Instrument [Line Items]
Principal amount		$ 175,000
Proceeds from issuance of senior notes		172,400
Variable Interest Entity, Primary Beneficiary | Senior Notes | Watford notes
Debt Instrument [Line Items]
Stated interest rate (percentage)	[5]		6.50%
Watford Holdings Ltd | Variable Interest Entity, Primary Beneficiary
Debt Instrument [Line Items]
Carrying amount			$ 172,418	$ 0
Watford Holdings Ltd | Variable Interest Entity, Primary Beneficiary | Senior Notes
Debt Instrument [Line Items]
Payments to Acquire Notes Receivable		$ 35,000
[1]	Senior notes of Arch Capital issued on May 4, 2004 and due May 1, 2034 (“2034 notes”).
[2]	Senior notes of Arch-U.S., a wholly-owned subsidiary of Arch Capital, issued on December 13, 2013 and due November 1, 2043 (“2043 notes”), fully and unconditionally guaranteed by Arch Capital.
[3]	Senior notes of Arch Capital Finance LLC (“Arch Finance”), a wholly-owned finance subsidiary of Arch Capital, issued on December 8, 2016 and due December 15, 2026 (“2026 notes”), fully and unconditionally guaranteed by Arch Capital.
[4]	Senior notes of Arch Finance issued on December 8, 2016 and due December 15, 2046 (“2046 notes”), fully and unconditionally guaranteed by Arch Capital
[5]	Senior notes of Watford issued on July 2, 2019 and due July 2, 2029, reflecting the elimination of amounts owned by Arch-U.S.

Debt and Financing Arrangemen_4

Debt and Financing Arrangements - Letter of Credit and Revolving Credit Facilities (Details) - USD ($) $ in Thousands	Dec. 17, 2019	Dec. 31, 2019	Dec. 31, 2018
Line of Credit Facility [Line Items]
Outstanding borrowings		$ 484,287	$ 455,682
Investments pledged as collateral		255,400
Credit Facility
Line of Credit Facility [Line Items]
Maximum borrowing capacity	$ 750,000
Credit facility term	5 years
Secured letter of credit facility
Line of Credit Facility [Line Items]
Maximum borrowing capacity	$ 250,000
Optional increased capacity		1,250,000
Remaining capacity		24,600
Outstanding borrowings		225,400
Unsecured revolving loan and letter of credit facility
Line of Credit Facility [Line Items]
Maximum borrowing capacity	$ 500,000
Arch Re US | Revolving Credit Facility
Line of Credit Facility [Line Items]
Outstanding borrowings		0	0
Other Arch Capital Subsidiaries | Secured letter of credit facility
Line of Credit Facility [Line Items]
Outstanding borrowings		18,100
Other Arch Capital Subsidiaries | Unsecured revolving loan and letter of credit facility
Line of Credit Facility [Line Items]
Outstanding borrowings		195,000
Watford Holdings Ltd
Line of Credit Facility [Line Items]
Outstanding borrowings		122,900
Watford Holdings Ltd | Secured letter of credit facility
Line of Credit Facility [Line Items]
Maximum borrowing capacity		100,000
Watford Holdings Ltd | Unsecured revolving loan and letter of credit facility
Line of Credit Facility [Line Items]
Maximum borrowing capacity		100,000
Watford Holdings Ltd | Secured credit facility expiring November 2021
Line of Credit Facility [Line Items]
Maximum borrowing capacity		800,000
Outstanding borrowings		484,287	$ 455,682
Letter of credit limit		$ 400,000

Goodwill and Intangible Asset_2

Goodwill and Intangible Assets - Analysis of goodwill and intangible assets (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019		Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2019	Dec. 31, 2018
Goodwill
Goodwill, beginning of year	$ 249,620		$ 198,236
Goodwill, acquisitions	74,780		51,476
Goodwill, impairment	0		0
Goodwill, foreign currency translation adjustment	2,151		(92)
Goodwill, end of year	326,551		249,620	$ 198,236
Intangible assets (indefinite life)
Intangible assets with an indefinite life, beginning of year	61,874		68,174
Intangible assets with an indefinite life, acquisitions	24,431		0
Intangible assets with an indefinite life, impairment	(1,000)	[1]	(6,300)
Intangible assets with an indefinite life, foreign currency translation adjustment	605		0
Intangible assets with an indefinite life, end of year	85,910		61,874	68,174
Intangible assets (finite life)
Intangible assets with a finite life, beginning of year	323,426		386,201
Intangible assets with a finite life, acquisitions	82,482		43,000
Intangible assets with a finite life, amortization	(82,104)		(105,670)	(125,778)
Intangible assets with a finite life, foreign currency translation adjustment	1,817		(105)
Intangible assets with a finite life, impairment	0		0
Intangible assets with a finite life, end of year	325,621		323,426	386,201
Total
Goodwill and intangible assets, beginning of year	634,920		652,611
Goodwill and intangible assets, acquisitions	181,693		94,476
Goodwill and intangible assets impairment	(1,000)		(6,300)
Goodwill and intangible assets, foreign currency movements and other adjustments	4,574		(197)
Goodwill and intangible assets, end of year	738,083		634,920	652,611
Goodwill and intangible assets, gross balance					$ 1,161,336
Intangible assets with a finite life, accumulated amortization					(419,294)	$ (337,190)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments					(3,959)	(8,533)
Goodwill and intangible assets	738,083		$ 634,920	$ 652,611	738,083	634,920
Goodwill
Goodwill
Goodwill, end of year	326,551
Total
Goodwill, gross balance					331,448
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments					(4,897)	$ (7,048)
Intangible assets with an indefinite life
Intangible assets (indefinite life)
Intangible assets with an indefinite life, end of year	85,910
Total
Indefinite-lived intangible assets, gross balance					85,305
Intangible assets with a finite life
Intangible assets (finite life)
Intangible assets with a finite life, end of year	$ 325,621
Total
Intangible assets with a finite life, gross balance					744,583
Intangible assets with a finite life, accumulated amortization					(419,294)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments					$ 332
[1]	The impairment to the indefinite-lived intangible assets during the year ended December 31, 2019 and 2018 of $1.0 million and $6.3 million

Goodwill and Intangible Asset_3

Goodwill and Intangible Assets - Summary of intangible assets by major class (Details) - USD ($) $ in Thousands	Dec. 31, 2019	Dec. 31, 2018
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	$ 1,161,336	$ 980,643
Intangible assets with a finite life, accumulated amortization	(419,294)	(337,190)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(3,959)	(8,533)
Goodwill and intangible assets, net balance	738,083	634,920
Intangible liability - unfavorable service contract
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	(9,533)	(9,533)
Intangible assets with a finite life, accumulated amortization	8,657	7,949
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	0	0
Goodwill and intangible assets, net balance	(876)	(1,584)
Intangible assets with a finite life
Schedule of Goodwill And Intangible Assets [Line Items]
Intangible assets with a finite life, accumulated amortization	(419,294)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	332
Intangible assets with a finite life | Acquired insurance contracts
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	452,470	435,067
Intangible assets with a finite life, accumulated amortization	(336,559)	(271,981)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	310	(150)
Goodwill and intangible assets, net balance	116,221	162,936
Intangible assets with a finite life | Operating platform
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	52,674	47,400
Intangible assets with a finite life, accumulated amortization	(39,571)	(35,402)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(259)	0
Goodwill and intangible assets, net balance	12,844	11,998
Intangible assets with a finite life | Distribution relationships
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	243,838	186,611
Intangible assets with a finite life, accumulated amortization	(50,542)	(36,718)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	212	(1,335)
Goodwill and intangible assets, net balance	193,508	148,558
Intangible assets with a finite life | Other
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	5,134	2,556
Intangible assets with a finite life, accumulated amortization	(1,279)	(1,038)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	70	0
Goodwill and intangible assets, net balance	3,925	1,518
Goodwill
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	331,448	256,668
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(4,897)	(7,048)
Goodwill and intangible assets, net balance	326,551	249,620
Intangible assets with an indefinite life | Insurance licenses
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	63,390	61,874
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	0	0
Goodwill and intangible assets, net balance	63,390	61,874
Intangible assets with an indefinite life | Syndicate capacity
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	21,915	0
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	605	0
Goodwill and intangible assets, net balance	$ 22,520	$ 0

Goodwill and Intangible Asset_4

Goodwill and Intangible Assets - Future amortization expense (Details) - USD ($) $ in Thousands	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Goodwill and Intangible Assets Disclosure [Abstract]
2019	$ 65,958
2020	48,063
2021	33,972
2022	31,731
2023	27,566
2024 and thereafter	118,331
Finite-Lived Intangible Assets, Net	$ 325,621	$ 323,426	$ 386,201

Goodwill and Intangible Asset_5

Goodwill and Intangible Assets - Narrative (Details)	12 Months Ended
	Dec. 31, 2019
Minimum
Finite-Lived Intangible Assets [Line Items]
Remaining useful lives of intangible assets	1 year
Maximum
Finite-Lived Intangible Assets [Line Items]
Remaining useful lives of intangible assets	17 years

Shareholders' Equity - Roll-for

Shareholders' Equity - Roll-forward of changes in issued and outstanding common shares (Details) - $ / shares		12 Months Ended
		Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017	May 31, 2018	Apr. 30, 2018
Common Shares:
Shares issued, beginning of year		570,737,283	549,872,226	523,932,303
Shares issued	[1]	2,835,994	2,757,506	3,388,344
Conversion of Series D preferred shares	[2]	0	17,022,600	21,265,860
Restricted shares issued, net of cancellations		1,043,918	1,084,951	1,285,719
Shares issued, end of year		574,617,195	570,737,283	549,872,226
Common shares held in treasury, end of year		(168,997,994)	(168,282,449)	(156,938,409)
Common shares outstanding, end of year		405,619,201	402,454,834	392,933,817
Authorized and Issued:
Common shares authorized		1,800,000,000			1,800,000,000	600,000,000
Common shares, par value per share		$ 0.0011	$ 0.0011		$ 0.0011	$ 0.0033
Preferred shares authorized		50,000,000
Preferred shares, par value per share		$ 0.01
[1]	Includes shares issued from the exercise of stock options and stock appreciation rights, and shares issued from the employee share purchase plan.
[2]	Such shares represent common shares that were issued upon conversion of the non-voting common equivalent preference shares issued in connection with the AIG acquisition.

Shareholders' Equity - Three-fo

Shareholders' Equity - Three-for-one common share split (Details)	1 Months Ended	12 Months Ended
	May 31, 2018$ / sharesshares	Dec. 31, 2018$ / shares	Dec. 31, 2019$ / sharesshares	Apr. 30, 2018$ / sharesshares
Stockholders' Equity Note [Abstract]
Share split conversion ratio	3	3
Number of common shares authorized | shares	1,800,000,000		1,800,000,000	600,000,000
Common shares, par value per share | $ / shares	$ 0.0011	$ 0.0011	$ 0.0011	$ 0.0033

Shareholders' Equity - Share re

Shareholders' Equity - Share repurchase program (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Class of Stock [Line Items]
Treasury stock, value of shares acquired	$ 2,871	$ 282,762	$ 0
Treasury stock, shares acquired (shares)	110,598	10,559,850	0
Treasury stock, average cost per share	$ 25.96	$ 26.78	$ 0
Common shares held in treasury (shares)	168,997,994	168,282,449	156,938,409
Common shares held in treasury, at cost	$ 2,406,047	$ 2,382,167
Common shares
Class of Stock [Line Items]
Remaining share repurchase authorization	$ 1,000,000
Cumulative number of shares acquired since inception of share repurchase program	386,300,000
Aggregate purchase price of shares acquired since inception of share repurchase program	$ 3,970,000

Shareholders' Equity - Converti

Shareholders' Equity - Convertible non-voting common equivalent preferred shares (Details) - shares		Dec. 31, 2016	Mar. 31, 2018	Jun. 30, 2017	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Class of Stock [Line Items]
Shares issued	[1]				2,835,994	2,757,506	3,388,344
Number of shares converted	[2]				0	17,022,600	21,265,860
Series D Preferred Shares
Class of Stock [Line Items]
Number of share in conversion					10
Number of underlying common shares		38,288,460
Shares issued			17,022,600	21,265,860
Number of shares converted			567,420	708,862
Number of preferred shares outstanding					0
United Guaranty Corporation | Series D Preferred Shares
Class of Stock [Line Items]
Number of shares issued		1,276,282
[1]	Includes shares issued from the exercise of stock options and stock appreciation rights, and shares issued from the employee share purchase plan.
[2]	Such shares represent common shares that were issued upon conversion of the non-voting common equivalent preference shares issued in connection with the AIG acquisition.

Shareholders' Equity - Preferre

Shareholders' Equity - Preferred shares (Details) - USD ($) $ / shares in Units, $ in Thousands, shares in Millions	Sep. 29, 2016	Nov. 30, 2017	Aug. 31, 2017	Nov. 30, 2017	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Class of Stock [Line Items]
Non-cumulative preferred shares					$ 780,000	$ 780,000
Preferred shares, par value per share					$ 0.01
Proceeds on issuance of preference shares					$ 0	$ 0	$ 319,694
Average cost per share					$ 25.96	$ 26.78	$ 0
Aggregate cost of share repurchase					$ 0	$ 92,555	$ 230,000
Series C Preferred Shares
Class of Stock [Line Items]
Preferred shares, dividend rate (as a percent)						6.75%
Preferred shares, redemption price per share						$ 25
Series E preferred shares
Class of Stock [Line Items]
Non-cumulative preferred shares	$ 450,000
Preferred shares, dividend rate (as a percent)	5.25%
Preferred shares, par value per share	$ 0.01
Liquidation preference per share	25,000
Preferred shares, redemption price per share	$ 25,000
Series E depositary share equivalent
Class of Stock [Line Items]
Preference shares, number of shares issued	18
Proportionate interest of preference shares, per depositary share	0.10%
Liquidation preference per share	$ 25
Preferred shares, redemption price per share	$ 25
Series F Preferred Shares
Class of Stock [Line Items]
Preferred shares issued		$ 100,000	$ 230,000	$ 330,000
Preferred shares, dividend rate (as a percent)				5.45%
Preferred shares, par value per share		$ 0.01		$ 0.01
Liquidation preference per share		25,000		25,000
Preferred shares, redemption price per share		$ 25,000		$ 25,000
Series F depositary share equivalent
Class of Stock [Line Items]
Preference shares, number of shares issued		13.2		13.2
Proportionate interest of preference shares, per depositary share		0.10%		0.10%
Liquidation preference per share		$ 25		$ 25
Preferred shares, redemption price per share		$ 25		$ 25

Share-Based Compensation - Long

Share-Based Compensation - Long Term Incentive Plan (Details) - shares	12 Months Ended
	Dec. 31, 2019	May 06, 2016
2018 Long Term Incentive and Share Award Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares reserved for issuance	34,500,000
Shares available for issuance transferred	25,201,143
2015 Long Term Incentive And Share Award Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares reserved for issuance	12,900,000
Shares available for issuance	390,156
2007 Employee Share Purchase Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares available for issuance	2,729,721	4,689,777
2012 Long Term Incentive and Share Award Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Total number of shares reserved under plan	22,301,772
Shares available for issuance	606,589

Share-Based Compensation - Valu

Share-Based Compensation - Valuation assumptions (Details)	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Share-based Payment Arrangement [Abstract]
Dividend yield	0.00%	0.00%	0.00%
Expected volatility	18.10%	21.30%	21.30%
Risk free interest rate	2.50%	2.80%	2.00%
Expected option life	6 years	6 years	6 years

Share-Based Compensation - Stoc

Share-Based Compensation - Stock option activity (Details) - Options and SARs $ / shares in Units, $ in Thousands	12 Months Ended
	Dec. 31, 2019USD ($)$ / sharesshares
Number of Options / SARs
Outstanding, beginning of year (in shares) | shares	20,076,593
Granted (in shares) | shares	1,228,280
Exercised (in shares) | shares	(2,355,216)
Forfeited or expired (in shares) | shares	(96,639)
Outstanding, end of year (in shares) | shares	18,853,018
Exercisable, end of year (in shares) | shares	15,517,508
Weighted Average Exercise Price
Outstanding, beginning of year, weighted average exercise price | $ / shares	$ 19.37
Granted, weighted average exercise price | $ / shares	32.86
Exercised, weighted average exercise price | $ / shares	13.45
Forfeited or expired, weighted average exercise price | $ / shares	29.19
Outstanding, end of year, weighted average exercise price | $ / shares	20.94
Exercisable, end of year, weighted average exercise price | $ / shares	$ 19.05
Weighted average contractual term, outstanding, end of year	5 years 10 days
Weighted average contractual term, exercisable, end of year	4 years 3 months 10 days
Aggregate intrinsic value, outstanding, end of year | $	$ 413,842
Aggregate intrinsic value, exercisable, end of year | $	$ 369,917

Share-Based Compensation - Opti

Share-Based Compensation - Options additional information (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Options and SARs
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Proceeds from stock options exercised	$ 13,100
Tax benefit from exercise of stock options and SARs	$ 6,900
Weighted average grant date fair value	$ 7.90	$ 7.50	$ 8.15
Aggregate intrinsic value of options exercised	$ 51,350	$ 43,468	$ 64,173

Share-Based Compensation - Rest

Share-Based Compensation - Restricted common shares and restricted stock units activity (Details)	12 Months Ended
	Dec. 31, 2019$ / sharesshares
Restricted Common Shares
Unvested Shares:
Unvested balance, beginning of year (in shares) | shares	1,619,285
Restricted shares and restricted unit awards granted | shares	384,926
Vested (in shares) | shares	(931,696)
Forfeited (in shares) | shares	(26,594)
Unvested balance, end of year (in shares) | shares	1,045,921
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year, weighted average grant date fair value | $ / shares	$ 28.88
Weighted average grant date fair value | $ / shares	33.43
Vested, weighted average grant date fair value | $ / shares	28.31
Forfeited, weighted average grant date fair value | $ / shares	30.15
Unvested balance, end of year, weighted average grant date fair value | $ / shares	$ 31.02
Restricted Unit Awards
Unvested Shares:
Unvested balance, beginning of year (in shares) | shares	1,254,558
Restricted shares and restricted unit awards granted | shares	810,815
Vested (in shares) | shares	(422,021)
Forfeited (in shares) | shares	(80,340)
Unvested balance, end of year (in shares) | shares	1,563,012
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year, weighted average grant date fair value | $ / shares	$ 27.58
Weighted average grant date fair value | $ / shares	32.64
Vested, weighted average grant date fair value | $ / shares	27.75
Forfeited, weighted average grant date fair value | $ / shares	29.36
Unvested balance, end of year, weighted average grant date fair value | $ / shares	$ 30.07

Share-Based Compensation - Re_2

Share-Based Compensation - Restricted stock additional information (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Restricted Common Shares And Restricted Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Restricted shares and restricted unit awards granted	1,195,741	1,563,287	1,747,176
Weighted average grant date fair value	$ 32.89	$ 26.86	$ 32.02
Aggregate fair value of vested restricted share and unit awards	$ 46,262	$ 39,898	$ 133,848
Aggregate intrinsic value of restricted units outstanding	$ 67,000

Share-Based Compensation - Perf

Share-Based Compensation - Performance shares and performance units activity (Details)	12 Months Ended
	Dec. 31, 2019$ / sharesshares
Performance Shares
Unvested Shares:
Unvested balance, beginning of year (in shares) | shares	715,328
Performance shares and units granted | shares	685,586
Vested (in shares) | shares	0
Forfeited (in shares) | shares	0
Unvested balance, end of year (in shares) | shares	1,400,914
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year, weighted average grant date fair value | $ / shares	$ 24.77
Weighted average grant date fair value | $ / shares	36.05
Vested, weighted average grant date fair value | $ / shares	0
Forfeited, weighted average grant date fair value | $ / shares	0
Unvested balance, end of year, weighted average grant date fair value | $ / shares	$ 30.29
Performance Units
Unvested Shares:
Unvested balance, beginning of year (in shares) | shares	12,993
Performance shares and units granted | shares	10,774
Vested (in shares) | shares	0
Forfeited (in shares) | shares	0
Unvested balance, end of year (in shares) | shares	23,767
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year, weighted average grant date fair value | $ / shares	$ 24.71
Weighted average grant date fair value | $ / shares	35.83
Vested, weighted average grant date fair value | $ / shares	0
Forfeited, weighted average grant date fair value | $ / shares	0
Unvested balance, end of year, weighted average grant date fair value | $ / shares	$ 29.75

Share-Based Compensation - Pe_2

Share-Based Compensation - Performance shares and units additional information (Details) - $ / shares	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Expected volatility	18.10%	21.30%	21.30%
Vesting period	3 years
Risk free interest rate	2.50%	2.80%	2.00%
Performance Common Shares and Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Expected volatility	17.10%	16.20%	0.00%
Vesting period	3 years
Performance shares and units granted	696,360	743,513	0
Weighted average grant date fair value	$ 36.05	$ 24.77	$ 0
Risk free interest rate	2.50%	2.60%	0.00%

Share-Based Compensation - Shar

Share-Based Compensation - Share-based compensation expense (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	$ 63,848	$ 55,935	$ 67,863
Share based compensation expense, net of tax	55,502	49,179	56,098
Options and SARs
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	12,866	16,272	18,536
Share based compensation expense, net of tax	11,450	14,894	16,219
Restricted Common Shares And Restricted Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	38,988	34,025	46,884
Share based compensation expense, net of tax	32,999	29,044	37,708
Performance Awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	8,949	4,414	0
Share based compensation expense, net of tax	8,295	4,127	0
Employee Share Purchase Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	3,045	1,224	2,443
Share based compensation expense, net of tax	$ 2,758	$ 1,114	$ 2,171

Share-Based Compensation - Unre

Share-Based Compensation - Unrecognized compensation cost and period for recognition (Details) $ in Millions	12 Months Ended
	Dec. 31, 2019USD ($)
Options and SARs
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation cost related to unvested awards	$ 12,823
Weighted average recognition period (years)	1 year 2 months 23 days
Restricted Common Shares And Restricted Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation cost related to unvested awards	$ 39,606
Weighted average recognition period (years)	1 year 3 months 21 days
Performance Common Shares and Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation cost related to unvested awards	$ 8,893
Weighted average recognition period (years)	1 year 21 days

Retirement Plans (Details)

Retirement Plans (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Retirement Benefits [Abstract]
Defined contribution plan, expense	$ 44.8	$ 40.8	$ 40.7

Statutory Information - Summar

Statutory Information - Summary of statutory capital, surplus and net income (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Bermuda
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	$ 13,511,729	$ 11,605,652
Required statutory capital and surplus	[1]	5,492,968	4,718,345
Statutory net income (loss)		1,876,416	919,554	$ 881,665
Ireland
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	721,439	653,055
Required statutory capital and surplus	[1]	542,703	429,117
Statutory net income (loss)		26,367	29,223	(14,438)
United States
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	4,440,848	4,195,477
Required statutory capital and surplus	[1]	1,697,640	1,783,268
Statutory net income (loss)		481,188	292,831	500,412
United Kingdom
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	748,276	386,892
Required statutory capital and surplus	[1]	349,328	271,864
Statutory net income (loss)		(17,423)	(18,467)	(33,257)
Canada
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	61,351	59,096
Required statutory capital and surplus	[1]	32,763	33,189
Statutory net income (loss)		$ (1,023)	$ 2,525	$ 158
[1]	Such amounts include ownership interests in affiliated insurance and reinsurance subsidiaries.

Statutory Information - Narrat

Statutory Information - Narrative (Details) $ in Thousands		12 Months Ended
		Dec. 31, 2019USD ($)subsidiary	Dec. 31, 2018USD ($)
Bermuda
Statutory Accounting Practices [Line Items]
Required statutory capital and surplus	[1]	$ 5,492,968	$ 4,718,345
Ireland
Statutory Accounting Practices [Line Items]
Number Of Subsidiaries | subsidiary		2
Required statutory capital and surplus	[1]	$ 542,703	429,117
United States
Statutory Accounting Practices [Line Items]
Dividends available for payment in 2020, total		177,800
Required statutory capital and surplus	[1]	$ 1,697,640	$ 1,783,268
Mortgage | North Carolina or Wisconsin
Statutory Accounting Practices [Line Items]
Required contingency loss reserve as a percentage of net earned premiums		50.00%
Withdrawal restriction period		10 years
Withdrawal restriction period, with prior approval		35.00%
Maximum risk to capital ratio		2500.00%
United Guaranty Residential Insurance Company [Member] | North Carolina
Statutory Accounting Practices [Line Items]
Dividends available for payment in 2020, total		$ 338,900
Arch Re US | United States
Statutory Accounting Practices [Line Items]
Dividends available for payment in 2020, total		$ 130,200
Arch Re Bermuda [Member] | Bermuda
Statutory Accounting Practices [Line Items]
Dividends, percentage permitted		25.00%
Dividend required notice period		7 days
Dividends available for payment in 2020 without prior regulatory approval		$ 3,100,000
[1]	Such amounts include ownership interests in affiliated insurance and reinsurance subsidiaries.

Unaudited Condensed Quarterly_3

Unaudited Condensed Quarterly Financial Information (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended								12 Months Ended
	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Quarterly Financial Information Disclosure [Abstract]
Net premiums written	$ 1,455,453	$ 1,613,457	$ 1,444,898	$ 1,525,259	$ 1,301,754	$ 1,333,553	$ 1,298,896	$ 1,412,544	$ 6,039,067	$ 5,346,747	$ 4,961,373
Net premiums earned	1,515,882	1,438,023	1,463,727	1,368,866	1,369,435	1,290,878	1,336,763	1,234,899	5,786,498	5,231,975	4,844,532
Net investment income	154,263	161,488	155,038	156,949	157,217	144,024	135,668	126,724	627,738	563,633	470,872
Net realized gains (losses)	41,474	62,518	120,806	141,565	(166,030)	(51,705)	(76,611)	(110,998)	366,363	(405,344)	149,141
Net impairment losses recognized in earnings	(644)	(1,163)	(49)	(1,309)	(1,705)	(492)	(470)	(162)	(3,165)	(2,829)	(7,138)
Underwriting income (loss)	251,421	231,262	293,134	260,148	166,955	234,581	235,465	236,997	1,035,965	873,998	447,430
Net income (loss) attributable to Arch	326,384	392,453	468,954	448,528	136,494	227,408	243,646	150,423	1,693,300	727,821	629,709
Preferred dividends	(10,403)	(10,403)	(10,403)	(10,403)	(10,403)	(10,402)	(10,403)	(10,437)	(41,612)	(41,645)	(46,041)
Net income available to Arch common shareholders	$ 315,981	$ 382,050	$ 458,551	$ 438,125	$ 126,091	$ 217,006	$ 233,243	$ 137,276	$ 1,594,707	$ 713,616	$ 566,502
Basic (per share)	$ 0.78	$ 0.95	$ 1.14	$ 1.09	$ 0.31	$ 0.54	$ 0.58	$ 0.34	$ 3.97	$ 1.76	$ 1.40
Diluted (per share)	$ 0.76	$ 0.92	$ 1.12	$ 1.07	$ 0.31	$ 0.53	$ 0.56	$ 0.33	$ 3.87	$ 1.73	$ 1.36

Guarantor Financial Informati_3

Guarantor Financial Information - Condensed consolidating balance sheet (Details) - USD ($) $ in Thousands	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016
Condensed Balance Sheet Statements, Captions [Line Items]
Percentage ownership of subsidiary	100.00%
Assets
Total investments	$ 24,402,246	$ 21,745,284
Cash	726,230	646,556	$ 606,199
Investment in subsidiaries	0	0
Due from subsidiaries and affiliates	0	0
Premiums receivable	1,778,717	1,299,150
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	4,346,816	2,919,372
Contractholder receivables	2,119,460	2,079,111
Ceded unearned premiums	1,234,683	975,469
Deferred acquisition costs	633,400	569,574
Goodwill and intangible assets	738,083	634,920
Other assets	1,905,726	1,348,893
Total assets	37,885,361	32,218,329	32,051,658
Liabilities
Reserve for losses and loss adjustment expenses	13,891,842	11,853,297	11,383,792	$ 10,200,960
Unearned premiums	4,339,549	3,753,636
Reinsurance balances payable	667,072	393,107
Contractholder payables	2,119,460	2,079,111
Collateral held for insured obligations	206,698	236,630
Senior notes	1,871,626	1,733,528
Revolving credit agreement borrowings	484,287	455,682
Due to subsidiaries and affiliates	0	0
Other liabilities	1,989,275	1,275,659
Total liabilities	25,569,809	21,780,650	21,805,723
Redeemable noncontrolling interests	55,404	206,292	205,922	$ 205,553
Shareholders’ Equity
Total shareholders' equity available to Arch	11,497,371	9,439,827	9,196,602
Non-redeemable noncontrolling interests	762,777	791,560	843,411
Total shareholders' equity	12,260,148	10,231,387	$ 10,040,013
Total liabilities, noncontrolling interests and shareholders' equity	37,885,361	32,218,329
Reportable legal entities | Arch Capital (Parent Guarantor)
Assets
Total investments	42	104
Cash	18,113	6,125
Investment in subsidiaries	11,786,861	9,735,256
Due from subsidiaries and affiliates	17	9
Premiums receivable	0	0
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	0	0
Contractholder receivables	0	0
Ceded unearned premiums	0	0
Deferred acquisition costs	0	0
Goodwill and intangible assets	0	0
Other assets	20,461	12,588
Total assets	11,825,494	9,754,082
Liabilities
Reserve for losses and loss adjustment expenses	0	0
Unearned premiums	0	0
Reinsurance balances payable	0	0
Contractholder payables	0	0
Collateral held for insured obligations	0	0
Senior notes	297,254	297,150
Revolving credit agreement borrowings	0	0
Due to subsidiaries and affiliates	0	0
Other liabilities	30,869	17,105
Total liabilities	328,123	314,255
Redeemable noncontrolling interests	0	0
Shareholders’ Equity
Total shareholders' equity available to Arch	11,497,371	9,439,827
Non-redeemable noncontrolling interests	0	0
Total shareholders' equity	11,497,371	9,439,827
Total liabilities, noncontrolling interests and shareholders' equity	11,825,494	9,754,082
Reportable legal entities | Arch-U.S. (Subsidiary Issuer)
Assets
Total investments	692,606	452,674
Cash	54,518	5,940
Investment in subsidiaries	4,347,806	3,999,243
Due from subsidiaries and affiliates	200,635	2
Premiums receivable	0	0
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	0	0
Contractholder receivables	0	0
Ceded unearned premiums	0	0
Deferred acquisition costs	0	0
Goodwill and intangible assets	0	0
Other assets	32,187	80,949
Total assets	5,327,752	4,538,808
Liabilities
Reserve for losses and loss adjustment expenses	0	0
Unearned premiums	0	0
Reinsurance balances payable	0	0
Contractholder payables	0	0
Collateral held for insured obligations	0	0
Senior notes	494,831	494,723
Revolving credit agreement borrowings	0	0
Due to subsidiaries and affiliates	536,805	536,805
Other liabilities	33,267	26,270
Total liabilities	1,064,903	1,057,798
Redeemable noncontrolling interests	0	0
Shareholders’ Equity
Total shareholders' equity available to Arch	4,262,849	3,481,010
Non-redeemable noncontrolling interests	0	0
Total shareholders' equity	4,262,849	3,481,010
Total liabilities, noncontrolling interests and shareholders' equity	5,327,752	4,538,808
Reportable legal entities | Other Arch Capital Subsidiaries
Assets
Total investments	23,748,432	21,307,206
Cash	653,599	634,491
Investment in subsidiaries	0	0
Due from subsidiaries and affiliates	1,901,865	1,802,686
Premiums receivable	2,547,130	1,834,389
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	9,711,773	8,618,660
Contractholder receivables	2,119,460	2,079,111
Ceded unearned premiums	2,230,164	1,730,262
Deferred acquisition costs	675,917	618,535
Goodwill and intangible assets	738,083	634,920
Other assets	1,981,598	1,466,438
Total assets	46,308,021	40,726,698
Liabilities
Reserve for losses and loss adjustment expenses	19,028,538	17,345,142
Unearned premiums	5,335,030	4,508,429
Reinsurance balances payable	1,435,485	928,346
Contractholder payables	2,119,460	2,079,111
Collateral held for insured obligations	206,698	236,630
Senior notes	1,114,541	941,655
Revolving credit agreement borrowings	484,287	455,682
Due to subsidiaries and affiliates	1,565,712	1,265,892
Other liabilities	2,324,793	1,699,768
Total liabilities	33,614,544	29,460,655
Redeemable noncontrolling interests	58,882	220,992
Shareholders’ Equity
Total shareholders' equity available to Arch	11,871,818	10,253,491
Non-redeemable noncontrolling interests	762,777	791,560
Total shareholders' equity	12,634,595	11,045,051
Total liabilities, noncontrolling interests and shareholders' equity	46,308,021	40,726,698
Consolidating adjustments and eliminations
Assets
Total investments	(38,834)	(14,700)
Cash	0	0
Investment in subsidiaries	(16,134,667)	(13,734,499)
Due from subsidiaries and affiliates	(2,102,517)	(1,802,697)
Premiums receivable	(768,413)	(535,239)
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	(5,364,957)	(5,699,288)
Contractholder receivables	0	0
Ceded unearned premiums	(995,481)	(754,793)
Deferred acquisition costs	(42,517)	(48,961)
Goodwill and intangible assets	0	0
Other assets	(128,520)	(211,082)
Total assets	(25,575,906)	(22,801,259)
Liabilities
Reserve for losses and loss adjustment expenses	(5,136,696)	(5,491,845)
Unearned premiums	(995,481)	(754,793)
Reinsurance balances payable	(768,413)	(535,239)
Contractholder payables	0	0
Collateral held for insured obligations		0
Senior notes	(35,000)	0
Revolving credit agreement borrowings	0	0
Due to subsidiaries and affiliates	(2,102,517)	(1,802,697)
Other liabilities	(399,654)	(467,484)
Total liabilities	(9,437,761)	(9,052,058)
Redeemable noncontrolling interests	(3,478)	(14,700)
Shareholders’ Equity
Total shareholders' equity available to Arch	(16,134,667)	(13,734,501)
Non-redeemable noncontrolling interests	0	0
Total shareholders' equity	(16,134,667)	(13,734,501)
Total liabilities, noncontrolling interests and shareholders' equity	$ (25,575,906)	$ (22,801,259)

Guarantor Financial Informati_4

Guarantor Financial Information - Condensed consolidating statement of income and comprehensive income (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Revenues
Net premiums earned	$ 1,515,882	$ 1,438,023	$ 1,463,727	$ 1,368,866	$ 1,369,435	$ 1,290,878	$ 1,336,763	$ 1,234,899	$ 5,786,498	$ 5,231,975	$ 4,844,532
Net investment income	154,263	161,488	155,038	156,949	157,217	144,024	135,668	126,724	627,738	563,633	470,872
Net realized gains (losses)	41,474	62,518	120,806	141,565	(166,030)	(51,705)	(76,611)	(110,998)	366,363	(405,344)	149,141
Net impairment losses recognized in earnings	(644)	(1,163)	(49)	(1,309)	(1,705)	(492)	(470)	(162)	(3,165)	(2,829)	(7,138)
Other underwriting income									24,861	15,073	30,253
Equity in net income of investments accounted for using the equity method									123,672	45,641	142,286
Other income (loss)									2,233	2,419	(2,571)
Total revenues									6,928,200	5,450,568	5,627,375
Expenses
Losses and loss adjustment expenses									3,133,452	2,890,106	2,967,446
Acquisition expenses									840,945	805,135	775,458
Other operating expenses									800,997	677,809	684,451
Corporate expenses									80,111	78,994	83,752
Amortization of intangible assets									82,104	105,670	125,778
Interest expense									120,872	120,484	117,431
Net foreign exchange losses (gains)									20,609	(69,402)	115,782
Total expenses									5,079,090	4,608,796	4,870,098
Income (loss) before income taxes									1,849,110	841,772	757,277
Income tax (expense) benefit									(155,810)	(113,951)	(127,568)
Income (loss) before equity in net income of subsidiaries									1,693,300	727,821	629,709
Equity in net income of subsidiaries									0	0	0
Net income	326,384	392,453	468,954	448,528	136,494	227,408	243,646	150,423	1,693,300	727,821	629,709
Net (income) loss attributable to noncontrolling interests									(56,981)	30,150	(10,431)
Net income available to Arch									1,636,319	757,971	619,278
Preferred dividends	(10,403)	(10,403)	(10,403)	(10,403)	(10,403)	(10,402)	(10,403)	(10,437)	(41,612)	(41,645)	(46,041)
Loss on redemption of preferred shares									0	(2,710)	(6,735)
Net income available to Arch common shareholders	$ 315,981	$ 382,050	$ 458,551	$ 438,125	$ 126,091	$ 217,006	$ 233,243	$ 137,276	1,594,707	713,616	566,502
Comprehensive Income									2,027,129	611,003	851,863
Reportable legal entities | Arch Capital (Parent Guarantor)
Revenues
Net premiums earned									0	0	0
Net investment income									212	49	243
Net realized gains (losses)									0	29	0
Net impairment losses recognized in earnings									0	0	0
Other underwriting income									0	0	0
Equity in net income of investments accounted for using the equity method									0	0	0
Other income (loss)									(762)	1,918	(482)
Total revenues									(550)	1,996	(239)
Expenses
Losses and loss adjustment expenses									0	0	0
Acquisition expenses									0	0	0
Other operating expenses									0	0	0
Corporate expenses									62,701	64,279	67,450
Amortization of intangible assets									0	0	0
Interest expense									22,154	22,147	23,560
Net foreign exchange losses (gains)									1	30	2
Total expenses									84,856	86,456	91,012
Income (loss) before income taxes									(85,406)	(84,460)	(91,251)
Income tax (expense) benefit									0	0	0
Income (loss) before equity in net income of subsidiaries									(85,406)	(84,460)	(91,251)
Equity in net income of subsidiaries									1,721,725	842,431	710,529
Net income									1,636,319	757,971	619,278
Net (income) loss attributable to noncontrolling interests									0	0	0
Net income available to Arch									1,636,319	757,971	619,278
Preferred dividends									(41,612)	(41,645)	(46,041)
Loss on redemption of preferred shares										(2,710)	(6,735)
Net income available to Arch common shareholders									1,594,707	713,616	566,502
Comprehensive Income									2,027,129	611,003	851,863
Reportable legal entities | Arch-U.S. (Subsidiary Issuer)
Revenues
Net premiums earned									0	0	0
Net investment income									14,270	3,902	1,420
Net realized gains (losses)									25,313	(2,676)	0
Net impairment losses recognized in earnings									0	0	0
Other underwriting income									0	0	0
Equity in net income of investments accounted for using the equity method									779	0	0
Other income (loss)									0	0	0
Total revenues									40,362	1,226	1,420
Expenses
Losses and loss adjustment expenses									0	0	0
Acquisition expenses									0	0	0
Other operating expenses									0	0	0
Corporate expenses									7,221	2,422	4,152
Amortization of intangible assets									0	0	0
Interest expense									47,951	48,103	47,993
Net foreign exchange losses (gains)									0	0	0
Total expenses									55,172	50,525	52,145
Income (loss) before income taxes									(14,810)	(49,299)	(50,725)
Income tax (expense) benefit									3,696	13,314	10,333
Income (loss) before equity in net income of subsidiaries									(11,114)	(35,985)	(40,392)
Equity in net income of subsidiaries									564,657	388,260	303,991
Net income									553,543	352,275	263,599
Net (income) loss attributable to noncontrolling interests									0	0	0
Net income available to Arch									553,543	352,275	263,599
Preferred dividends									0	0	0
Loss on redemption of preferred shares										0	0
Net income available to Arch common shareholders									553,543	352,275	263,599
Comprehensive Income									751,210	292,973	288,752
Reportable legal entities | Other Arch Capital Subsidiaries
Revenues
Net premiums earned									5,786,498	5,231,975	4,844,532
Net investment income									706,038	649,394	559,963
Net realized gains (losses)									352,771	(410,014)	149,141
Net impairment losses recognized in earnings									(3,165)	(2,829)	(7,138)
Other underwriting income									24,861	15,073	30,253
Equity in net income of investments accounted for using the equity method									122,893	45,641	142,286
Other income (loss)									2,995	501	(2,089)
Total revenues									6,992,891	5,529,741	5,716,948
Expenses
Losses and loss adjustment expenses									3,133,452	2,890,106	2,967,446
Acquisition expenses									840,945	805,135	775,458
Other operating expenses									800,997	677,809	684,451
Corporate expenses									10,189	12,293	12,150
Amortization of intangible assets									82,104	105,670	125,778
Interest expense									142,662	138,672	135,342
Net foreign exchange losses (gains)									22,188	(59,607)	68,900
Total expenses									5,032,537	4,570,078	4,769,525
Income (loss) before income taxes									1,960,354	959,663	947,423
Income tax (expense) benefit									(159,506)	(127,265)	(137,901)
Income (loss) before equity in net income of subsidiaries									1,800,848	832,398	809,522
Equity in net income of subsidiaries									0	0	0
Net income									1,800,848	832,398	809,522
Net (income) loss attributable to noncontrolling interests									(57,868)	28,875	(11,721)
Net income available to Arch									1,742,980	861,273	797,801
Preferred dividends									0	0	0
Loss on redemption of preferred shares										0	0
Net income available to Arch common shareholders									1,742,980	861,273	797,801
Comprehensive Income									2,124,455	730,828	983,475
Consolidating adjustments and eliminations
Revenues
Net premiums earned									0	0	0
Net investment income									(92,782)	(89,712)	(90,754)
Net realized gains (losses)									(11,721)	7,317	0
Net impairment losses recognized in earnings									0	0	0
Other underwriting income									0	0	0
Equity in net income of investments accounted for using the equity method									0	0	0
Other income (loss)									0	0	0
Total revenues									(104,503)	(82,395)	(90,754)
Expenses
Losses and loss adjustment expenses									0	0	0
Acquisition expenses									0	0	0
Other operating expenses									0	0	0
Corporate expenses									0	0	0
Amortization of intangible assets									0	0	0
Interest expense									(91,895)	(88,438)	(89,464)
Net foreign exchange losses (gains)									(1,580)	(9,825)	46,880
Total expenses									(93,475)	(98,263)	(42,584)
Income (loss) before income taxes									(11,028)	15,868	(48,170)
Income tax (expense) benefit									0	0	0
Income (loss) before equity in net income of subsidiaries									(11,028)	15,868	(48,170)
Equity in net income of subsidiaries									(2,286,382)	(1,230,691)	(1,014,520)
Net income									(2,297,410)	(1,214,823)	(1,062,690)
Net (income) loss attributable to noncontrolling interests									887	1,275	1,290
Net income available to Arch									(2,296,523)	(1,213,548)	(1,061,400)
Preferred dividends									0	0	0
Loss on redemption of preferred shares										0	0
Net income available to Arch common shareholders									(2,296,523)	(1,213,548)	(1,061,400)
Comprehensive Income									$ (2,875,665)	$ (1,023,801)	$ (1,272,227)

Guarantor Financial Informati_5

Guarantor Financial Information - Condensed consolidating statement of cash flows (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Operating Activities
Net Cash Provided by (Used in) Operating Activities		$ 2,048,459	$ 1,559,322	$ 1,094,878
Investing Activities
Purchases of fixed maturity investments		(30,053,777)	(33,327,660)	(36,806,913)
Purchases of equity securities		(811,967)	(1,001,149)	(1,021,016)
Purchases of other investments		(1,470,545)	(2,014,622)	(2,020,624)
Proceeds from the sale of fixed maturity investments		28,595,865	31,513,271	35,686,779
Proceeds from sales of equity securities		429,818	1,118,445	1,056,401
Proceeds from sales, redemptions and maturities of other investments		1,209,559	1,561,958	1,528,617
Proceeds from redemptions and maturities of fixed maturity investments		643,265	892,755	907,417
Net settlements of derivative instruments		59,982	44,699	(28,563)
Proceeds from investment in joint venture				0
Net (purchases) sales of short-term investments		39,833	485,473	(734,554)
Change in cash collateral related to securities lending		(62,193)	180,883	12,540
Contributions to subsidiaries		0	0	0
Issuance of intercompany loans		0		0
Repayment of intercompany loans				0
Purchases of fixed assets		(37,837)	(29,809)	(22,841)
Other		(348,486)	21,736	90,875
Net Cash Provided by (Used in) Investing Activities		(1,806,483)	(554,020)	(1,351,882)
Financing Activities
Proceeds from issuance of preferred shares, net		0	0	319,694
Redemption of preferred shares		0	(92,555)	(230,000)
Purchases of common shares under share repurchase program		(2,871)	(282,762)	0
Proceeds from common shares issued, net		6,203	(7,608)	(21,048)
Proceeds from intercompany loans		0		0
Proceeds from borrowings		200,083	218,259	253,415
Repayments of intercompany loans				0
Repayments of borrowings		(49,182)	(576,401)	(197,000)
Change in cash collateral related to securities lending		62,193	(180,883)	(12,540)
Change in third party investment in non-redeemable noncontrolling interests		(75,056)	0	0
Change in third party investment in redeemable noncontrolling interests		(161,882)	0	0
Dividends paid to redeemable noncontrolling interests		(12,515)	(17,989)	(17,989)
Dividends paid to parent	[1]	0	0	0
Other		(6,023)	(7,226)	(51,896)
Preferred dividends paid		(41,612)	(41,645)	(46,041)
Net Cash Provided by (Used in) Financing Activities		(80,662)	(988,810)	(3,405)
Effects of exchange rate changes on foreign currency cash and restricted cash		17,741	(19,133)	18,124
Increase (decrease) in cash and restricted cash		179,055	(2,641)	(242,285)
Cash and restricted cash, beginning of year		724,643	727,284	969,569
Cash and restricted cash, end of year		903,698	724,643	727,284
Reportable legal entities | Arch Capital (Parent Guarantor)
Operating Activities
Net Cash Provided by (Used in) Operating Activities		52,487	324,319	159,130
Investing Activities
Purchases of fixed maturity investments		0	0	0
Purchases of equity securities		0	0	0
Purchases of other investments		0	0	0
Proceeds from the sale of fixed maturity investments		0	0	0
Proceeds from sales of equity securities		0	0	0
Proceeds from sales, redemptions and maturities of other investments		0	0	0
Proceeds from redemptions and maturities of fixed maturity investments		0	0	0
Net settlements of derivative instruments		0	0	0
Proceeds from investment in joint venture				0
Net (purchases) sales of short-term investments		61	96,476	(93,864)
Change in cash collateral related to securities lending		0	0	0
Contributions to subsidiaries		(2,121)	0	20,457
Issuance of intercompany loans		0		0
Repayment of intercompany loans				0
Purchases of fixed assets		(162)	(110)	(18)
Other		0	(4)	0
Net Cash Provided by (Used in) Investing Activities		(2,222)	96,362	(73,425)
Financing Activities
Proceeds from issuance of preferred shares, net				319,694
Redemption of preferred shares			(92,555)	(230,000)
Purchases of common shares under share repurchase program		(2,871)	(282,762)	0
Proceeds from common shares issued, net		6,203	(7,608)	(21,048)
Proceeds from intercompany loans		0		0
Proceeds from borrowings		0	0	0
Repayments of intercompany loans				0
Repayments of borrowings		0	0	(100,000)
Change in cash collateral related to securities lending		0	0	0
Change in third party investment in non-redeemable noncontrolling interests		0
Change in third party investment in redeemable noncontrolling interests		0
Dividends paid to redeemable noncontrolling interests		0	0	0
Dividends paid to parent	[1]	0	0	0
Other		0	0	0
Preferred dividends paid		(41,612)	(41,645)	(46,041)
Net Cash Provided by (Used in) Financing Activities		(38,280)	(424,570)	(77,395)
Effects of exchange rate changes on foreign currency cash and restricted cash		0	0	0
Increase (decrease) in cash and restricted cash		11,985	(3,889)	8,310
Cash and restricted cash, beginning of year		6,159	10,048	1,738
Cash and restricted cash, end of year		18,144	6,159	10,048
Reportable legal entities | Arch-U.S. (Subsidiary Issuer)
Operating Activities
Net Cash Provided by (Used in) Operating Activities		486,252	481,751	(10,289)
Investing Activities
Purchases of fixed maturity investments		(878,577)	(906,482)	0
Purchases of equity securities		(155,890)	(44,830)	0
Purchases of other investments		(28,490)	0	0
Proceeds from the sale of fixed maturity investments		806,603	535,947	0
Proceeds from sales of equity securities		7,441	0	0
Proceeds from sales, redemptions and maturities of other investments		1,634	0	0
Proceeds from redemptions and maturities of fixed maturity investments		0	0	0
Net settlements of derivative instruments		0	0	0
Proceeds from investment in joint venture				0
Net (purchases) sales of short-term investments		34,372	7,674	(4,586)
Change in cash collateral related to securities lending		0	0	0
Contributions to subsidiaries		(6,000)	(98,500)	(73,700)
Issuance of intercompany loans		(200,000)		0
Repayment of intercompany loans				47,000
Purchases of fixed assets		0	0	0
Other		(18,767)	0	0
Net Cash Provided by (Used in) Investing Activities		(437,674)	(506,191)	(31,286)
Financing Activities
Proceeds from issuance of preferred shares, net				0
Redemption of preferred shares			0	0
Purchases of common shares under share repurchase program		0	0	0
Proceeds from common shares issued, net		0	0	0
Proceeds from intercompany loans		0		0
Proceeds from borrowings		0	0	0
Repayments of intercompany loans				0
Repayments of borrowings		0	0	0
Change in cash collateral related to securities lending		0	0	0
Change in third party investment in non-redeemable noncontrolling interests		0
Change in third party investment in redeemable noncontrolling interests		0
Dividends paid to redeemable noncontrolling interests		0	0	0
Dividends paid to parent	[1]	0	0	0
Other		0	0	0
Preferred dividends paid		0	0	0
Net Cash Provided by (Used in) Financing Activities		0	0	0
Effects of exchange rate changes on foreign currency cash and restricted cash		0	0	0
Increase (decrease) in cash and restricted cash		48,578	(24,440)	(41,575)
Cash and restricted cash, beginning of year		5,940	30,380	71,955
Cash and restricted cash, end of year		54,518	5,940	30,380
Reportable legal entities | Other Arch Capital Subsidiaries
Operating Activities
Net Cash Provided by (Used in) Operating Activities		2,138,195	1,703,181	1,649,751
Investing Activities
Purchases of fixed maturity investments		(29,347,333)	(33,662,541)	(36,806,913)
Purchases of equity securities		(726,820)	(956,319)	(1,021,016)
Purchases of other investments		(1,442,055)	(2,014,622)	(2,020,624)
Proceeds from the sale of fixed maturity investments		27,937,616	32,218,687	35,686,779
Proceeds from sales of equity securities		493,120	1,118,445	1,056,401
Proceeds from sales, redemptions and maturities of other investments		1,207,925	1,561,958	1,528,617
Proceeds from redemptions and maturities of fixed maturity investments		643,265	892,755	907,417
Net settlements of derivative instruments		59,982	44,699	(28,563)
Proceeds from investment in joint venture				0
Net (purchases) sales of short-term investments		5,400	381,323	(636,104)
Change in cash collateral related to securities lending		(62,193)	180,883	12,540
Contributions to subsidiaries		(57,039)	98,500	(423,998)
Issuance of intercompany loans		(87,783)		(47,000)
Repayment of intercompany loans				80,840
Purchases of fixed assets		(37,675)	(29,699)	(22,823)
Other		(329,719)	21,740	111,516
Net Cash Provided by (Used in) Investing Activities		(1,743,309)	(144,191)	(1,622,931)
Financing Activities
Proceeds from issuance of preferred shares, net				0
Redemption of preferred shares			0	0
Purchases of common shares under share repurchase program		0	0	0
Proceeds from common shares issued, net		65,160	0	477,244
Proceeds from intercompany loans		287,783		47,000
Proceeds from borrowings		235,083	218,259	253,415
Repayments of intercompany loans				127,840
Repayments of borrowings		(49,182)	(576,401)	(97,000)
Change in cash collateral related to securities lending		62,193	(180,883)	(12,540)
Change in third party investment in non-redeemable noncontrolling interests		(75,056)
Change in third party investment in redeemable noncontrolling interests		(173,103)
Dividends paid to redeemable noncontrolling interests		(13,402)	(19,264)	(19,264)
Dividends paid to parent	[1]	(627,588)	(948,654)	(702,442)
Other		(6,023)	(7,226)	(72,537)
Preferred dividends paid		0	0	0
Net Cash Provided by (Used in) Financing Activities		(294,135)	(1,514,169)	(253,964)
Effects of exchange rate changes on foreign currency cash and restricted cash		17,741	(19,133)	18,124
Increase (decrease) in cash and restricted cash		118,492	25,688	(209,020)
Cash and restricted cash, beginning of year		712,544	686,856	895,876
Cash and restricted cash, end of year		831,036	712,544	686,856
Consolidating adjustments and eliminations
Operating Activities
Net Cash Provided by (Used in) Operating Activities		(628,475)	(949,929)	(703,714)
Investing Activities
Purchases of fixed maturity investments		172,133	1,241,363	0
Purchases of equity securities		70,743	0	0
Purchases of other investments		0	0	0
Proceeds from the sale of fixed maturity investments		(148,354)	(1,241,363)	0
Proceeds from sales of equity securities		(70,743)	0	0
Proceeds from sales, redemptions and maturities of other investments		0	0	0
Proceeds from redemptions and maturities of fixed maturity investments		0	0	0
Net settlements of derivative instruments		0	0	0
Proceeds from investment in joint venture				0
Net (purchases) sales of short-term investments		0	0	0
Change in cash collateral related to securities lending		0	0	0
Contributions to subsidiaries		65,160	0	477,241
Issuance of intercompany loans		287,783		47,000
Repayment of intercompany loans				(127,840)
Purchases of fixed assets		0	0	0
Other		0	0	(20,641)
Net Cash Provided by (Used in) Investing Activities		376,722	0	375,760
Financing Activities
Proceeds from issuance of preferred shares, net				0
Redemption of preferred shares			0	0
Purchases of common shares under share repurchase program		0	0	0
Proceeds from common shares issued, net		(65,160)	0	(477,244)
Proceeds from intercompany loans		(287,783)		(47,000)
Proceeds from borrowings		(35,000)	0	0
Repayments of intercompany loans				(127,840)
Repayments of borrowings		0	0	0
Change in cash collateral related to securities lending		0	0	0
Change in third party investment in non-redeemable noncontrolling interests		0
Change in third party investment in redeemable noncontrolling interests		11,221
Dividends paid to redeemable noncontrolling interests		887	1,275	1,275
Dividends paid to parent	[1]	627,588	948,654	702,442
Other		0	0	20,641
Preferred dividends paid		0	0	0
Net Cash Provided by (Used in) Financing Activities		251,753	949,929	327,954
Effects of exchange rate changes on foreign currency cash and restricted cash		0	0	0
Increase (decrease) in cash and restricted cash		0	0	0
Cash and restricted cash, beginning of year		0	0	0
Cash and restricted cash, end of year		$ 0	$ 0	$ 0
[1]	ncluded in net cash provided by (used for) operating activities in the Arch Capital (Parent Guarantor) and/or Arch-U.S. (Subsidiary Issuer) columns.

Subsequent Event - (Details)

Subsequent Event - (Details) - Subsequent Event - Coface € / shares in Units, € in Millions	Feb. 25, 2020EUR (€)€ / shares
Subsequent Event [Line Items]
Percentage ownership	29.50%
Share price | € / shares	€ 10.70
Total estimated purchase price | €	€ 480

Schedule III - Supplementary _2

Schedule III - Supplementary Insurance Information (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs		$ 633,400	$ 569,574	$ 535,824
Reserves for Losses and Loss Adjustment Expenses		13,891,842	11,853,297	11,383,792
Unearned Premiums		4,339,549	3,753,636	3,622,314
Net Premiums Earned		5,786,498	5,231,975	4,844,532
Net Losses and Loss Adjustment Expenses Incurred		3,133,452	2,890,106	2,967,446
Amortization of Deferred Acquisition Costs		840,945	805,135	775,458
Other Operating Expenses	[1]	800,997	677,809	684,451
Net Premiums Written		6,039,067	5,346,747	4,961,373
Other
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs		64,044	80,858	85,961
Reserves for Losses and Loss Adjustment Expenses		1,263,629	1,032,760	798,262
Unearned Premiums		438,907	390,114	330,644
Net Premiums Earned		556,689	578,862	531,727
Net Losses and Loss Adjustment Expenses Incurred		453,135	441,255	436,402
Amortization of Deferred Acquisition Costs		105,980	125,558	129,971
Other Operating Expenses	[1]	51,651	37,889	31,928
Net Premiums Written		532,862	604,175	553,117
Underwriting segments | Insurance
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs		188,684	152,360	159,224
Reserves for Losses and Loss Adjustment Expenses		7,900,328	7,093,018	6,952,676
Unearned Premiums		1,991,496	1,549,183	1,451,390
Net Premiums Earned		2,397,080	2,205,661	2,113,018
Net Losses and Loss Adjustment Expenses Incurred		1,615,475	1,520,680	1,622,444
Amortization of Deferred Acquisition Costs		361,614	349,702	323,639
Other Operating Expenses	[1]	454,770	364,138	359,524
Net Premiums Written		2,641,726	2,212,125	2,122,440
Underwriting segments | Reinsurance
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs		197,856	166,276	150,582
Reserves for Losses and Loss Adjustment Expenses		4,270,013	3,215,909	3,053,694
Unearned Premiums		971,776	710,774	633,810
Net Premiums Earned		1,466,389	1,261,216	1,142,621
Net Losses and Loss Adjustment Expenses Incurred		1,011,329	846,882	773,923
Amortization of Deferred Acquisition Costs		239,032	211,280	221,250
Other Operating Expenses	[1]	141,484	133,350	146,663
Net Premiums Written		1,602,723	1,372,572	1,174,474
Underwriting segments | Mortgage
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs		182,816	170,080	140,057
Reserves for Losses and Loss Adjustment Expenses		457,872	511,610	579,160
Unearned Premiums		937,370	1,103,565	1,206,470
Net Premiums Earned		1,366,340	1,186,236	1,057,166
Net Losses and Loss Adjustment Expenses Incurred		53,513	81,289	134,677
Amortization of Deferred Acquisition Costs		134,319	118,595	100,598
Other Operating Expenses	[1]	153,092	142,432	146,336
Net Premiums Written		$ 1,261,756	$ 1,157,875	$ 1,111,342
[1]	Certain other operating expenses relate to the Company’s corporate segment (non-underwriting). Such amounts are not reflected in the table above. See note 4, “Segment Information,” to our consolidated financial statements in Item 8 for information related to the corporate segment.

Schedule IV - Reinsurance (Deta

Schedule IV - Reinsurance (Details) - USD ($) $ in Thousands		3 Months Ended								12 Months Ended
		Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2018	Sep. 30, 2018	Jun. 30, 2018	Mar. 31, 2018	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount										$ 5,681,523	$ 4,838,902	$ 4,447,457
Ceded to other Companies										(2,099,893)	(1,614,257)	(1,407,052)
Assumed From Other Companies										2,457,437	2,122,102	1,920,968
Net Amount		$ 1,455,453	$ 1,613,457	$ 1,444,898	$ 1,525,259	$ 1,301,754	$ 1,333,553	$ 1,298,896	$ 1,412,544	$ 6,039,067	$ 5,346,747	$ 4,961,373
Percentage of Amount Assumed to Net										40.70%	39.70%	38.70%
Other
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount										$ 339,169	$ 253,760	$ 133,858
Ceded to other Companies	[1]									(222,019)	(130,840)	(47,187)
Assumed From Other Companies	[1]									415,712	481,255	466,446
Net Amount										$ 532,862	$ 604,175	$ 553,117
Percentage of Amount Assumed to Net										78.00%	79.70%	84.30%
Underwriting segments
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Ceded to other Companies										$ (2,189,440)	$ (1,791,851)	$ (1,679,998)
Net Amount										5,506,205	4,742,572	4,408,256
Underwriting segments | Insurance
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount										3,879,752	3,232,234	3,050,876
Ceded to other Companies	[1]									(1,266,267)	(1,050,207)	(958,646)
Assumed From Other Companies	[1]									28,241	30,098	30,210
Net Amount										$ 2,641,726	$ 2,212,125	$ 2,122,440
Percentage of Amount Assumed to Net										1.10%	1.40%	1.40%
Underwriting segments | Reinsurance
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount										$ 238,229	$ 213,809	$ 152,404
Ceded to other Companies	[1]									(720,500)	(539,950)	(465,925)
Assumed From Other Companies	[1]									2,084,994	1,698,713	1,487,995
Net Amount										$ 1,602,723	$ 1,372,572	$ 1,174,474
Percentage of Amount Assumed to Net										130.10%	123.80%	126.70%
Underwriting segments | Mortgage
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount										$ 1,224,373	$ 1,139,099	$ 1,110,319
Ceded to other Companies	[1]									(204,509)	(202,833)	(256,796)
Assumed From Other Companies	[1]									241,892	221,609	257,819
Net Amount										$ 1,261,756	$ 1,157,875	$ 1,111,342
Percentage of Amount Assumed to Net										19.20%	19.10%	23.20%
[1]	Certain amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

Schedule VI - Supplementary I_2

Schedule VI - Supplementary Information For Property and Casualty Insurance Underwriters (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
SEC Schedule, 12-18, Supplemental Information, Property-Casualty Insurance Underwriters [Line Items]
Net Losees and Loss Adjustment Expenses Incurred Related to Current Year	$ 3,297,037	$ 3,162,818	$ 3,205,428
Net Losses and Loss Adjustment Expenses Incurred Related to Prior Years	(163,585)	(272,712)	(237,982)
Consolidated Subsidiaries
SEC Schedule, 12-18, Supplemental Information, Property-Casualty Insurance Underwriters [Line Items]
Deferred Acquisition Costs	633,400	569,574	535,824
Reserves for Losses and Loss Adjustment Expenses	13,891,842	11,853,297	11,383,792
Discount, if any, deducted in Column C	22,012	21,145	20,016
Unearned Premiums	4,339,549	3,753,636	3,622,314
Net Premiums Earned	5,786,498	5,231,975	4,844,532
Net investment income	627,738	563,633	470,872
Net Losees and Loss Adjustment Expenses Incurred Related to Current Year	3,297,037	3,162,818	3,205,428
Net Losses and Loss Adjustment Expenses Incurred Related to Prior Years	(163,585)	(272,712)	(237,982)
Amortization of Deferred Acquisition Costs	840,945	805,135	775,458
Net Paid Losses and Loss Adjustment Expenses	2,383,255	2,206,164	2,352,912
Net Premiums Written	$ 6,039,067	$ 5,346,747	$ 4,961,373