Arch Capital (ACGL) 10-K 25 Feb 22 2020 FY Annual report Financial data

Document and Entity Information

Document and Entity Information - USD ($) $ in Billions	12 Months Ended
	Dec. 31, 2021	Feb. 21, 2022	Jun. 30, 2021
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, 2021
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
ICFR Auditor Attestation Flag	true
Entity Shell Company	false
Entity Public Float			$ 14.3
Entity Common Stock, Shares Outstanding		379,042,099
Documents Incorporated by Reference	Portions of Part III and Part IV incorporate by reference our definitive proxy statement for the 2022 annual meeting of shareholders to be filed with the Securities and Exchange Commission pursuant to Regulation 14A within 120 days after December 31, 2021.
Entity Central Index Key	0000947484
Current Fiscal Year End Date	--12-31
Document Fiscal Year Focus	2020
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
Series F depositary share equivalent
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
Series G depositary share equivalent
Entity Listings [Line Items]
Title of 12(b) Security	Depositary shares, each representing a 1/1,000th interest in a 4.55% Series G preferred share
Trading Symbol	ACGLN
Security Exchange Name	NASDAQ

Audit Information

Audit Information	12 Months Ended
	Dec. 31, 2021
Audit Information [Abstract]
Auditor Name	PricewaterhouseCoopers LLP
Auditor Location	New York, New York
Auditor Firm ID	238

Consolidated Balance Sheets

Consolidated Balance Sheets - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020
Investments:
Fixed maturities available for sale, at fair value (amortized cost: $17,973,823 and $18,143,305; net of allowance for credit losses: $2,883 and $2,397)	$ 17,998,109	$ 18,717,825
Short-term investments available for sale, at fair value (amortized cost: $1,734,738 and $1,924,292; net of allowance for credit losses: $0 and $0 )	1,734,716	1,924,922
Collateral received under securities lending, at fair value (amortized cost: $0 and $301,089)	0	301,096
Equity securities, at fair value	1,804,170	1,444,830
Other investments (portion measured at fair value: $1,973,550 and $3,824,796)	1,973,550	4,324,796
Investments accounted for using the equity method	3,077,611	2,047,889
Total investments	26,588,156	28,761,358
Cash	858,668	906,448
Accrued investment income	85,453	103,299
Securities pledged under securities lending, at fair value (amortized cost: $0 and $294,493)	0	294,912
Investment in operating affiliates	1,135,655	129,291
Premiums receivable (net of allowance for credit losses: $39,958 and $37,781)	2,633,280	2,064,586
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $13,230 and $11,636)	5,880,735	4,500,802
Contractholder receivables (net of allowance for credit losses: $3,437 and $8,638)	1,828,691	1,986,924
Ceded unearned premiums	1,729,455	1,234,075
Deferred acquisition costs	901,841	790,708
Receivable for securities sold	60,179	92,743
Goodwill and intangible assets	944,983	692,863
Other assets	2,453,849	1,724,288
Total assets	45,100,945	43,282,297
Liabilities
Reserve for losses and loss adjustment expenses	17,757,156	16,513,929
Unearned premiums	6,011,942	4,838,965
Reinsurance balances payable	1,583,253	683,263
Contractholder payables	1,832,127	1,995,562
Collateral held for insured obligations	242,352	215,581
Senior notes	2,724,394	2,861,113
Revolving credit agreement borrowings	0	155,687
Securities lending payable	0	301,089
Payable for securities purchased	64,850	218,779
Other liabilities	1,329,742	1,510,888
Total liabilities	31,545,816	29,294,856
Commitments and Contingencies
Redeemable noncontrolling interests	9,233	58,548
Shareholders’ Equity
Non-cumulative preferred shares	830,000	780,000
Common shares ($0.0011 par, shares issued: 583,289,850 and 579,000,841)	648	643
Additional paid-in capital	2,085,075	1,977,794
Retained earnings	14,455,868	12,362,463
Accumulated other comprehensive income (loss), net of deferred income tax	(64,600)	488,895
Common shares held in treasury, at cost (shares: 204,365,956 and 172,280,199)	(3,761,095)	(2,503,909)
Total shareholders' equity available to Arch	13,545,896	13,105,886
Non-redeemable noncontrolling interests	0	823,007
Total shareholders' equity	13,545,896	13,928,893
Total liabilities, noncontrolling interests and shareholders' equity	$ 45,100,945	$ 43,282,297

Consolidated Balance Sheets (Pa

Consolidated Balance Sheets (Parentheticals) - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020
Fixed maturities available for sale, at amortized cost	$ 17,973,823	$ 18,143,305
Short-term investments available for sale, at amortized cost	1,734,738	1,924,292
Allowance for credit losses on investments	2,883	2,397
Collateral received under securities lending agreements, at amortized cost	0	301,089
Investments accounted for using the fair value option	1,973,550	3,824,796
Securities pledged under securities lending, at amortized cost	0	294,493
Allowance for credit losses on premiums receivable	39,958	37,781
Allowance for credit losses on reinsurance recoverable	13,230	11,636
Allowance for credit loss on contractholder receivable	$ 3,437	$ 8,638
Common shares, par value per share	$ 0.0011	$ 0.0011
Common shares issued (shares)	583,289,850	579,000,841
Common shares held in treasury (shares)	204,365,956	172,280,199
Short-term investments
Short-term investments available for sale, at amortized cost	$ 1,734,738	$ 1,924,292
Allowance for credit losses on investments	0	0
Fixed maturities
Allowance for credit losses on investments	$ 2,883	$ 2,397

Consolidated Statements of Inco

Consolidated Statements of Income - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Revenues
Net premiums earned	$ 8,082,298	$ 6,991,935	$ 5,786,498
Net investment income	389,118	519,608	627,738
Net realized gains (losses)	379,845	823,460	363,198
Other underwriting income	22,073	26,784	24,861
Equity in net income of investments accounted for using the equity method	366,402	146,693	123,672
Other income (loss)	10,244	29	0
Total revenues	9,249,980	8,508,509	6,925,967
Expenses
Losses and loss adjustment expenses	4,584,803	4,689,599	3,133,452
Acquisition expenses	1,303,178	1,004,842	840,945
Other operating expenses	998,595	875,176	800,997
Corporate expenses	79,157	81,988	80,111
Amortization of intangible assets	82,955	69,031	82,104
Interest expense	139,470	143,456	120,872
Net foreign exchange losses (gains)	(41,529)	83,634	20,609
Total expenses	7,146,629	6,947,726	5,079,090
Income (loss) before income taxes and income (loss) from operating affiliates	2,103,351	1,560,783	1,846,877
Income taxes:
Current tax expense (benefit)	295,533	197,662	144,361
Deferred tax expense (benefit)	(166,951)	(85,824)	11,449
Income tax expense	128,582	111,838	155,810
Income (loss) from operating affiliates	264,693	16,766	2,233
Net income	2,239,462	1,465,711	1,693,300
Net (income) loss attributable to noncontrolling interests	(82,613)	(60,190)	(56,981)
Net income available to Arch	2,156,849	1,405,521	1,636,319
Preferred share dividends	(48,343)	(41,612)	(41,612)
Loss on redemption of preferred shares	(15,101)	0	0
Net income available to Arch common shareholders	$ 2,093,405	$ 1,363,909	$ 1,594,707
Net income per common share and common share equivalent
Basic (per share)	$ 5.34	$ 3.38	$ 3.97
Diluted (per share)	$ 5.23	$ 3.32	$ 3.87
Weighted average common shares and common share equivalents outstanding
Basic (shares)	391,748,715	403,062,179	401,802,815
Diluted (shares)	400,345,936	410,259,455	411,609,478

Consolidated Statements of Comp

Consolidated Statements of Comprehensive Income - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Comprehensive Income
Net income	$ 2,239,462	$ 1,465,711	$ 1,693,300
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during year	(386,929)	678,717	500,771
Reclassification of net realized (gains) losses, included in net income	(116,068)	(426,187)	(118,941)
Foreign currency translation adjustments	(64,482)	33,336	18,110
Comprehensive income	1,671,983	1,751,577	2,093,240
Net (income) loss attributable to noncontrolling interests	(82,613)	(60,190)	(56,981)
Other comprehensive (income) loss attributable to noncontrolling interests	13,984	(9,062)	(9,130)
Comprehensive income available to Arch	$ 1,603,354	$ 1,682,325	$ 2,027,129

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	Retained earningsCumulative Effect, Period of Adoption, Adjustment	Retained earningsCumulative Effect, Period of Adoption, Adjusted Balance	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
Balance at beginning of year at Dec. 31, 2018		$ 780,000	$ 634	$ 1,793,781	$ 9,426,299	$ 0	$ 9,426,299	$ (178,720)	$ (114,178)	$ (64,542)	$ (2,382,167)
Preferred shares issued		0
Preferred shares redeemed		0
Common shares issued, net			4
Issue costs on preferred shares issued				0
Loss on redemption of preferred shares	$ 0			0	0
Amortization of share-based compensation				64,152
Other changes				31,750
Net income	1,693,300				1,693,300
Net (income) loss attributable to noncontrolling interests	(56,981)				(56,981)
Preferred share dividends	(41,612)				(41,612)
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	(22,452)	10,998,554	212,091	258,486	(46,395)	(2,406,047)
Non-redeemable noncontrolling interests	762,777
Total shareholders' equity	12,260,148
Preferred shares issued		0
Preferred shares redeemed		0
Common shares issued, net			5
Issue costs on preferred shares issued				0
Loss on redemption of preferred shares	0			0	0
Amortization of share-based compensation				70,535
Other changes				17,576
Net income	1,465,711				1,465,711
Net (income) loss attributable to noncontrolling interests	(60,190)				(60,190)
Preferred share dividends	(41,612)				(41,612)
Unrealized holding gains (losses) during period, net of reclassification adjustment									252,530
Unrealized holding gains (losses) during period attributable to noncontrolling interests									(9,721)
Foreign currency translation adjustments	33,336									33,336
Foreign currency translation adjustments attributable to noncontrolling interests										659
Shares repurchased for treasury	(83,472)										(97,862)
Balance at end of year at Dec. 31, 2020	$ 13,105,886	780,000	643	1,977,794	12,362,463	$ 0	$ 12,362,463	488,895	501,295	(12,400)	(2,503,909)
Accounting Standards Update [Extensible Enumeration]	Accounting Standards Update 2016-13 [Member]
Non-redeemable noncontrolling interests	$ 823,007
Total shareholders' equity	13,928,893
Preferred shares issued		500,000
Preferred shares redeemed		(450,000)
Common shares issued, net			5
Issue costs on preferred shares issued				(14,179)
Loss on redemption of preferred shares	(15,101)			15,101	(15,101)
Amortization of share-based compensation				86,053
Other changes				20,306
Net income	2,239,462				2,239,462
Net (income) loss attributable to noncontrolling interests	(82,613)				(82,613)
Preferred share dividends	(48,343)				(48,343)
Unrealized holding gains (losses) during period, net of reclassification adjustment									(502,997)
Unrealized holding gains (losses) during period attributable to noncontrolling interests									15,188
Foreign currency translation adjustments	(64,482)									(64,482)
Foreign currency translation adjustments attributable to noncontrolling interests										(1,204)
Shares repurchased for treasury	(1,234,294)										(1,257,186)
Balance at end of year at Dec. 31, 2021	13,545,896	$ 830,000	$ 648	$ 2,085,075	$ 14,455,868			$ (64,600)	$ 13,486	$ (78,086)	$ (3,761,095)
Non-redeemable noncontrolling interests	0
Total shareholders' equity	$ 13,545,896

Consolidated Statements of Cash

Consolidated Statements of Cash Flows - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Operating Activities
Net income	$ 2,239,462	$ 1,465,711	$ 1,693,300
Adjustments to reconcile net income to net cash provided by operating activities:
Net realized (gains) losses	(427,367)	(844,625)	(377,967)
Equity in net income or loss of investments accounted for using the equity method and other income or loss	(464,050)	(47,951)	(14,013)
Amortization of intangible assets	82,955	69,031	82,104
Share-based compensation	87,094	71,262	66,417
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	1,762,190	2,113,827	489,981
Unearned premiums, net of ceded unearned premiums	936,039	445,781	252,569
Premiums receivable	(685,214)	(318,643)	(237,752)
Deferred acquisition costs	(263,243)	(143,948)	(47,260)
Reinsurance balances payable	500,065	65,950	182,132
Other items, net	(340,376)	10,110	(41,052)
Net cash provided by operating activities	3,427,555	2,886,505	2,048,459
Investing Activities:
Purchases of fixed maturity investments	(35,451,858)	(39,765,277)	(30,053,777)
Purchases of equity securities	(1,175,480)	(1,595,010)	(811,967)
Purchases of other investments	(1,859,096)	(1,808,727)	(1,470,545)
Proceeds from the sale of fixed maturity investments	33,577,445	37,949,346	28,595,865
Proceeds from sales of equity securities	918,145	1,147,264	429,818
Proceeds from sales, redemptions and maturities of other investments	1,765,533	1,029,578	1,209,559
Proceeds from redemptions and maturities of fixed maturity investments	1,628,755	871,134	643,265
Net settlements of derivative instruments	(40,072)	179,006	59,982
Net (purchases) sales of short-term investments	165,272	(1,029,681)	39,833
Change in cash collateral related to securities lending	0	81,210	(62,193)
Purchase of operating affiliate	(753,916)	0	0
Impact of the deconsolidation of the variable interest entity	(349,202)	0	0
Purchases of fixed assets	(41,394)	(39,872)	(37,837)
Other	(523,864)	(62,197)	(348,486)
Net cash provided by (used for) investing activities	(2,139,732)	(3,043,226)	(1,806,483)
Financing Activities:
Proceeds from issuance of preferred shares, net	485,821	0	0
Redemption of preferred shares	(450,000)	0	0
Purchases of common shares under share repurchase program	(1,234,294)	(83,472)	(2,871)
Proceeds from common shares issued, net	6,418	1,876	6,203
Proceeds from borrowings	0	1,018,793	200,083
Repayments of borrowings	0	(359,000)	(49,182)
Change in cash collateral related to securities lending	0	(81,210)	62,193
Change in third party investment in non-redeemable noncontrolling interests	15,971	(2,867)	(75,056)
Change in third party investment in redeemable noncontrolling interests	0	0	(161,882)
Dividends paid to redeemable noncontrolling interests	(1,907)	(4,945)	(12,515)
Other	(3,278)	73,715	(6,023)
Preferred dividends paid	(48,280)	(41,612)	(41,612)
Net Cash Provided by (Used in) Financing Activities	(1,229,549)	521,278	(80,662)
Effects of exchange rate changes on foreign currency cash and restricted cash	(34,047)	22,289	17,741
Increase (decrease) in cash and restricted cash	24,227	386,846	179,055
Cash and restricted cash, beginning of year	1,290,544	903,698	724,643
Cash and restricted cash, end of year	1,314,771	1,290,544	903,698
Supplemental cash flow information
Income taxes paid (received)	286,810	202,940	109,463
Interest paid	$ 139,301	$ 133,491	$ 126,945

General

General	12 Months Ended
	Dec. 31, 2021
Organization, Consolidation and Presentation of Financial Statements [Abstract]
General	Arch Capital Group Ltd. (“Arch Capital”) is a publicly listed Bermuda exempted 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 included the results of Somers Holdings Ltd. (formerly Watford Holdings Ltd.) and its wholly owned subsidiaries (“Somers”) through June 30, 2021. Effective July 1, 2021, Somers is wholly owned by Greysbridge Holdings Ltd., (“Greysbridge”) and Greysbridge is owned 40% by the Company, 30% by certain investment funds managed by Kelso & Company (“Kelso”) and 30% by certain investment funds managed by Warburg Pincus LLC (“Warburg”). Based on the governing documents of Greysbridge, the Company concluded that, while it retains significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of Somers in its consolidated financial statements and footnotes. See note 12, “Variable Interest Entity and Noncontrolling Interests” . The Company has reclassified the presentation of certain prior year information to conform to the current presentation, including the correct presentation of ‘income (loss) from operating affiliates’ on its consolidated statements of income for all periods presented to reclass such item from ‘other income (loss)’. The Company also changed its presentation of ‘investment in operating affiliates’ on its consolidated balance sheet for all periods presented to reclass such item from ‘other assets’. Such reclassifications had no effect on the Company’s net income, comprehensive income, shareholders’ equity or cash flows. Management views the impact of the prior period misclassification as not material to the financial statements on a quantitative and qualitative basis. See note 9 . Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted.

Acquisitions

Acquisitions	12 Months Ended
	Dec. 31, 2021
Business Combinations [Abstract]
Business Acquired	Westpac Lenders Mortgage Insurance Limited (“WLMI”) On August 31, 2021, the Company completed the acquisition of WLMI, an Australian Prudential Regulation Authority authorized captive lenders mortgage insurance (“LMI”) provider to the Westpac Banking Corporation (“Westpac”). As part of the acquisition, WLMI will retain its existing risk in force and remain Westpac’s exclusive provider of LMI on new mortgage originations for a period of 10 years. Upon completion of this transaction, the Company renamed WLMI to Arch Lenders Mortgage Indemnity Limited (“Arch Indemnity”). Arch Indemnity will become the Company’s primary provider of LMI to the Australian market. Somerset Bridge Group Limited, Southern Rock Holdings Limited and affiliates (“Somerset Group”) On August 6, 2021, the Company completed the acquisition of Somerset Group. The acquisition includes Somerset Group’s motor insurance managing general agent, distribution capabilities through direct and aggregator channels, affiliated insurer and fully integrated claims operation. In connection with the acquisitions noted above, the Company increased its goodwill and intangible assets by $350.1 million. Barbican Group Holdings Limited On November 29, 2019, the Company closed the acquisition of Barbican Group Holdings Limited and its subsidiaries (collectively, “Barbican”). 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.

Significant Accounting Policies

Significant Accounting Policies	12 Months Ended
	Dec. 31, 2021
Accounting Policies [Abstract]
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 Capital Group (U.S.) Inc.(“Arch-U.S.”), Arch Insurance Company, Arch Specialty Insurance Company, Arch Property & Casualty Insurance Company (“Arch P&C”), Arch Indemnity Insurance Company (“Arch Indemnity Insurance”), Arch Insurance Canada Ltd. (“Arch Insurance Canada”), Arch Reinsurance Europe Designated Activity Company (“Arch Re Europe”), Arch Mortgage Insurance Company (“AMIC”), Arch Mortgage Guaranty Company, United Guaranty Residential Insurance Company (“UGRIC”), Arch Indemnity, Arch Insurance (EU) Designated Activity Company (“Arch Insurance (EU)”), Arch Insurance (U.K.) Limited (“Arch Insurance (U.K.)”) and the Company’s participation on Lloyd’s of London syndicates 2012 (“Arch Syndicate 2012”) and 1955 (“Arch Syndicate 1955”). 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 allowance for credit losses; • The valuation of purchased intangible assets; • The assessment of goodwill and intangible assets for impairment; and • The valuation of deferred tax assets. (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 that 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. 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. 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. 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. Premiums receivable include amounts receivable from agents, brokers and insured that are both currently due and amounts not yet due on insurance, reinsurance and mortgage insurance policies. Premiums receivable balances are reported net of an allowance for expected credit losses. The Company monitors credit risk associated with premiums receivable through its ongoing review of amounts outstanding, aging of the receivable, historical loss data, and counterparty financial strength measures. The allowance also includes estimated uncollectible amounts related to dispute risk. In certain instances, credit risk may be reduced by the Company’s right to offset loss obligations or unearned premiums against premiums receivable. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. See note 7, “Allowance for Expected Credit Losses” for additional information. 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 2021, 2020 or 2019. (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 8, “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. Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. In certain instances, the Company obtains collateral, including letters of credit and trust accounts to further reduce the credit exposure on its reinsurance recoverables. The Company reports its reinsurance recoverables net of an allowance for expected credit loss. The allowance is based upon the Company’s ongoing review of amounts outstanding, the financial condition of its reinsurers, amounts and form of collateral obtained and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit loss. Any allowance for credit losses is charged to net realized gains (losses) in the period the recoverable is recorded and revised in s ubsequent periods to reflect changes in the Company’s estimate of expected credit losses . See note 7, “Allowance for Expected Credit Losses” for additional information. (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. Prior to the termination of its program in 2021, the Company entered into securities lending agreements with financial institutions to enhance investment income whereby it loaned 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 maintained legal control over the securities it lent, retained the earnings and cash flows associated with the loaned securities and received a fee from the borrower for the temporary use of the securities. Collateral received was required at a rate of 102% or greater of the fair value of the loaned securities including accrued investment income and was 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 three 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, short-term investments 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 reverse repurchase agreements that are generally treated as collateralized receivables. Receivables for reverse repurchase agreements are reflected in “Other investments” or “Short-term investments” in the Company's consolidated balance sheet depending on their terms. These agreements are recorded at their contracted resale amount plus accrued interest, other than those that are accounted for at fair value. In reverse repurchase transactions, the Company obtains an interest in the purchased assets that are received as collateral. 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 and other investments. 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 conducts a periodic review to identify and evaluate credit based impairments related to the Company’s available for sale investments. The Company derives estimated credit losses by comparing expected future cash flows to be collected to the amortized cost of the security. Estimates of expected future cash flows consider among other things, macroeconomic conditions as well as the financial condition, near-term and long-term prospects for the issuer, and the likelihood of the recoverability of principal and interest. Effective January 1, 2020, credit losses are recognized through an allowance account subject to reversal, rather than a reduction in amortized cost. Declines in value attributable to factors other than credit are reported in other comprehensive income while the allowance for credit loss is charged to net realized gains (losses). For available for sale investments that the Company intends to sell or for which it is more likely than not that the Company would be required to sell before an anticipated recovery in value, the full amount of the impairment is included in net realized gains (losses). The new cost basis of the investment is the previous amortized cost basis reduced by the impairment recognized in net realized gains (losses). The new cost basis is not adjusted for any subsequent recoveries in fair value. The Company reports accrued investment income separately from investment balances and has elected not to measure an allowance for credit losses for accrued investment income . Any uncollectible accrued interest income is written off in the period it is deemed uncollectible. Prior to January 1, 2020, the Company performed quarterly reviews of its investments to determine whether declines in fair value below the cost basis were considered other-than-temporary in accordance with applicable accounting guidance regarding the recognition and presentation of OTTI. The process of determining whether a security was other-than-temporarily impaired required judgment and involved analyzing many factors. These factors included (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 were credit-related losses associated with debt securities for which the Company did not have an intent to sell and it was more likely than not that it would not be required to sell the security before recovery of its cost basis, the amount of the OTTI related to a credit loss was recognized in earnings and the amount of the OTTI related to other factors ( e.g. , interest rates, market conditions, etc.) was recorded as a component of other comprehensive income (loss). The amount of the credit loss of an impaired debt security was 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 existed but it was more likely than not that the Company would have to sell the debt security prior to the anticipated recovery, the decline in fair value below amortized cost was recognized as an OTTI in earnings. In periods after the recognition of an OTTI on debt securities, the Company accounted 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 would be accreted or amortized into net investment income. See note 9, “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 2021, 2020, and 2019, the Company did not designate any derivative instruments as hedges under the relevant accounting guidance. See note 11, “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

Segment Information

Segment Information	12 Months Ended
	Dec. 31, 2021
Segment Reporting [Abstract]
Segment Information	The Company classifies its businesses into three underwriting segments– insurance, reinsurance and mortgage– and two operating segments– corporate and ‘other.’ 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 Chief Executive Officer of Arch Capital, Chief Financial Officer and Treasurer of Arch Capital and the President and Chief Underwriting 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. primary mortgage insurance, U.S. credit risk transfer (“CRT”) which are predominately with government sponsored enterprises (“GSE”) and international mortgage insurance and reinsurance operations. 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 GSE. Arch MI U.S. also includes Arch Mortgage Guaranty Company, which is not a GSE-approved entity. The corporate segment results include net investment income, net realized gains or losses (which includes changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings), equity in net income or loss of investments accounted for using the equity method, other income (loss), corporate expenses, transaction costs and other, amortization of intangible assets, interest expense, net foreign exchange gains or losses, income taxes, income or loss from operating affiliates and items related to the Company’s non-cumulative preferred shares. Such amounts exclude the results of the ‘other’ segment. The ‘other’ segment included the results of Somers through June 30, 2021. In July 2021, the Company completed the previously disclosed acquisition of Somers by Greysbridge. Based on the governing documents of Greysbridge, the Company concluded that, while it retains significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, Arch no longer consolidates the results of Somers in its consolidated financial statements (see note 12, “Variable Interest Entity and Noncontrolling Interests” ). 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, 2021 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 5,867,734 $ 5,093,930 $ 1,507,825 $ 12,463,788 $ 457,465 $ 12,752,487 Premiums ceded (1,719,541) (1,839,556) (246,757) (3,800,153) (102,763) (3,734,150) Net premiums written 4,148,193 3,254,374 1,261,068 8,663,635 354,702 9,018,337 Change in unearned premiums (521,725) (413,931) 22,351 (913,305) (22,734) (936,039) Net premiums earned 3,626,468 2,840,443 1,283,419 7,750,330 331,968 8,082,298 Other underwriting income (loss) — 3,669 17,665 21,334 739 22,073 Losses and loss adjustment expenses (2,344,365) (1,924,719) (56,677) (4,325,761) (259,042) (4,584,803) Acquisition expenses (606,265) (536,754) (97,418) (1,240,437) (62,741) (1,303,178) Other operating expenses (558,906) (212,810) (194,010) (965,726) (32,869) (998,595) Underwriting income (loss) $ 116,932 $ 169,829 $ 952,979 1,239,740 (21,945) 1,217,795 Net investment income 346,808 42,310 389,118 Net realized gains (losses) 299,207 80,638 379,845 Equity in net income (loss) of investments accounted for using the equity method 366,402 — 366,402 Other income (loss) 10,244 — 10,244 Corporate expenses (77,119) — (77,119) Transaction costs and other (1,103) (935) (2,038) Amortization of intangible assets (82,057) (898) (82,955) Interest expense (131,060) (8,410) (139,470) Net foreign exchange gains (losses) 42,854 (1,325) 41,529 Income (loss) before income taxes and income (loss) from operating affiliates 2,013,916 89,435 2,103,351 Income tax expense (128,348) (234) (128,582) Income (loss) from operating affiliates 264,693 — 264,693 Net income (loss) 2,150,261 89,201 2,239,462 Amounts attributable to redeemable noncontrolling interests (2,346) (1,953) (4,299) Amounts attributable to nonredeemable noncontrolling interests — (78,314) (78,314) Net income (loss) available to Arch 2,147,915 8,934 2,156,849 Preferred dividends (48,343) — (48,343) Loss on redemption of preferred shares (15,101) — (15,101) Net income (loss) available to Arch common shareholders $ 2,084,471 $ 8,934 $ 2,093,405 Underwriting Ratios Loss ratio 64.6 % 67.8 % 4.4 % 55.8 % 78.0 % 56.7 % Acquisition expense ratio 16.7 % 18.9 % 7.6 % 16.0 % 18.9 % 16.1 % Other operating expense ratio 15.4 % 7.5 % 15.1 % 12.5 % 9.9 % 12.4 % Combined ratio 96.7 % 94.2 % 27.1 % 84.3 % 106.8 % 85.2 % Goodwill and intangible assets $ 256,434 $ 183,523 $ 505,026 $ 944,983 $ — $ 944,983 Total investable assets $ 27,442,153 $ — $ 27,442,153 Total assets 45,100,945 — 45,100,945 Total liabilities 31,545,816 — 31,545,816 (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, 2020 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 4,688,562 $ 3,472,086 $ 1,473,999 $ 9,632,691 $ 728,546 $ 10,088,068 Premiums ceded (1,525,655) (1,014,716) (194,149) (2,732,564) (190,957) (2,650,352) Net premiums written 3,162,907 2,457,370 1,279,850 6,900,127 537,589 7,437,716 Change in unearned premiums (291,487) (295,141) 118,085 (468,543) 22,762 (445,781) Net premiums earned 2,871,420 2,162,229 1,397,935 6,431,584 560,351 6,991,935 Other underwriting income (31) 4,454 20,316 24,739 2,045 26,784 Losses and loss adjustment expenses (2,092,453) (1,628,320) (528,344) (4,249,117) (440,482) (4,689,599) Acquisition expenses, net (418,483) (354,048) (134,240) (906,771) (98,071) (1,004,842) Other operating expenses (489,153) (168,011) (162,202) (819,366) (55,810) (875,176) Underwriting income (loss) $ (128,700) $ 16,304 $ 593,465 481,069 (31,967) 449,102 Net investment income 401,908 117,700 519,608 Net realized gains (losses) 813,781 9,679 823,460 Equity in net income (loss) of investments accounted for using the equity method 146,693 — 146,693 Other income (loss) 29 — 29 Corporate expenses (68,492) — (68,492) Transaction costs and other (9,456) (4,040) (13,496) Amortization of intangible assets (69,031) — (69,031) Interest expense (120,214) (23,242) (143,456) Net foreign exchange gains (losses) (80,161) (3,473) (83,634) Income (loss) before income taxes and income (loss) from operating affiliates 1,496,126 64,657 1,560,783 Income tax (expense) benefit (111,812) (26) (111,838) Income (loss) from operating affiliates 16,766 — 16,766 Net income (loss) 1,401,080 64,631 1,465,711 Amounts attributable to redeemable noncontrolling interests (2,997) (4,117) (7,114) Amounts attributable to nonredeemable noncontrolling interests — (53,076) (53,076) Net income (loss) available to Arch 1,398,083 7,438 1,405,521 Preferred dividends (41,612) — (41,612) Net income (loss) available to Arch common shareholders $ 1,356,471 $ 7,438 $ 1,363,909 Underwriting Ratios Loss ratio 72.9 % 75.3 % 37.8 % 66.1 % 78.6 % 67.1 % Acquisition expense ratio 14.6 % 16.4 % 9.6 % 14.1 % 17.5 % 14.4 % Other operating expense ratio 17.0 % 7.8 % 11.6 % 12.7 % 10.0 % 12.5 % Combined ratio 104.5 % 99.5 % 59.0 % 92.9 % 106.1 % 94.0 % Goodwill and intangible assets $ 280,978 $ 18,963 $ 385,272 $ 685,213 $ 7,650 $ 692,863 Total investable assets $ 26,856,295 $ 2,657,612 $ 29,513,907 Total assets 39,791,983 3,490,314 43,282,297 Total liabilities 26,789,149 2,505,707 29,294,856 (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, 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 — 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, net (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) 348,037 15,161 363,198 Equity in net income (loss) of investments accounted for using the equity method 123,672 — 123,672 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 and income (loss) from operating affiliates 1,785,204 61,673 1,846,877 Income tax benefit (155,790) (20) (155,810) Income (loss) from operating affiliates 2,233 — 2,233 Net income 1,631,647 61,653 1,693,300 Amounts 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) 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. 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, 2021 2020 2019 Net premiums earned (1) Professional Lines (2) $ 942,817 $ 655,872 $ 499,224 Property, energy, marine and aviation 702,693 517,247 298,966 Programs 506,867 432,854 414,103 Construction and national accounts 381,306 387,934 325,687 Excess and surplus casualty (3) 318,027 270,620 200,615 Travel, accident and health 255,590 190,944 305,085 Lenders products 153,958 114,687 66,079 Other (4) 365,210 301,262 287,321 Total $ 3,626,468 $ 2,871,420 $ 2,397,080 Net premiums written by underwriting location (1) United States $ 2,813,039 $ 2,158,415 $ 1,983,476 Europe 1,125,192 856,572 559,214 Other 209,962 147,920 99,036 Total $ 4,148,193 $ 3,162,907 $ 2,641,726 (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, 2021 2020 2019 Net premiums earned (1) Property excluding property catastrophe $ 836,573 $ 562,208 $ 362,841 Other Specialty (2) 818,801 626,409 478,517 Casualty (3) 666,754 549,056 429,288 Property catastrophe 280,738 237,736 90,934 Marine and aviation 152,955 109,624 48,274 Other (4) 84,622 77,196 56,535 Total $ 2,840,443 $ 2,162,229 $ 1,466,389 Net premiums written by underwriting location (1) United States $ 828,504 $ 687,622 $ 529,943 Bermuda 1,557,294 1,001,990 578,618 Europe and other 868,576 767,758 494,162 Total $ 3,254,374 $ 2,457,370 $ 1,602,723 (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, 2021 2020 2019 Net premiums earned by underwriting location United States $ 970,507 $ 1,158,563 $ 1,134,849 Other 312,912 239,372 231,491 Total $ 1,283,419 $ 1,397,935 $ 1,366,340 Net premiums written by underwriting location United States $ 914,477 $ 1,021,950 $ 1,032,868 Other 346,591 257,900 228,888 Total $ 1,261,068 $ 1,279,850 $ 1,261,756 OTHER SEGMENT Year Ended December 31, 2021 2020 2019 Net premiums earned (1) Casualty (2) $ 138,551 $ 245,272 $ 246,894 Other specialty (3) 118,356 186,717 185,547 Property catastrophe 15,235 23,037 13,399 Property excluding property catastrophe 6,578 1,130 3,503 Marine and aviation 190 429 — Other (4) 53,058 103,766 107,346 Total $ 331,968 $ 560,351 $ 556,689 Net premiums written by underwriting location (1) United States $ 63,403 $ 115,471 $ 127,176 Europe 91,499 $ 97,753 $ 52,065 Bermuda 199,800 $ 324,365 $ 353,621 Total $ 354,702 $ 537,589 $ 532,862 (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, US programs and other.

Reserve for Losses and Loss Adj

Reserve for Losses and Loss Adjustment Expenses	12 Months Ended
	Dec. 31, 2021
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]
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, 2021 2020 2019 Reserve for losses and loss adjustment expenses at beginning of year $ 16,513,929 $ 13,891,842 $ 11,853,297 Unpaid losses and loss adjustment expenses recoverable 4,314,855 4,082,650 2,814,291 Net reserve for losses and loss adjustment expenses at beginning of year 12,199,074 9,809,192 9,039,006 Net incurred losses and loss adjustment expenses relating to losses occurring in: Current year 4,940,987 4,851,051 3,297,037 Prior years (356,184) (161,452) (163,585) Total net incurred losses and loss adjustment expenses 4,584,803 4,689,599 3,133,452 Net losses and loss adjustment expense reserves of acquired business (1) 104,176 — 209,486 Retroactive reinsurance transactions (2) (444,147) 182,210 (225,500) Impact of deconsolidation of Somers (3) (1,460,611) — — Foreign exchange (gains) losses and other 1,181 179,190 36,003 Net paid losses and loss adjustment expenses relating to losses occurring in: Current year (734,846) (661,529) (621,202) Prior years (2,091,705) (1,999,588) (1,762,053) Total net paid losses and loss adjustment expenses (2,826,551) (2,661,117) (2,383,255) Net reserve for losses and loss adjustment expenses at end of year 12,157,925 12,199,074 9,809,192 Unpaid losses and loss adjustment expenses recoverable 5,599,231 4,314,855 4,082,650 Reserve for losses and loss adjustment expenses at end of year $ 17,757,156 $ 16,513,929 $ 13,891,842 ( 1) Represents activity related to the Company’s acquisitions in the 2021 and the 2019 period. See Note 2 . (2) See ‘Retroactive Reinsurance Transactions’ section. (3) See note 12 Development on Prior Year Loss Reserves Year Ended December 31, 2021 During 2021, the Company recorded estimated net favorable development on prior year loss reserves of $356.2 million, which consisted of net favorable development of $16.2 million from the insurance segment, $178.8 million from the reinsurance segment, $169.6 million from the mortgage segment, partially offset by $8.4 million of adverse development from the ‘other’ segment (activity prior to the deconsolidation of Somers). The insurance segment’s net favorable development of $16.2 million, or 0.4 points of net earned premium, consisted of $109.8 million of net favorable development in short-tailed and long-tailed lines mostly offset by $93.5 million of net adverse development from medium-tailed lines. Net favorable development of $81.7 million in short-tailed lines reflected $38.9 million of favorable development from property (excluding marine), primarily from the 2018 to 2020 accident years ( i.e. , the year in which a loss occurred), $26.7 million of favorable development in lenders products, primarily from the 2020 accident year, and $16.2 million of favorable development on travel and accident, primarily from the 2016 to 2020 accident years. Net favorable development of $28.1 million in long-tailed lines reflected favorable development in construction, national accounts and alternative markets, primarily from the 2016 to 2019 accident years, partially offset by adverse development in executive assurance, primarily from the 2015, 2017 and 2018 accident years. Net adverse development in medium-tailed lines reflected $57.6 million of adverse development in contract binding, primarily from the 2013 to 2019 accident years and $30.8 million of adverse development in professional liability, primarily from the 2018 to 2020 accident years. The reinsurance segment’s net favorable development of $178.8 million, or 6.3 points of net earned premium, consisted of $184.1 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $5.3 million of net adverse development from long-tailed lines. Net favorable development of $175.5 million in short-tailed lines reflected $123.3 million from other specialty lines, primarily from the 2014 to 2019 underwriting years ( i.e. , losses attributable to contracts having an inception or renewal date within the given twelve-month period), and $88.6 million of favorable development from property other than property catastrophe business, primarily from the 2015 to 2020 underwriting years. Such amounts were partially offset by adverse development of $36.4 million from property catastrophe, primarily from the 2020 underwriting year. Adverse development in long-tailed lines reflected an increase in casualty reserves, primarily from the 2018 underwriting year. The mortgage segment’s net favorable development of $169.6 million, or 13.2 points of net earned premium. Approximately a third of this development came from the U.S. first lien portfolio, which benefited from improving economic conditions and rising home prices, resulting in reduced claim rate assumptions primarily associated with pre-pandemic delinquencies. Various vintage CRT contracts also experienced similar effects and contributed to the favorable development, including the effect of contracts called by the GSEs. Subrogation recoveries on second lien and student loan business and international business also contributed to the favorable development. Year Ended December 31, 2020 During 2020, the Company recorded estimated net favorable development on prior year loss reserves of $161.5 million, which consisted of net favorable development of $7.8 million from the insurance segment, $134.0 million from the reinsurance segment, $19.0 million from the mortgage segment, and $0.7 million from the ‘other’ segment. The insurance segment’s net favorable development of $7.8 million, or 0.3 points of net earned premium, consisted of $83.0 million of net favorable development in short-tailed and long-tailed lines partially offset by $75.2 million of net adverse development from medium-tailed lines. Net favorable development of $33.6 million in short-tailed lines reflected $21.6 million of favorable development from property (excluding marine), primarily from the 2015 to 2018 accident years, and $8.4 million of favorable development on travel and accident, primarily from the 2019 accident year. Net favorable development of $49.4 million in long-tailed lines included $38.8 million of favorable development related to other business, including alternative markets and excess workers’ compensation, across all accident years, and $9.3 million of favorable development related to construction business. Net adverse development in medium-tailed lines reflected $37.9 million of adverse development in surety business, primarily from the 2019 accident year, $23.1 million in contract binding business, primarily from the 2016 to 2019 accident years, and $16.0 million in program business, primarily from the 2016 to 2019 accident years. The reinsurance segment’s net favorable development of $134.0 million, or 6.2 points of net earned premium, consisted of $155.9 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $21.9 million of net adverse development from long-tailed lines. Net favorable development of $144.0 million in short-tailed lines reflected $87.7 million related to property catastrophe and property other than property catastrophe business, primarily from the 2015 to 2019 underwriting years, and $53.6 million from other specialty lines, across most 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 2020. Adverse development in long-tailed lines reflected an increase in casualty reserves, primarily from the 2012 to 2015 underwriting years. The mortgage segment’s net favorable development of $19.0 million, or 1.4 points of net earned premium, included $16.2 million of favorable development on U.S. primary mortgage insurance business. Such development was primarily driven by subrogation recoveries on second lien business and student loan business. Year Ended December 31, 2019 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 0.7 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, 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 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 insurance business. Such development was primarily driven by lower than expected claim rates on first lien business and subrogation recoveries on second lien business. Retroactive Reinsurance Transactions In 2021, the Company entered into a retroactive reinsurance transaction with third party reinsurer to reinsure run-off liabilities associated with certain U.S. insurance exposures. In 2021, the Company entered into a reinsurance to close with the related party, in connection with the 2018 and prior years of account for certain London syndicate business. See Note 16 . In 2020, the Company entered into a reinsurance-to-close agreement related to a third party arrangement covering the 2017 and prior years of account for certain London syndicate business.

Short Duration Contracts

Short Duration Contracts	12 Months Ended
	Dec. 31, 2021
Short Duration Contracts Disclosure [Abstract]
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) 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, (ii) certain reinsurance business, including casualty clash and non-traditional lines and (iii) amounts associated with Southern Rock Holdings Limited. See Note 2 . 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 projection 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 2021 and 2018, the Company entered into loss portfolio transfer and adverse development cover reinsurance agreements accounted for as retroactive reinsurance. The agreements transfers Loss Reserves and future favorable or adverse development on certain runoff programs and certain third party occurrence business, within multi-line and other specialty 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. Unpaid loss and loss adjustment expenses recoverable at December 31, 2021 included $390.1 million related to such 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, 2021 Total of IBNR liabilities plus expected development on reported claims Cumulative Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2012 $ 233,149 $ 232,498 $ 205,776 $ 199,469 $ 197,005 $ 192,993 $ 190,770 $ 178,616 $ 178,250 $ 178,343 $ 627 4,245 2013 159,102 156,785 149,199 143,400 134,952 133,869 128,624 127,290 126,276 25 4,243 2014 148,368 145,957 147,465 136,201 132,307 134,329 135,032 134,942 3,098 3,884 2015 112,409 109,865 103,995 102,515 97,852 91,830 91,892 3,804 4,536 2016 104,449 101,306 105,657 100,471 96,437 92,553 874 6,160 2017 280,715 246,291 235,951 230,439 231,228 8,248 6,426 2018 180,981 186,030 173,693 170,057 9,136 5,020 2019 179,056 178,564 165,477 6,667 5,080 2020 359,394 329,362 66,698 4,186 2021 426,870 158,163 2,951 Total $ 1,947,000 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 $ 20,638 $ 93,394 $ 138,977 $ 161,831 $ 167,540 $ 179,945 $ 181,307 $ 173,184 $ 174,032 $ 174,384 2013 32,292 84,936 110,808 120,111 122,244 125,475 123,356 124,688 124,841 2014 25,881 53,751 77,892 84,195 87,812 98,553 115,383 122,296 2015 23,580 64,953 76,338 86,253 87,926 86,246 87,316 2016 24,828 83,552 98,683 97,506 95,002 91,241 2017 30,228 139,867 195,532 211,708 215,895 2018 30,026 102,285 134,858 142,838 2019 26,130 105,380 133,911 2020 55,619 194,487 2021 90,423 Total 1,377,632 All outstanding liabilities before 2012, net of reinsurance 17,517 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 586,885 Third party occurrence business ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2021 Total of IBNR liabilities plus expected development on reported claims Cumulative Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2012 $ 241,368 $ 263,451 $ 269,204 $ 272,004 $ 258,371 $ 253,758 $ 243,863 $ 244,448 $ 242,332 $ 239,075 $ 43,924 65,731 2013 283,228 297,225 307,152 302,165 282,122 274,717 272,849 269,754 270,558 54,640 67,113 2014 330,015 336,019 338,890 343,113 339,701 344,197 342,934 343,569 66,498 75,904 2015 359,058 391,884 398,908 392,143 391,455 382,722 386,801 91,081 78,785 2016 389,832 394,485 406,082 399,571 374,896 367,818 115,303 79,005 2017 417,377 417,941 422,624 412,512 407,115 145,130 84,692 2018 430,415 453,190 450,937 451,459 189,965 77,700 2019 456,353 487,547 481,045 253,849 84,895 2020 607,249 616,910 428,750 89,560 2021 622,713 543,386 65,477 Total $ 4,187,063 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 $ 6,984 $ 30,915 $ 58,650 $ 83,637 $ 108,660 $ 130,098 $ 143,885 $ 155,085 $ 163,016 $ 168,119 2013 6,857 29,265 71,449 101,293 122,288 149,292 164,403 174,946 184,800 2014 9,228 40,346 71,624 112,702 162,123 191,305 211,643 224,101 2015 11,139 44,605 88,515 139,492 181,704 211,715 227,697 2016 11,709 41,979 87,616 136,870 164,662 194,773 2017 13,408 52,356 99,874 135,111 165,606 2018 17,025 63,848 115,137 154,248 2019 18,431 73,222 121,859 2020 24,509 76,743 2021 26,301 Total 1,544,247 All outstanding liabilities before 2012, net of reinsurance 242,741 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 2,885,557 Third party claims-made business ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2021 Total of IBNR liabilities plus expected development on reported claims Cumulative Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2012 $ 317,654 $ 320,207 $ 318,453 $ 313,907 $ 291,316 $ 275,665 $ 277,683 $ 285,163 $ 285,527 $ 286,118 $ 11,570 15,576 2013 301,956 320,659 324,442 320,524 294,674 291,205 281,996 271,501 273,948 11,739 15,696 2014 264,537 279,846 299,104 279,043 282,058 298,017 292,247 288,318 22,336 15,676 2015 258,989 277,615 276,492 260,063 255,432 252,478 267,925 20,617 14,724 2016 275,394 291,645 308,453 314,747 322,042 327,230 42,509 15,749 2017 271,088 286,565 312,554 308,917 323,854 60,718 16,404 2018 273,521 315,085 320,653 337,083 85,411 15,854 2019 290,217 318,469 318,498 119,673 12,982 2020 384,852 414,580 240,888 10,049 2021 516,420 435,910 8,550 Total $ 3,353,974 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 $ 17,718 $ 69,069 $ 121,211 $ 164,724 $ 190,395 $ 209,295 $ 227,389 $ 251,313 $ 255,337 $ 260,173 2013 19,032 87,458 137,963 179,395 198,008 217,132 238,951 245,687 247,078 2014 13,817 63,312 129,712 173,089 208,074 229,958 243,791 249,960 2015 9,066 52,046 100,089 126,499 174,161 193,186 216,986 2016 10,568 68,226 127,286 158,230 205,596 242,431 2017 9,306 67,669 113,208 143,340 196,125 2018 12,287 68,424 118,361 158,709 2019 12,418 65,477 122,362 2020 17,161 87,547 2021 23,349 Total 1,804,720 All outstanding liabilities before 2012, net of reinsurance 64,171 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 1,613,425 Multi-line and other specialty ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2021 Total of IBNR liabilities plus expected development on reported claims Cumulative Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2012 $ 254,684 $ 265,479 $ 259,582 $ 257,240 $ 256,379 $ 248,066 $ 248,310 $ 245,205 $ 245,260 $ 243,849 $ 2,057 55,219 2013 266,089 274,285 265,594 265,672 253,554 254,916 250,252 247,443 246,682 3,461 71,613 2014 303,053 327,098 319,706 319,418 318,297 314,300 311,097 310,097 5,770 109,575 2015 335,250 358,587 357,364 365,362 357,123 349,895 347,669 7,201 148,924 2016 409,367 431,760 428,579 416,724 410,610 408,621 11,032 175,261 2017 483,414 502,068 492,166 501,753 505,135 16,867 219,810 2018 513,466 565,717 563,969 566,283 32,467 247,052 2019 568,337 613,673 641,832 63,880 235,824 2020 622,241 572,265 192,056 149,004 2021 637,258 361,237 75,250 Total $ 4,479,691 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 $ 78,523 $ 166,414 $ 190,754 $ 209,916 $ 223,798 $ 232,640 $ 233,862 $ 237,221 $ 240,191 $ 239,928 2013 86,911 151,897 181,721 214,941 226,769 235,801 237,863 238,792 239,831 2014 108,003 197,609 235,079 267,959 282,104 292,638 294,049 295,551 2015 138,393 236,516 278,265 306,313 321,395 327,082 330,872 2016 176,238 305,250 342,345 363,392 379,885 385,890 2017 181,454 343,049 381,419 424,219 446,749 2018 212,316 390,009 443,644 480,852 2019 212,629 386,894 488,094 2020 173,123 311,112 2021 157,346 Total 3,376,225 All outstanding liabilities before 2012, net of reinsurance 22,375 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 1,125,841 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, 2021: 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 19.3 % 43.5 % 19.1 % 6.6 % 1.4 % 2.3 % 3.2 % 0.5 % 0.3 % 0.2 % Third party occurrence business 3.3 % 9.3 % 11.6 % 11.0 % 9.8 % 8.7 % 5.4 % 4.1 % 3.5 % 2.1 % Third party claims-made business 4.4 % 18.0 % 17.8 % 12.3 % 12.7 % 7.9 % 7.0 % 4.3 % 1.0 % 1.7 % Multi-line and other specialty 34.7 % 29.5 % 11.0 % 8.6 % 4.6 % 2.8 % 0.7 % 0.7 % 0.8 % (0.1) % 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 projection 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, 2021 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 (the year in which business is underwritten). Each quarter, as part of the reserving process, the Company’s actuaries reaffirm that the assumptions used in the reserving process continue to form a sound basis for projection of liabilities. If actual loss activity dif

Allowance for Expected Credit L

Allowance for Expected Credit Losses	12 Months Ended
	Dec. 31, 2021
Credit Loss [Abstract]
Allowance for expected credit losses	Premiums Receivable The following table provides a roll forward of the allowance for expected credit losses of the Company’s premium receivables: Year Ended December 31, 2021 Premium Receivables, Net of Allowance Allowance for Expected Credit Losses Balance at beginning of period $ 2,064,586 $ 37,781 Change for provision of expected credit losses (2) 2,177 Balance at end of period $ 2,633,280 $ 39,958 Year Ended December 31, 2020 Balance at beginning of period $ 1,778,717 $ 21,003 Cumulative effect of accounting change (1) 6,539 Change for provision of expected credit losses (2) 10,239 Balance at end of period $ 2,064,586 $ 37,781 (1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”. (2) Amounts deemed uncollectible are written-off in operating expenses. For the 2021 and 2020 periods, amounts written off totaled $3.8 million and $2.8 million, respectively. 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 provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables: Year Ended December 31, 2021 Reinsurance Recoverables, Net of Allowance Allowance for Expected Credit Losses Balance at beginning of period $ 4,500,802 $ 11,636 Change for provision of expected credit losses 1,594 Balance at end of period $ 5,880,735 $ 13,230 Year Ended December 31, 2020 Balance at beginning of period $ 4,346,816 $ 1,364 Cumulative effect of accounting change (1) 12,010 Change for provision of expected credit losses (1,738) Balance at end of period 4,500,802 $ 11,636 (1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”. The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums) at December 31, 2021 and 2020: December 31, 2021 2020 Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses $ 5,880,735 $ 4,500,802 % due from carriers with A.M. Best rating of “A-” or better 69.7 % 63.9 % % due from all other rated carriers 0.1 % 0.1 % % due from all other carriers with no A.M. Best rating (1) 30.2 % 36.0 % Largest balance due from any one carrier as % of total shareholders’ equity (2) 6.7 % 1.8 % (1) At December 31, 2021 and 2020 period, over 91% and 94% of such amount is collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively. (2) The 2021 period included impact of deconsolidation of Somers. See note 12. Contractholder Receivables The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables: Year Ended December 31, 2021 Contractholder Receivables, Net of Allowance Allowance for Expected Credit Losses Balance at beginning of period $ 1,986,924 $ 8,638 Change for provision of expected credit losses (5,201) Balance at end of period $ 1,828,691 $ 3,437 Year Ended December 31, 2020 Balance at beginning of period $ 2,119,460 $ — Cumulative effect of accounting change (1) 6,663 Change for provision of expected credit losses 1,975 Balance at end of period 1,986,924 $ 8,638 (1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.

Reinsurance

Reinsurance	12 Months Ended
	Dec. 31, 2021
Reinsurance Disclosures [Abstract]
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, 2021 2020 2019 Premiums Written Direct $ 7,706,832 $ 6,553,910 $ 5,681,523 Assumed 5,045,655 3,534,158 2,457,437 Ceded (3,734,150) (2,650,352) (2,099,893) Net $ 9,018,337 $ 7,437,716 $ 6,039,067 Premiums Earned Direct $ 7,149,794 $ 6,361,451 $ 5,447,829 Assumed 4,333,873 3,213,873 2,337,950 Ceded (3,401,369) (2,583,389) (1,999,281) Net $ 8,082,298 $ 6,991,935 $ 5,786,498 Losses and Loss Adjustment Expenses Direct $ 4,266,758 $ 4,392,392 $ 2,953,072 Assumed 2,826,820 2,204,323 1,602,528 Ceded (2,508,775) (1,907,116) (1,422,148) Net $ 4,584,803 $ 4,689,599 $ 3,133,452 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 Note 12, “Variable Interest Entity and Noncontrolling Interests.” The following table summarizes the respective coverages and retentions at December 31, 2021: December 31, 2021 Initial Coverage at Issuance Current Remaining Retention, Net Bellemeade 2017-1 Ltd. (1) $ 368,114 $ 108,368 $ 125,926 Bellemeade 2018-1 Ltd. (2) 374,460 181,136 122,118 Bellemeade 2018-3 Ltd. (3) 506,110 302,563 128,020 Bellemeade 2019-1 Ltd. (4) 341,790 181,324 97,845 Bellemeade 2019-2 Ltd. (5) 621,022 398,316 156,419 Bellemeade 2019-3 Ltd. (6) 700,920 409,859 181,583 Bellemeade 2019-4 Ltd. (7) 577,267 411,954 116,292 Bellemeade 2020-2 Ltd. (8) 449,167 218,877 222,567 Bellemeade 2020-3 Ltd. (9) 451,816 365,141 154,732 Bellemeade 2020-4 Ltd. (10) 337,013 186,065 129,824 Bellemeade 2021-1 Ltd. (11) 643,577 630,163 149,189 Bellemeade 2021-2 Ltd. (12) 616,017 616,017 139,763 Bellemeade 2021-3 Ltd. (13) 639,391 639,391 140,545 Total $ 6,626,664 $ 4,649,174 $ 1,864,823 (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. (8) Issued in September 2020, covering in-force policies issued between January 1, 2020 and May 31, 2020. $423 million was directly funded by Bellemeade 2020-2 Ltd. with an additional $26 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers. (9) Issued in November 2020, covering in-force policies issued between June 1, 2020 and August 31, 2020. $418 million was directly funded by Bellemeade 2020-3 Ltd. with an additional $34 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers. (10) Issued in December 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $321 million was directly funded by Bellemeade 2020-4 Ltd. with an additional $16 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers. (11) Issued in March 2021, covering in-force policies issued between September 1, 2020 and November 30, 2020. $580 million was directly funded by Bellemeade Re 2021-1 Ltd. with an additional $64 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers. (12) Issued in June 2021, covering in-force policies issued between December 1, 2020 and March 31, 2021. $523 million was directly funded by Bellemeade Re 2021-2 Ltd. via insurance-linked notes, with an additional $93 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers. (13) Issued in September 2021, covering in-force policies issued between April 1, 2021 and June 30, 2021. $508 million was directly funded by Bellemeade Re 2021-3 Ltd. via insurance-linked notes, with an additional $131 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

Investment Information

Investment Information	12 Months Ended
	Dec. 31, 2021
Disclosure Investment Information [Abstract]
Investment Information	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 Gross Unrealized Gains Gross Unrealized Losses Allowance for Expected Credit Losses (2) Cost or December 31, 2021 Fixed maturities: Corporate bonds $ 6,553,333 $ 104,170 $ (69,194) $ (2,037) $ 6,520,394 Mortgage backed securities 408,477 2,825 (5,410) (48) 411,110 Municipal bonds 404,666 18,724 (1,409) (2) 387,353 Commercial mortgage backed securities 1,046,484 1,740 (3,117) (6) 1,047,867 U.S. government and government agencies 4,772,764 10,076 (45,967) — 4,808,655 Non-U.S. government securities 2,120,294 54,048 (34,749) (82) 2,101,077 Asset backed securities 2,692,091 6,540 (11,108) (708) 2,697,367 Total 17,998,109 198,123 (170,954) (2,883) 17,973,823 Short-term investments 1,734,716 568 (590) — 1,734,738 Total $ 19,732,825 $ 198,691 $ (171,544) $ (2,883) $ 19,708,561 December 31, 2020 Fixed maturities (1): Corporate bonds $ 7,856,571 $ 414,247 $ (34,388) $ (896) $ 7,477,608 Mortgage backed securities 630,001 8,939 (5,028) (278) 626,368 Municipal bonds 494,522 27,291 (3,835) (11) 471,077 Commercial mortgage backed securities 389,900 8,722 (2,954) (122) 384,254 U.S. government and government agencies 5,557,077 22,612 (12,611) — 5,547,076 Non-U.S. government securities 2,433,733 153,891 (8,060) — 2,287,902 Asset backed securities 1,634,804 19,225 (10,715) (1,090) 1,627,384 Total 18,996,608 654,927 (77,591) (2,397) 18,421,669 Short-term investments 1,924,922 2,693 (2,063) — 1,924,292 Total $ 20,921,530 $ 657,620 $ (79,654) $ (2,397) $ 20,345,961 (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.” In 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions. (2) Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal. 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 Gross Unrealized Losses Estimated Fair Gross Unrealized Losses Estimated Fair Gross Unrealized Losses December 31, 2021 Fixed maturities: Corporate bonds $ 3,639,582 $ (63,938) $ 98,867 $ (5,256) $ 3,738,449 $ (69,194) Mortgage backed securities 222,176 (3,545) 46,809 (1,865) 268,985 (5,410) Municipal bonds 26,665 (385) 16,361 (1,024) 43,026 (1,409) Commercial mortgage backed securities 675,603 (2,805) 5,908 (312) 681,511 (3,117) U.S. government and government agencies 4,211,621 (44,180) 33,373 (1,787) 4,244,994 (45,967) Non-U.S. government securities 1,511,301 (31,983) 62,957 (2,766) 1,574,258 (34,749) Asset backed securities 1,667,002 (9,853) 33,082 (1,255) 1,700,084 (11,108) Total 11,953,950 (156,689) 297,357 (14,265) 12,251,307 (170,954) Short-term investments 284,733 (590) — — 284,733 (590) Total $ 12,238,683 $ (157,279) $ 297,357 $ (14,265) $ 12,536,040 $ (171,544) December 31, 2020 Fixed maturities (1): Corporate bonds $ 747,442 $ (33,086) $ 3,934 $ (1,302) $ 751,376 $ (34,388) Mortgage backed securities 284,619 (4,788) 3,637 (240) 288,256 (5,028) Municipal bonds 67,937 (3,835) — — 67,937 (3,835) Commercial mortgage backed securities 126,624 (2,916) 2,655 (38) 129,279 (2,954) U.S. government and government agencies 1,285,907 (12,611) — — 1,285,907 (12,611) Non-U.S. government securities 543,844 (7,658) 2,441 (402) 546,285 (8,060) Asset backed securities 634,470 (9,110) 57,737 (1,605) 692,207 (10,715) Total 3,690,843 (74,004) 70,404 (3,587) 3,761,247 (77,591) Short-term investments 97,920 (2,063) — — 97,920 (2,063) Total $ 3,788,763 $ (76,067) $ 70,404 $ (3,587) $ 3,859,167 $ (79,654) (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.” In 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions. At December 31, 2021, on a lot level basis, approximately 4,700 security lots out of a total of approximately 10,240 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 $1.1 million. The Company believes that such securities were temporarily impaired at December 31, 2021. At December 31, 2020, on a lot level basis, approximately 2,320 security lots out of a total of approximately 11,180 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 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, 2021 December 31, 2020 Maturity Estimated Fair Value Amortized Cost Estimated Fair Value Amortized Cost Due in one year or less $ 300,889 $ 299,772 $ 348,200 $ 339,951 Due after one year through five years 8,355,255 8,339,387 10,629,959 10,340,819 Due after five years through 10 years 4,689,155 4,684,393 4,881,564 4,654,754 Due after 10 years 505,758 493,927 482,180 448,139 13,851,057 13,817,479 16,341,903 15,783,663 Mortgage backed securities 408,477 411,110 630,001 626,368 Commercial mortgage backed securities 1,046,484 1,047,867 389,900 384,254 Asset backed securities 2,692,091 2,697,367 1,634,804 1,627,384 Total (1) $ 17,998,109 $ 17,973,823 $ 18,996,608 $ 18,421,669 (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.” In 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions. Securities Lending Agreements In 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions to enhance investment income. Prior to the termination of this program, the Company loaned certain of its securities to third parties, primarily major brokerage firms, for short periods of time through a lending agent. The Company maintained legal control over the securities it lent (shown as ‘Securities pledged under securities lending, at fair value’ on the Company’s balance sheet), retained the earnings and cash flows associated with the loaned securities and received a fee from the borrower for the temporary use of the securities. An indemnification agreement with the lending agent protected the Company in the event a borrower became insolvent or failed to return any of the securities on loan from the Company. The Company receives collateral (shown as ‘Collateral received under securities lending, at fair value’ on the Company’s balance sheet) in the form of cash or U.S. government and government agency securities. At December 31, 2021, the Company had no cash collateral or security collateral due to the termination of the program. At December 31, 2020, the fair value of the cash collateral received on securities lending was nil and the fair value of security collateral received was $301.1 million. The carrying value of collateral held under the Company’s securities lending transactions by significant investment category and remaining contractual maturity of the underlying agreements was as follows at December 31, 2020 (no balances at December 31, 2021 due to the termination of the program): Remaining Contractual Maturity of the Agreements Overnight and Continuous Less than 30 Days 30-90 Days 90 Days or More Total December 31, 2020 U.S. government and government agencies $ 142,317 $ — $ 139,290 $ — $ 281,607 Corporate bonds 3,021 — — — 3,021 Equity securities 16,461 — — — 16,461 Total $ 161,799 $ — $ 139,290 $ — $ 301,089 Gross amount of recognized liabilities for securities lending in offsetting disclosure in Note 11 — Amounts related to securities lending not included in offsetting disclosure in Note 11 $ 301,089 Equity Securities, at Fair Value At December 31, 2021, the Company held $1.8 billion of equity securities, at fair value, compared to $1.4 billion at December 31, 2020. Net Investment Income The components of net investment income were derived from the following sources: Year Ended December 31, 2021 2020 2019 Fixed maturities $ 330,061 $ 412,481 $ 505,399 Term loans 34,843 84,149 98,949 Equity securities 42,396 28,958 15,857 Short-term investments 6,928 10,840 15,820 Other (1) 62,895 72,395 80,618 Gross investment income 477,123 608,823 716,643 Investment expenses (88,005) (89,215) (88,905) Net investment income $ 389,118 $ 519,608 $ 627,738 (1) Includes income distributions from investment funds and other items Net Realized Gains (Losses) Net realized gains (losses) were as follows: Year Ended December 31, 2021 2020 2019 Available for sale securities: Gross gains on investment sales $ 313,886 $ 595,941 $ 235,655 Gross losses on investment sales (156,791) (117,282) (104,612) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities 7,953 15,881 41,910 Other investments 116,781 13,656 (35,734) Equity securities 13,028 14,629 15,869 Short-term investments 601 2,279 3,801 Equity securities, at fair value : Net realized gains (losses) on securities sold 122,606 26,849 11,313 Net unrealized gains (losses) on equity securities still held at reporting date 48,746 102,394 97,768 Allowance for credit losses: Investments related (2,100) (3,597) — Underwriting related 1,062 (10,007) — Net impairment losses — (533) (3,165) Derivative instruments (1) (32,390) 179,675 119,741 Other (2) (53,537) 3,575 (19,348) Net realized gains (losses) $ 379,845 $ 823,460 $ 363,198 (1) See Note 11 for information on the Company’s derivative instruments. (2) 2021 periods reflected $33.1 million of losses related to the Company’s deconsolidation of Somers. Other Investments The following table summarizes the Company’s other investments and other investable assets: December 31, 2021 2020 Fixed maturities $ 416,698 $ 843,354 Other investments 1,432,553 2,331,885 Short-term investments 97,806 557,008 Equity securities 26,493 92,549 Investments accounted for using the fair value option 1,973,550 3,824,796 Other investable assets (1) — 500,000 Total other investments $ 1,973,550 $ 4,324,796 (1) Participation interests in a receivable of a reverse repurchase agreement. The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy: December 31, 2021 2020 Lending 536,345 572,636 Term loan investments 484,950 1,231,731 Investment grade fixed income 147,810 138,646 Private equity 91,126 48,750 Energy 81,692 65,813 Credit related funds 70,278 90,780 Infrastructure 20,352 165,516 Real estate — 18,013 Total $ 1,432,553 $ 2,331,885 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, 2021 2020 Credit related funds $ 1,022,334 $ 740,060 Private equity 436,042 235,289 Real estate 396,395 258,518 Equities 395,090 343,058 Lending 376,649 179,629 Infrastructure 230,070 175,882 Energy 119,141 115,453 Fixed income 101,890 — Total $ 3,077,611 $ 2,047,889 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 three 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 $366.4 million for 2021, compared to $146.7 million for 2020 and $123.7 million for 2019. 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 market value of the underlying securities in the funds). A summary of financial information for the Company’s investment funds and operating affiliates accounted for using the equity method is as follows: December 31, 2021 2020 Invested assets $ 58,508,009 $ 44,131,377 Total assets 69,648,905 49,078,464 Total liabilities 17,944,325 6,054,189 Net assets $ 51,704,580 $ 43,024,275 Year Ended December 31, 2021 2020 2019 Total revenues $ 11,785,949 $ 5,762,098 $ 164,669 Total expenses 3,238,606 1,656,029 528,762 Net income (loss) $ 8,547,343 $ 4,106,069 $ (364,093) 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. 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, 2021 2020 Investments accounted for using the equity method (1) $ 3,077,611 $ 2,047,889 Investments accounted for using the fair value option (2) 170,595 184,720 Total $ 3,248,206 $ 2,232,609 (1) Aggregate unfunded commitments were $2.6 billion at December 31, 2021, compared to $1.8 billion at December 31, 2020. (2) Aggregate unfunded commitments were $18.8 million at December 31, 2021, compared to $35.6 million at December 31, 2020. Investments in Operating Affiliates Investments in which the Company has significant influence over the operating and financial policies are classified as ‘investments in operating affiliates’ on the Company’s balance sheets and are accounted for under the equity method. Such investments primarily include the Company’s investment in Coface SA (“Coface”), Greysbridge and Premia. Investments in Coface and Premia are generally recorded on a three In 2021, the Company completed the share purchase agreement with Natixis to purchase 29.5% of the common equity of Coface, a France-based leader in the global trade credit insurance market. The consideration paid was €9.95 per share, or an aggregate €453 million (approximately $546 million) including related fees. Income (loss) from operating affiliates reflected a one-time gain of $74.5 million realized from the acquisition. As a result of equity method accounting rules, approximately $36 million of additional gain was deferred and will generally be recognized over the next five years. As of December 31, 2021, the Company owned approximately 29.86% of the issued shares of Coface, or 30.10% excluding treasury shares, with a carrying value of $630.5 million. In July 2021, the Company announced the completion of the previously disclosed acquisition of Somers by Greysbridge for a cash purchase price of $35.00 per common share. Effective July 1, 2021, Somers is wholly owned by Greysbridge, and Greysbridge is owned 40% by the Company, 30% by certain investment funds managed by Kelso and 30% by certain investment funds managed by Warburg. At December 31, 2021 the Company’s carrying value in Greysbridge was $375.7 million, which reflected the Company’s aggregate purchase price of $278.9 million along with income (loss) from operating affiliates, which included a one-time gain of $95.7 million recognized from the acquisition. In addition, the ‘net realized gains (losses)’ line on the Company’s consolidated statements of income included a $33.1 million loss as a result of deconsolidation of Somers in the Company’s financial statements following the close of the transaction. See note 12 . The Company recorded income from operating affiliates of $264.7 million for 2021, compared to income of $16.8 million for 2020 and $2.2 million for 2019. The income from operating affiliates for the 2021 period, primarily related to the Company’s recent investments in Coface and Greysbridge. Allowance for Expected Credit Losses The following table provides a roll forward of the allowance for expected credit losses of the Company’s securities classified as available for sale: Year Ended December 31, 2021 Structured Securities (1) Municipal Corporate Total Balance at beginning of period $ 1,490 $ 11 $ 896 $ 2,397 Additions for current-period provision for expected credit losses 602 — 2,858 3,460 Additions (reductions) for previously recognized expected credit losses (847) (9) (320) (1,176) Reductions due to disposals (3) (443) — (1,355) (1,798) Balance at end of period $ 802 $ 2 $ 2,079 $ 2,883 Year Ended December 31, 2020 Balance at beginning of period $ — $ — $ — $ — Cumulative effect of accounting change (2) 517 — 117 634 Additions for current-period provision for expected credit losses 2,942 67 7,644 10,653 Additions (reductions) for previously recognized expected credit losses (1,398) 6 (5,638) (7,030) Reductions due to disposals (571) (62) (1,227) (1,860) Balance at end of period $ 1,490 $ 11 $ 896 $ 2,397 (1) Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities. (2) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”. (3) Reduction for the 2021 periods primarily related to the Company’s deconsolidation of Somers. 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, 2021 2020 Assets used for collateral or guarantees: Affiliated transactions $ 4,223,955 $ 4,643,334 Third party agreements 2,721,160 3,083,324 Deposits with U.S. regulatory authorities 798,100 827,552 Deposits with non-U.S. regulatory authorities 506,517 179,099 Total restricted assets (1) $ 8,249,732 $ 8,733,309 (1) 2020 balances included $1.036 billion related to Somers. See note 12 . Reconciliation of Cash and Restricted Cash The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets: December 31, 2021 2020 2019 Cash $ 858,668 $ 906,448 $ 726,230 Restricted cash (included in ‘other assets’) 456,103 384,096 177,468 Cash and restricted cash $ 1,314,771 $ 1,290,544 $ 903,698

Fair Value

Fair Value	12 Months Ended
	Dec. 31, 2021
Fair Value Disclosures [Abstract]
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 $23.8 billion of financial assets and liabilities measured at fair value at December 31, 2021, approximately $7.7 million, or 0.0%, were priced using non-binding broker-dealer quotes. Of the $26.5 billion of financial assets and liabilities measured at fair value at December 31, 2020, approximately $150.1 million, or 0.6%, 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. 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. 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. 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. Residential mortgage loans The Company’s residential mortgage loans (included in ‘other assets’ in the consolidated balance sheets) include amounts related to the Company’s whole mortgage loan purchase and sell program. Fair values of residential mortgage loans are generally determined based on market prices. As significant inputs used in pricing process for these residential mortgage loans are observable market inputs, the fair value of these securities 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 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, 2021: Fair Value Measurement Using: Estimated Quoted Prices in Active Markets for Identical Assets Significant Other Observable Inputs Significant Unobservable Inputs Assets measured at fair value: Available for sale securities: Fixed maturities: Corporate bonds $ 6,553,333 $ — $ 6,553,320 $ 13 Mortgage backed securities 408,477 — 408,477 — Municipal bonds 404,666 — 404,666 — Commercial mortgage backed securities 1,046,484 — 1,046,484 — U.S. government and government agencies 4,772,764 4,744,517 28,247 — Non-U.S. government securities 2,120,294 — 2,120,294 — Asset backed securities 2,692,091 — 2,688,744 3,347 Total 17,998,109 4,744,517 13,250,232 3,360 Short-term investments 1,734,716 1,052,822 681,894 — Equity securities, at fair value 1,804,170 1,762,864 38,388 2,918 Derivative instruments (3) 127,121 — 127,121 — Residential mortgage loans 49,847 — 49,847 — Fair value option: Corporate bonds 388,546 — 388,546 — Non-U.S. government bonds 23,785 — 23,785 — Asset backed securities 4,367 — 4,367 — Short-term investments 97,806 528 97,278 — Equity securities 26,493 21,745 — 4,748 Other investments 310,798 20,352 262,465 27,981 Other investments measured at net asset value (1) 1,121,755 Total 1,973,550 42,625 776,441 32,729 Total assets measured at fair value $ 23,687,513 $ 7,602,828 $ 14,923,923 $ 39,007 Liabilities measured at fair value: Contingent consideration liabilities $ (16,960) $ — $ — $ (16,960) Securities sold but not yet purchased (2) — — — — Derivative instruments (3) (54,224) — (54,224) — Total liabilities measured at fair value $ (71,184) $ — $ (54,224) $ (16,960) (1) 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. (2) 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. (3) See Note 11. The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2020: Fair Value Measurement Using: Estimated Quoted Prices in Active Markets for Identical Assets Significant Other Observable Inputs Significant Unobservable Inputs Assets measured at fair value (1): Available for sale securities: Fixed maturities: Corporate bonds $ 7,856,571 $ — $ 7,856,558 $ 13 Mortgage backed securities 630,001 — 630,001 — Municipal bonds 494,522 — 494,522 — Commercial mortgage backed securities 389,900 — 389,900 — U.S. government and government agencies 5,557,077 5,463,356 93,721 — Non-U.S. government securities 2,433,733 — 2,433,733 — Asset backed securities 1,634,804 — 1,631,378 3,426 Total 18,996,608 5,463,356 13,529,813 3,439 Equity securities, at fair value 1,460,959 1,401,653 17,291 42,015 Short-term investments 1,924,922 1,920,565 4,357 — Derivative instruments (4) 177,383 — 177,383 — Fair value option: Corporate bonds 651,294 — 650,309 985 Non-U.S. government bonds 35,263 — 35,263 — Mortgage backed securities 3,282 — 3,282 — Commercial mortgage backed securities 1,090 — 1,090 — Asset backed securities 152,151 — 152,151 — U.S. government and government agencies 274 164 110 — Short-term investments 557,008 420,131 136,877 — Equity securities 92,549 23,373 188 68,988 Other investments 1,134,229 51,149 1,015,977 67,103 Other investments measured at net asset value (2) 1,197,656 Total 3,824,796 494,817 1,995,247 137,076 Total assets measured at fair value $ 26,384,668 $ 9,280,391 $ 15,724,091 $ 182,530 Liabilities measured at fair value: Contingent consideration liabilities $ (461) $ — $ — $ (461) Securities sold but not yet purchased (3) (21,679) — (21,679) — Derivative instruments (4) (108,705) — (108,705) — Total liabilities measured at fair value $ (130,845) $ — $ (130,384) $ (461) (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 9. (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 11. 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 2021 and 2020: Assets Liabilities Available For Sale Fair Value Option Fair Value Structured Securities (1) Corporate Bonds Corporate Bonds Other Investments Equity Securities Equity Securities Contingent Year Ended December 31, 2021 Balance at beginning of year $ 3,426 $ 13 $ 985 $ 67,103 $ 68,988 $ 42,015 $ (461) Total gains or (losses) (realized/unrealized) Included in earnings (2) (135) — 13 868 4,941 1,958 — Included in other comprehensive income 133 — — — — — — Purchases, issuances, sales and settlements Purchases — — — 13,213 — 5,718 (16,494) Issuances — — — — — — — Sales (3) — — (998) (53,203) (69,181) (46,773) — Settlements (77) — — — — — (5) Transfers in and/or out of Level 3 — — — — — — — Balance at end of year $ 3,347 $ 13 $ — $ 27,981 $ 4,748 $ 2,918 $ (16,960) Year Ended December 31, 2020 Balance at beginning of year $ 5,216 $ 8,851 $ 932 $ 68,817 $ 58,094 $ 55,889 $ (7,998) Total gains or (losses) (realized/unrealized) Included in earnings (2) — (5,865) (13) (314) 10,894 8,214 (72) Included in other comprehensive income (169) 397 — — — — — Purchases, issuances, sales and settlements Purchases — — 66 52,449 — 4,030 — Issuances — — — — — — — Sales — — — (56,833) — (26,118) — Settlements (1,413) (1,462) — — — — 7,609 Transfers in and/or out of Level 3 (208) (1,908) — 2,984 — — — Balance at end of year $ 3,426 $ 13 $ 985 $ 67,103 $ 68,988 $ 42,015 $ (461) (1) Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities. (2) Gains or losses were included in net realized gains (losses). (3) Sales for the 2021 period primarily relates to the Company’s deconsolidation of Somers. 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, 2021, 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, 2021, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.7 billion and had a fair value of $3.3 billion. At December 31, 2020, the Company’s senior notes were carried at their cost, net of debt issuance costs, of $2.9 billion and had a fair value of $3.7 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 annually 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.

Derivative Instruments

Derivative Instruments	12 Months Ended
	Dec. 31, 2021
Derivative Instruments and Hedging Activities Disclosure [Abstract]
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 December 31, 2021 Futures contracts (2) $ 34,999 $ (9,808) $ 2,826,564 Foreign currency forward contracts (2) 7,734 (11,390) 915,962 TBAs 11,227 — 11,227 Other (2) 73,161 (33,026) 3,736,773 Total $ 127,121 $ (54,224) December 31, 2020 Futures contracts (2) $ 11,046 $ (4,496) $ 3,099,796 Foreign currency forward contracts (2) 52,716 (6,202) 1,656,729 TBAs — — — Other (2) 113,621 (98,007) 5,763,919 Total $ 177,383 $ (108,705) (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.’ The Company did not hold any derivatives which were designated as hedging instruments at December 31, 2021 or 2020. 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. At December 31, 2021, $122.3 million and $53.9 million, respectively, of asset derivatives and liability derivatives were subject to a master netting agreement compared to $138.8 million and $93.0 million, respectively, at December 31, 2020. The remaining derivatives included in the table above were not subject to a master netting agreement. 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, 2021 2020 2019 Net realized gains (losses): Futures contracts $ (15,262) $ 114,987 $ 114,123 Foreign currency forward contracts (39,755) 49,974 (9,499) TBAs (233) 1,129 463 Other 22,860 13,585 14,654 Total $ (32,390) $ 179,675 $ 119,741

Variable Interest Entity and No

Variable Interest Entity and Noncontrolling Interests	12 Months Ended
	Dec. 31, 2021
Variable Interest Entity and Noncontrolling Interest Disclosure [Abstract]
Variable Interest Entity and Noncontrolling Interests	Somers Holdings Ltd. In March 2014, the Company invested $100.0 million and acquired 2,500,000 common shares of Somers. Somers was considered a VIE and the Company concluded that it was the primary beneficiary of Somers, through June 30, 2021. As such, the results of Somers were included in the Company’s consolidated financial statements as of and for the periods ended June 30, 2021. In the 2020 fourth quarter, Arch Capital, Somers and Greysbridge, a wholly-owned subsidiary of Arch Capital, entered into an Agreement and Plan of Merger (as amended, the “Merger Agreement”). The merger and the related Greysbridge equity financing closed on July 1, 2021. Effective July 1, 2021, Somers is wholly owned by Greysbridge, and Greysbridge is owned 40% by the Company, 30% by certain investment funds managed by Kelso and 30% by certain investment funds managed by Warburg. Based on the governing documents of Greysbridge, the Company concluded that, while it retains significant influence over Somers, Somers no longer constitutes a variable interest entity. Accordingly, effective July 1, 2021, the Company no longer consolidates the results of Somers in its consolidated financial statements and footnotes. Beginning in the 2021 third quarter, the Company classifies its investment as ‘investments in operating affiliates’ on the Company’s balance sheets and is accounted for under the equity method. The following table provides the carrying amount and balance sheet caption in which the assets and liabilities of Somers were reported: December 31, 2020 Assets Investments accounted for using the fair value option (1) $ 1,790,385 Fixed maturities available for sale, at fair value 655,249 Equity securities, at fair value 52,410 Cash 211,451 Accrued investment income 14,679 Premiums receivable 224,377 Reinsurance recoverable on unpaid and paid losses and LAE 286,590 Ceded unearned premiums 122,339 Deferred acquisition costs, net 53,705 Receivable for securities sold 37,423 Goodwill and intangible assets 7,650 Other assets 75,801 Total assets of consolidated VIE $ 3,532,059 Liabilities Reserves for losses and loss adjustment expenses $ 1,519,583 Unearned premiums 407,714 Reinsurance balances payable 63,269 Revolving credit agreement borrowings 155,687 Senior notes 172,689 Payable for securities purchased 25,881 Other liabilities 193,494 Total liabilities of consolidated VIE $ 2,538,317 Redeemable noncontrolling interests $ 52,398 (1) Included in “other investments” on the Company’s balance sheet. The following table summarizes Somers’ cash flow from operating, investing and financing activities. Year Ended December 31, 2021 2020 2019 Total cash provided by (used for): Operating activities 46,991 181,736 239,284 Investing activities 96,325 258,589 (140,620) Financing activities (2,042) (335,776) (61,433) Non-redeemable noncontrolling interests Through June 30, 2021, the Company accounted for the portion of Somers’ common equity attributable to third party investors in the shareholders’ equity section of its consolidated balance sheets. The non-controlling ownership in Somers common shares was approximately 87% at December 31, 2020. The portion of Somers’ income or loss attributable to third party investors was 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, 2021 2020 Balance, beginning of year $ 823,007 $ 762,777 Impact of deconsolidation of Somers (918,874) — Additional paid in capital attributable to noncontrolling interests 22,113 1,334 Repurchases attributable to non-redeemable noncontrolling interests — (2,867) Amounts attributable to noncontrolling interests 78,314 53,076 Other amounts attributable to noncontrolling interests — (375) Other comprehensive (income) loss attributable to noncontrolling interests (4,560) 9,062 Balance, end of year $ — $ 823,007 Redeemable noncontrolling interests Through June 30, 2021, the Company accounted for redeemable noncontrolling interests in the mezzanine section of its consolidated balance sheets in accordance with applicable accounting guidance. Such redeemable noncontrolling interests primarily related to the Somers 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 Somers Preference Shares were issued at a discounted amount of $24.50 per share. Because the redemption features are not solely within the control of Somers, the Company accounted for the redeemable noncontrolling interests in the Somers Preference Shares in the mezzanine section of its consolidated balance sheets. On August 1, 2019, Somers redeemed 6,919,998 of its 9,065,200 issued and outstanding preference shares (“Somers 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 Somers Preference Shares. Preferred dividends on the Somers Preference Shares, including the accretion of the discount and issuance costs, was $2.1 million for 2021, compared to $4.4 million for 2020 and $17.8 million for 2019. The following table sets forth activity in the redeemable noncontrolling interests: December 31, 2021 2020 2019 Balance, beginning of year $ 58,548 $ 55,404 $ 206,292 Impact of deconsolidation of Somers (48,919) — — Redemption of noncontrolling interests — — (157,709) Accretion of preference share issuance costs — 93 244 Other (396) 3,051 6,577 Balance, end of year $ 9,233 $ 58,548 $ 55,404 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, 2021 2020 2019 Amounts attributable to non-redeemable noncontrolling interests $ (78,314) $ (53,076) $ (40,072) Amounts attributable to redeemable noncontrolling interests (4,299) (7,114) (16,909) Net (income) loss attributable to noncontrolling interests $ (82,613) $ (60,190) $ (56,981) Bellemeade Re The Company has entered into 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 benchmark index for each respective transaction and short term invested trust asset yields. The benchmark index for agreements effective prior to 2021 is based on one-month LIBOR, while the 2021 agreements benchmark index is based on the Secured Overnight Financing Rate (“SOFR”). SOFR is a measure of the cost of borrowing cash overnight, collateralized by U.S. Treasury securities, and is based on directly observable U.S. Treasury-backed repurchase transactions. Dec 31, 2021 Dec 31, 2020 Maximum Exposure to Loss Maximum Exposure to Loss Bellemeade Entities (Issue Date) Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total Bellemeade 2017-1 Ltd. (Oct-17) $ 108,368 $ (159) $ 424 $ 265 $ 145,573 $ (245) $ 844 $ 599 Bellemeade 2018-1 Ltd. (Apr-18) 181,136 (528) 1,268 740 250,095 (903) 2,245 1,342 Bellemeade 2018-2 Ltd. (Aug-18) — — — — 108,395 (138) 280 142 Bellemeade 2018-3 Ltd. (Oct-18) 302,563 (1,018) 2,496 1,478 302,563 (1,320) 3,262 1,942 Bellemeade 2019-1 Ltd. (Mar-19) 181,324 (380) 5,807 5,427 219,256 (1,361) 8,461 7,100 Bellemeade 2019-2 Ltd. (Apr-19) 398,316 (515) 3,998 3,483 398,316 (730) 5,201 4,471 Bellemeade 2019-3 Ltd. (Jul-19) 409,859 (584) 3,190 2,606 528,084 (861) 5,079 4,218 Bellemeade 2019-4 Ltd. (Oct-19) 411,954 (462) 4,759 4,297 468,737 (890) 6,676 5,786 Bellemeade 2020-1 Ltd. (Jun-20) — — — — 275,068 (178) 1,012 834 Bellemeade 2020-2 Ltd. (Sep-20) (1) 217,766 (177) 1,984 1,807 423,420 (556) 6,839 6,283 Bellemeade 2020-3 Ltd. (Nov-20) (2) 348,818 (128) 5,793 5,665 418,158 (631) 9,605 8,974 Bellemeade 2020-4 Ltd. (Dec-20) (3) 176,826 (50) 1,630 1,580 321,393 (156) 6,816 6,660 Bellemeade 2021-1 Ltd. (Mar-21) (4) 568,986 (303) 3,283 2,980 — — — — Bellemeade 2021-2 Ltd. (Jun-21) (5) 522,807 281 4,124 4,405 — — — — Bellemeade 2021-3 Ltd. (Sep-21) (6) 507,873 (411) 3,446 3,035 — — — — Total $ 4,336,596 $ (4,434) $ 42,202 $ 37,768 $ 3,859,058 $ (7,969) $ 56,320 $ 48,351 (1) At December 31, 2021, $1 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table). (2) At December 31, 2021, $16 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table). (3) At December 31, 2021, $9 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table). (4) At December 31, 2021, $61 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table). (5) At December 31, 2021, $93 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table).

Other Comprehensive Income

Other Comprehensive Income	12 Months Ended
	Dec. 31, 2021
Comprehensive Income Note Disclosure [Abstract]
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, 2021 Beginning balance $ 501,295 $ (12,400) $ 488,895 Other comprehensive income (loss) before reclassifications (371,741) (65,686) (437,427) Amounts reclassified from accumulated other comprehensive income (116,068) — (116,068) Net current period other comprehensive income (loss) (487,809) (65,686) (553,495) Ending balance $ 13,486 $ (78,086) $ (64,600) Year Ended December 31, 2020 Beginning balance $ 258,486 $ (46,395) $ 212,091 Other comprehensive income (loss) before reclassifications 668,996 33,995 702,991 Amounts reclassified from accumulated other comprehensive income (426,187) — (426,187) Net current period other comprehensive income (loss) 242,809 33,995 276,804 Ending balance $ 501,295 $ (12,400) $ 488,895 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 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 2021 2020 2019 Unrealized appreciation on available-for-sale investments Net realized gains (losses) $ 157,095 $ 478,659 $ 131,043 Provision for credit losses (2,099) (3,597) — Other-than-temporary impairment losses — (533) (3,165) Total before tax 154,996 474,529 127,878 Income tax (expense) benefit (38,928) (48,342) (8,937) Net of tax $ 116,068 $ 426,187 $ 118,941 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, 2021 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (406,774) $ (19,845) $ (386,929) Less reclassification of net realized gains (losses) included in net income 154,996 38,928 116,068 Foreign currency translation adjustments (64,423) 59 (64,482) Other comprehensive income (loss) $ (626,193) $ (58,714) $ (567,479) Year Ended December 31, 2020 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ 754,572 $ 75,855 $ 678,717 Less reclassification of net realized gains (losses) included in net income 474,529 48,342 426,187 Foreign currency translation adjustments 33,706 370 33,336 Other comprehensive income (loss) $ 313,749 $ 27,883 $ 285,866 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

Earnings Per Common Share

Earnings Per Common Share	12 Months Ended
	Dec. 31, 2021
Earnings Per Share [Abstract]
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, 2021 2020 2019 Numerator: Net income $ 2,239,462 $ 1,465,711 $ 1,693,300 Amounts attributable to noncontrolling interests (82,613) (60,190) (56,981) Net income available to Arch 2,156,849 1,405,521 1,636,319 Preferred dividends (48,343) (41,612) (41,612) Loss on redemption of preferred shares (15,101) — — Net income available to Arch common shareholders $ 2,093,405 $ 1,363,909 $ 1,594,707 Denominator: Weighted average common shares outstanding 391,748,715 403,062,179 401,802,815 Effect of dilutive common share equivalents: Nonvested restricted shares 1,996,524 1,682,309 1,673,770 Stock options (1) 6,600,697 5,514,967 8,132,893 Weighted average common shares and common share equivalents outstanding – diluted 400,345,936 410,259,455 411,609,478 Earnings per common share: Basic $ 5.34 $ 3.38 $ 3.97 Diluted $ 5.23 $ 3.32 $ 3.87 (1) 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 2021, 2020 and 2019, the number of stock options excluded were 2,398,608, 2,249,821 and 1,302,017, respectively.

Income Taxes

Income Taxes	12 Months Ended
	Dec. 31, 2021
Income Tax Disclosure [Abstract]
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. Kingdom, Ireland, Canada, Switzerland, Australia and Denmark. The components of income taxes attributable to operations were as follows: Year Ended December 31, 2021 2020 2019 Current expense (benefit): United States $ 284,274 $ 181,571 $ 139,407 Non-U.S. 11,259 16,091 4,954 295,533 197,662 144,361 Deferred expense (benefit): United States (123,261) (89,170) 11,849 Non-U.S. (43,690) 3,346 (400) (166,951) (85,824) 11,449 Income tax expense $ 128,582 $ 111,838 $ 155,810 The Company’s income or loss before income taxes was earned in the following jurisdictions: Year Ended December 31, 2021 2020 2019 Income (Loss) Before Income Taxes: Bermuda $ 1,518,616 $ 1,114,117 $ 1,122,952 United States 643,239 409,893 701,480 Other 206,187 53,539 24,678 Total $ 2,368,042 $ 1,577,549 $ 1,849,110 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 2021 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 (12.5%), Australia (30.0%), Hong Kong (16.5%) and the Netherlands (25.0%). 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, 2021 2020 2019 Expected income tax expense (benefit) computed on pre-tax income at weighted average income tax rate $ 158,269 $ 111,947 $ 149,799 Addition (reduction) in income tax expense (benefit) resulting from: Tax-exempt investment income (23,572) (1,824) (3,091) Meals and entertainment 379 547 1,134 State taxes, net of U.S. federal tax benefit 20,978 5,027 3,314 Foreign branch taxes 1,998 2,094 1,231 Prior year adjustment (1,432) 3,983 632 Foreign exchange gains & losses 1,190 (1,736) 436 Changes in applicable tax rate 447 — — Dividend withholding taxes 12,211 7,105 6,510 Change in valuation allowance (40,425) 13,190 1,628 Contingent consideration — 9 190 Share based compensation (5,339) (2,533) (6,592) Intercompany loan write-off — (22,083) — Other 3,878 (3,888) 619 Income tax expense (benefit) $ 128,582 $ 111,838 $ 155,810 The effect of a change in tax laws or rates on deferred tax assets and liabilities is recognized in income in the period in which such change is enacted. 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, 2021 2020 Deferred income tax assets: Net operating loss $ 87,960 $ 67,142 Uncrystallized losses — 2,926 Discounting of net loss reserves 72,001 74,247 Net unearned premium reserve 75,483 66,368 Compensation liabilities 28,062 27,351 Foreign tax credit carryforward 20,058 19,160 Interest expense 755 622 Goodwill and intangible assets — 14,450 Bad debt reserves 10,252 10,842 Depreciation and amortization 115,041 — Lease liability 21,453 23,604 Net unrealized foreign exchange gains 166 165 Other, net — 2,318 Deferred tax assets before valuation allowance 431,231 309,195 Valuation allowance (43,953) (88,255) Deferred tax assets net of valuation allowance 387,278 220,940 Deferred income tax liabilities: Depreciation and amortization — (495) Deposit accounting liability (1,578) (1,751) Goodwill and intangibles (70,549) — Lloyds year of account deferral (12,514) — Contingency reserve (49,486) (64,593) Deferred policy acquisition costs (25,612) (42,045) Investment related (7,492) (9,571) Net unrealized appreciation of investments (8,377) (66,681) Right-of-use asset (17,406) (19,239) Other, net (218) (843) Total deferred tax liabilities (193,232) (205,218) Net deferred income tax assets $ 194,046 $ 15,722 The Company provides a valuation allowance to reduce the net value of certain deferred tax assets to an amount which management expects to more likely than not be realized. As of December 31, 2021, the Company’s valuation allowance was $44.0 million, compared to $88.3 million at December 31, 2020. The valuation allowance at December 31, 2021, was primarily attributable to valuation allowances on the Company’s U.K., Canadian and Hong Kong operations and certain other deferred tax assets relating to loss carryforwards that have a limited use. At December 31, 2021, the Company’s net operating loss carryforwards and tax credits were as follows: Year Ended December 31, 2021 Expiration Operating Loss Carryforwards United Kingdom $ 259,235 No expiration Ireland 9,032 No expiration Australia 39,981 No expiration Hong Kong 23,203 No expiration United States (1) 29,508 2029 - 2038 Tax Credits U.K. foreign tax credits 20,058 No expiration (1) 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 $7.6 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 $31.6 million at December 31, 2021, compared to $88.1 million at December 31, 2020. 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, 2021, 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, 2021 2020 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, its subsidiaries and branches file income tax returns in various federal, state and local 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 2015-2021 United Kingdom 2020-2021 Ireland 2017-2021 Canada 2017-2021 Switzerland 2018-2021 Denmark 2017-2021 Australia 2017-2021 As of December 31, 2021, the Company’s current income tax payable (included in “Other liabilities”) was $14.8 million.

Transactions with Related Parti

Transactions with Related Parties	12 Months Ended
	Dec. 31, 2021
Related Party Transactions [Abstract]
Transactions with Related Parties	In 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 2021 first quarter, as part of the Company’s acquisition of Barbican, the Company entered into an agreement with Premia Managing Agency Limited for the reinsurance to close of Syndicate 1955’s 2018 underwriting year of account into Premia Syndicate 1884’s 2021 underwriting year of account. The reinsurance to close covers legacy business underwritten by Syndicate 1955 on the underwriting 2018 and prior years of account and under the agreement, approximately $380 million of net liabilities was transferred to Syndicate 1884, with an effective date of January 1, 2021. The Company had no reinsurance recoverable on unpaid and paid losses or funds held liability at December 31, 2021, compared to $199.8 million and $149.6 million, respectively, at December 31, 2020. In July 2021, following consummation of the Merger Agreement and the related Greysbridge equity financing, pursuant to which Somers is wholly owned by Greysbridge, and Greysbridge is owned 40% by the Company, 30% by certain funds managed by Kelso and 30% by certain funds managed by Warburg, the Company entered into certain reinsurance transactions with Somers. For 2021, the Company ceded premiums written related to such transactions of $453.9 million (which includes reinsurance transactions in force as well as those entered into in conjunction with the Merger Agreement). In addition, Somers paid certain acquisition costs and administrative fees to the Company. At December 31, 2021, the Company recorded a reinsurance recoverable on unpaid and paid losses from Somers of $902.8 million and a reinsurance balance payable to Somers of $258.4 million. See note 12, “Variable Interest Entity and Noncontrolling Interests.” The Company has a put/call option that was entered into in connection with the Greysbridge equity financing, whereby beginning January 1, 2024 the Company will have a call right (but not the obligation) and Warburg and Kelso will each have a put right (but not the obligation) to buy/sell one third of their initial shares annually at the tangible book value per share of Greysbridge for the most recently ended fiscal quarter. As of December 31, 2021, the Company owns $35.0 million in aggregate principal amount of Somers 6.5% senior notes, due July 2, 2029 and approximately 6.6% of Somers’ preference shares.

Leases

Leases	12 Months Ended
	Dec. 31, 2021
Leases [Abstract]
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, 2021 2020 Operating lease costs $ 31,691 $ 31,826 Cash payments included in the measurement of lease liabilities reported in operating cash flows $ 32,094 $ 30,365 Right-of-use assets obtained in exchange for new lease liabilities $ 22,686 $ 12,060 Right-of-use assets (1) $ 106,836 $ 115,911 Operating lease liability (1) $ 126,711 $ 136,015 Weighted average discount rate 3.9 % 3.9 % Weighted average remaining lease term 5.9 years 5.8 years (1) The right-of-use assets are included in ‘ other assets The following table presents the contractual maturities of the Company's operating lease liabilities at December 31, 2021: Years Ending December 31, 2022 $ 31,682 2023 25,288 2024 22,102 2025 16,253 2026 13,430 2027 and thereafter 34,173 Total undiscounted lease liability 142,928 Less: present value adjustment (16,217) Operating lease liability 126,711 All of these leases are for the rental of office space, with expiration terms that range from 2022 to 2033. Rental expense was approximately $31.7 million, $31.8 million and $30.5 million for 2021, 2020 and 2019, respectively.

Commitments and Contingencies

Commitments and Contingencies	12 Months Ended
	Dec. 31, 2021
Commitments and Contingencies Disclosure [Abstract]
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, 2021 2020 2019 Marsh & McLennan Companies and its subsidiaries 18.3 % 13.3 % 9.6 % Aon Corporation and its subsidiaries 12.2 % 12.0 % 12.2 % No other broker and no one insured or reinsured accounted for more than 10% of gross premiums written for 2021, 2020 and 2019. 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, 2021 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 $3.0 billion and $2.1 billion at December 31, 2021 and 2020, respectively. 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 $114.1 million and $73.0 million at December 31, 2021 and 2020, respectively. Employment and Other Arrangements At December 31, 2021, 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, 2021
Debt Disclosure [Abstract]
Debt and Financing Arrangements	Debt and Financing Arrangements The Company’s senior notes payable at December 31, 2021 and 2020 were as follows: Carrying Amount at Interest Principal December 31, (Fixed) Amount 2021 2020 2034 notes (1) 7.350 % 300,000 297,488 297,367 2043 notes (2) 5.144 % 500,000 495,063 494,944 2026 notes (3) 4.011 % 500,000 497,633 497,211 2046 notes (4) 5.031 % 450,000 445,490 445,402 2050 notes (5) 3.635 % 1,000,000 988,720 988,500 Somers notes (6) 137,689 $ 2,750,000 $ 2,724,394 $ 2,861,113 (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 Arch Capital issued on June 30, 2020 and due June 30, 2050 (“2050 notes”). (6) Senior notes of Somers issued on July 2, 2019 and due July 2, 2029 (“Somers Senior Notes”), reflecting the elimination of amounts owned by Arch-U.S. Effective July 1, 2021, the Company no longer consolidates Somers in its financials. See note 12. 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. The 2050 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 2050 notes are due on June 30 and December 30 of each year. Arch Capital may redeem the 2050 notes at any time and from time to time, in whole or in part, at a “make-whole” redemption price. Interest payments on the Somers Senior Notes due on each January 2 and July 2, commencing January 2, 2020. The Company purchased $35.0 million in aggregate principal amount of the Somers Senior Notes. Effective July 1, 2021, the Company no longer consolidates the results of Somers in its consolidated financial statements and footnotes. See note 12, “Variable Interest Entity and Noncontrolling Interests.” 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 aggregate of $1.3 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, 2021. 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 $240.4 million of letters of credit outstanding and remaining capacity of $9.6 million at December 31, 2021. In addition, certain of Arch Capital’s subsidiaries had outstanding secured and unsecured letters of credit of $26.0 million and $290.0 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, 2021, these letters of credit were secured by investments with a fair value of $348.4 million. The Company’s outstanding revolving credit agreement borrowings were as follows: Year Ended December 31, 2021 2020 Arch Capital $ — $ — Somers 155,687 Total $ — $ 155,687 Federal Home Loan Bank Membership Certain subsidiaries of the Company are members of Federal Home Loan Banks (“FHLBs”). Members may borrow from the FHLBs at competitive rates subject to certain conditions. Conditions include maintaining sufficient collateral deposits for funding and a requirement to hold stock in the FHLBs related to both membership and outstanding advances. At December 31, 2021 and 2020, the Company had $80.0 million of advances outstanding under the FHLB program, included in ‘other liabilities’ on the Company’s balance sheet, secured by investments with a fair value of $80.2 million.

Goodwill and Intangible Assets

Goodwill and Intangible Assets	12 Months Ended
	Dec. 31, 2021
Goodwill and Intangible Assets Disclosure [Abstract]
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, 2019 $ 326,551 $ 85,911 $ 325,621 $ 738,083 Acquisitions — — 39,178 39,178 Amortization — — (69,031) (69,031) Foreign currency movements and other adjustments (11,922) (6,692) 3,247 (15,367) Net balance at Dec. 31, 2020 314,629 79,219 299,015 692,863 Acquisitions (1) 31,677 — 318,459 350,136 Amortization — — (82,955) (82,955) Impact of deconsolidation of Somers (2) — (7,650) — (7,650) Foreign currency movements and other adjustments (1,441) (212) (5,758) (7,411) Net balance at Dec. 31, 2021 $ 344,865 $ 71,357 $ 528,761 $ 944,983 Gross balance at Dec. 31, 2021 $ 342,842 $ 70,246 $ 1,102,298 $ 1,515,386 Accumulated amortization — — (571,839) (571,839) Foreign currency movements and other adjustments 2,023 1,111 (1,698) 1,436 Net balance at Dec. 31, 2021 $ 344,865 $ 71,357 $ 528,761 $ 944,983 (1) Certain amounts for the Company’s 2021 acquisitions are considered provisional. (2) See note 12 . The following table presents the components of goodwill and intangible assets: Gross Balance Accumulated Foreign Currency Translation Adjustment and Other Net Dec. 31, 2021 Acquired insurance contracts $ 451,505 $ (409,592) $ 339 $ 42,252 Operating platform 52,674 (48,838) 56 3,892 Distribution relationships 602,518 (120,302) (2,207) 480,009 Goodwill 342,842 — 2,023 344,865 Insurance licenses 48,331 — — 48,331 Syndicate capacity 21,915 — 1,111 23,026 Unfavorable service contract (9,533) 9,435 — (98) Other 5,134 (2,542) 114 2,706 Total $ 1,515,386 $ (571,839) $ 1,436 $ 944,983 Dec. 31, 2020 Acquired insurance contracts $ 451,505 $ (381,349) $ 284 $ 70,440 Operating platform 52,674 (44,347) 60 8,387 Distribution relationships 285,141 (71,383) 3,450 217,208 Goodwill 318,043 — (3,414) 314,629 Insurance licenses 55,981 — — 55,981 Syndicate capacity 21,915 — 1,324 23,239 Unfavorable service contract (9,533) 9,147 — (386) Other 5,134 (1,896) 127 3,365 Total $ 1,180,860 $ (489,828) $ 1,831 $ 692,863 The estimated remaining amortization expense for the Company’s intangible assets with finite lives is as follows: 2022 $ 109,144 2023 99,620 2024 79,410 2025 44,523 2026 35,252 2027 and thereafter 160,812 Total $ 528,761 one

Shareholders' Equity

Shareholders' Equity	12 Months Ended
	Dec. 31, 2021
Stockholders' Equity Note [Abstract]
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, 2021 2020 2019 Common Shares: Shares issued and outstanding, beginning of year 579,000,841 574,617,195 570,737,283 Shares issued (1) 2,669,229 2,646,164 2,835,994 Restricted shares issued, net of cancellations 1,619,780 1,737,482 1,043,918 Shares issued and outstanding, end of year 583,289,850 579,000,841 574,617,195 Common shares in treasury, end of year (204,365,956) (172,280,199) (168,997,994) Shares issued and outstanding, end of year 378,923,894 406,720,642 405,619,201 (1) Includes shares issued from the exercise of stock options and stock appreciation rights, the vesting of restricted share units and shares issued from the employee share purchase plan. 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, 2021, $1.2 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, 2022. 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, 2021, Arch Capital held 204.4 million shares for an aggregate cost of $3.8 billion in treasury, at cost. The Company’s repurchases under the share repurchase program were as follows: Year Ended December 31, 2021 2020 2019 Aggregate cost of shares repurchased $ 1,234,294 $ 83,472 $ 2,871 Shares repurchased 31,486,830 2,850,102 110,598 Average price per share repurchased $ 39.20 $ 29.29 $ 25.96 Since the inception of the share repurchase program through December 31, 2021, Arch Capital has repurchased approximately 420.7 million common shares for an aggregate purchase price of $5.3 billion. Series G Preferred Shares In June 2021, Arch Capital completed a $500 million underwritten public offering of 20.0 million depositary shares (the “Depositary Shares”), each of which represents a 1/1,000th interest in a share of its 4.55% Non-Cumulative Preferred Shares, Series G, $0.01 par value and $25,000 liquidation preference per share (equivalent to $25 liquidation preference per Depositary Share) (the “Series G Preferred Shares”). Each 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 G Preferred Shares represented thereby (including any dividend, liquidation, redemption and voting rights). Holders of Series G Preferred Shares will be entitled to receive dividend payments only when, as and if declared by the Company’s 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 4.55%. Dividends on the Series G 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 G Preferred Shares. The Company may not declare or pay a dividend on the Series G Preferred Shares under certain circumstances, including if the Company is or, after giving effect to such payment, would be in breach of applicable individual or group solvency and liquidity requirements or applicable individual or group enhanced capital requirements ("ECR"). The Series G Preferred Shares may not be redeemed at any time if the ECR would be breached immediately before or after giving effect to such redemption, unless the Company replaces the capital represented by preference shares to be redeemed with capital having equal or better capital treatment. Except in specified circumstances relating to certain tax or corporate events, the Series G Preferred Shares are not redeemable prior to June 11, 2026. On and after that date, the Series G 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 G 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 Depositary Shares will be redeemed if and to the extent the related Series G Preferred Shares are redeemed by the Company. Neither the Depositary Shares nor the Series G Preferred Shares have a stated maturity, nor will they be subject to any sinking fund or mandatory redemption. The Series G Preferred Shares are not convertible into any other securities. The Series G Preferred Shares do not have voting rights, except under limited circumstances. The net proceeds from the Series G Preferred Share offerings were used to redeem the Company’s outstanding 5.25% Series E Non-Cumulative Preferred Shares. 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 In September, 2021, Arch Capital redeemed all outstanding 5.25% Series E 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, 2021
Share-based Payment Arrangement [Abstract]
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, 2021, 9,909,950 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, 2021, 606,942 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, 2021, 320,272 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, 2021, 1,608,354 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 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, 2021 2020 2019 Dividend yield — % — % — % Expected volatility 24.2 % 16.6 % 18.1 % Risk free interest rate 1.0 % 1.2 % 2.5 % 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 2021 is presented below: Year Ended December 31, 2021 Number of Weighted Average Exercise Price Weighted Average Contractual Term Aggregate Intrinsic Value Outstanding, beginning of year 17,839,333 $ 23.32 Granted 1,243,984 $ 35.90 Exercised (1,931,320) $ 15.57 Forfeited or expired (68,837) $ 35.39 Outstanding, end of year 17,083,160 $ 25.06 4.41 $ 331,214 Exercisable, end of year 14,730,147 $ 23.20 3.78 $ 312,966 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 2021, the Company received proceeds of $10.1 million from the exercise of stock options and recognized a tax benefit of $5.4 million from the exercise of stock options and SARs. Year Ended December 31, 2021 2020 2019 Weighted average grant date fair value $ 9.22 $ 8.14 $ 7.90 Aggregate intrinsic value of Options/SARs exercised $ 47,074 $ 59,723 $ 51,350 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 A summary of restricted share and restricted unit activity under the Company’s Long Term Incentive and Share Award Plans for 2021 is presented below: Restricted Common Shares Restricted Unit Awards Unvested Shares: Unvested balance, beginning of year 1,635,845 1,121,719 Granted 1,085,811 175,962 Vested (549,892) (555,870) Forfeited (100,927) (41,945) Unvested balance, end of year 2,070,837 699,866 Weighted Average Grant Date Fair Value: Unvested balance, beginning of year $ 36.34 $ 31.43 Granted $ 36.14 $ 35.94 Vested $ 35.94 $ 30.46 Forfeited $ 36.28 $ 32.23 Unvested balance, end of year $ 36.35 $ 33.29 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, 2021 2020 2019 Restricted shares and restricted unit awards granted 1,261,773 1,535,330 1,195,741 Weighted average grant date fair value $ 36.12 $ 37.55 $ 32.89 Aggregate fair value of vested restricted share and unit awards $ 65,477 $ 39,703 $ 46,262 The aggregate intrinsic value of restricted units outstanding at December 31, 2021 was $31.1 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 Ended December 31, 2021 2020 2019 Expected volatility 37.5 % 18.1 % 17.1 % Risk free interest rate 0.3 % 1.1 % 2.5 % Performance Shares Performance Units Unvested Shares: Unvested balance, beginning of year 1,851,382 32,065 Granted 674,406 10,698 Performance adjustment (1) (2) (39,510) 11,447 Vested (624,518) (24,440) Unvested balance, end of year 1,861,760 29,770 Weighted Average Grant Date Fair Value: Unvested balance, beginning of year $ 34.42 $ 33.48 Granted $ 37.38 $ 37.38 Performance adjustment (1) (2) 24.78 24.71 Vested $ 24.78 $ 24.71 Unvested balance, end of year $ 38.93 $ 38.71 (1) The performance adjustment represents the difference between the number of performance shares granted and earned, which vested following the end of the performance period. The performance shares were granted at the maximum level of achievement. (2) The performance adjustment represents the change in PSUs, which vested following the end of the performance period. The performance units were granted at the target level of achievement. The following table presents the weighted average grant date fair values of performance awards granted. Year Ended December 31, 2021 2020 2019 Performance awards 685,104 557,204 696,360 Weighted average grant date fair value $ 37.38 $ 44.17 $ 36.05 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, 2021 2020 2019 Pre-Tax Stock options and SARs $ 12,316 $ 11,744 $ 12,866 Restricted share and unit awards 46,817 41,284 38,988 Performance awards 23,696 14,729 8,949 ESPP 3,751 2,135 3,045 Total $ 86,580 $ 69,892 $ 63,848 After-Tax Stock options and SARs $ 10,927 $ 10,388 $ 11,450 Restricted share and unit awards 39,349 34,599 32,999 Performance awards 21,920 13,380 8,295 ESPP 3,471 1,978 2,758 Total $ 75,667 $ 60,345 $ 55,502 December 31, 2021 Stock Options and SARs Restricted Common Performance Common Shares and Units Unrecognized compensation cost related to unvested awards $ 8,233 $ 45,936 $ 7,635 Weighted average recognition period (years) 0.91 1.23 0.52

Retirement Plans

Retirement Plans	12 Months Ended
	Dec. 31, 2021
Retirement Benefits [Abstract]
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 2021, 2020 and 2019, the Company expensed $60.4 million, $52.0 million and $44.8 million, respectively, related to these retirement plans.

Legal Proceedings

Legal Proceedings	12 Months Ended
	Dec. 31, 2021
Disclosure Legal Proceedings [Abstract]
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, 2021, 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, 2021
Disclosure Statutory Information [Abstract]
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, 2021 and 2020: December 31, 2021 2020 Actual capital and surplus (1): Bermuda $ 17,528,510 $ 17,390,943 Ireland 958,200 883,337 United States 5,600,652 4,904,840 United Kingdom 902,002 967,440 Canada 70,063 64,286 Australia 283,693 64,507 Required capital and surplus: Bermuda $ 5,661,301 $ 5,234,121 Ireland 794,933 701,161 United States 1,717,646 1,644,324 United Kingdom 563,164 601,662 Canada 42,513 37,441 Australia 214,022 19,370 (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 2021, 2020 and 2019 was as follows: Year Ended December 31, 2021 2020 2019 Statutory net income (loss): Bermuda $ 2,370,746 $ 1,579,889 $ 1,801,486 Ireland 25,191 18,397 26,367 United States 345,790 143,271 481,188 United Kingdom 35,286 4,078 (17,423) Canada 6,985 (1,049) (1,023) Australia 11,874 (8,601) (6,199) Bermuda Under the Bermuda Insurance Act 1978 and related regulations, each as amended (the “Insurance Act”), Arch Re Bermuda, the Company’s Bermuda reinsurance and insurance subsidiary, is registered as a Class 4 insurer and long-term insurer and is required to maintain minimum statutory capital and surplus equal to the greater of a minimum solvency margin and the enhanced capital requirement (“ECR”) as determined by the Bermuda Monetary Authority (“BMA”). The ECR 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, 2021 and 2020, the actual and required capital and surplus were based on the economic balance sheet requirements. 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 BMA 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 $3.8 billion to Arch Capital during 2022 without providing an affidavit to the BMA. Ireland The Company has three Irish subsidiaries: Arch Re Europe, an authorized life and non-life reinsurer, Arch Insurance (EU), an authorized non-life insurer and Arch Underwriting Europe, a registered insurance and reinsurance intermediary. Irish authorized reinsurers and insurers, such as Arch Re Europe, Arch Insurance (EU) and Irish intermediaries, such as Arch Underwriters Europe, are also subject to the general body of Irish laws and regulations including the provisions of the Companies Act 2014. As part of the Company’s Brexit plan, Arch Insurance (EU) received approval from the Central Bank of Ireland (“CBOI”) to expand the nature of its business in 2019 commenced writing insurance lines in the European Economic Area in 2020, and the Part VII Transfer was completed at the end of December 2020. Arch Re Europe, Arch Insurance (EU) and Arch Underwriters Europe are subject to the supervision of the CBOI and must comply with Irish insurance acts and regulations as well as with directions and guidance issued by the CBOI. Arch Re Europe and Arch Insurance (EU) are required to maintain a minimum level of capital. At December 31, 2021 and 2020, 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 $217.5 million of dividends during 2022 subject to the approval of the Commissioner of the Delaware Department of Insurance. AMIC and UGRIC 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 AMIC and Arch Mortgage Guaranty Company, the North Carolina Department of Insurance (“NC DOI”) for UGRIC, 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 $194.1 million of ordinary dividends in 2022, however, dividend capacity is limited by the respective companies unassigned surplus amounts. 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 U.K. insurance operations are conducted through Arch Insurance (U.K.), Arch Syndicate 2012 and Arch Syndicate 1955. Arch Managing Agency Limited (“AMAL”) is the managing agent of Arch Syndicate 2012 and Arch Syndicate 1955. Arch Syndicate 2012 and Arch Syndicate 1955 provide access to Lloyd’s extensive distribution network and worldwide licenses. AMAL also acts as managing agent for third party members of Arch Syndicate 1955. 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.) and AMAL 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. At December 31, 2021 and 2020, our subsidiaries were in compliance with these requirements. As corporate members of Lloyd’s, AMAL (as managing agent of Arch Syndicate 2012 and Arch Syndicate 1955) and each syndicate’s respective corporate members 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 Arch Syndicate 1955 in the form of pledged assets and letters of credit 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.) and AMAL. 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). Australia The Australian Prudential Regulation Authority (“APRA”) is an independent statutory authority responsible for prudential supervision of institutions across banking, insurance and superannuation and promotes financial stability in Australia. Arch Indemnity has been authorized to conduct monoline lenders’ mortgage insurance business in Australia since June 2002 and was acquired by Arch Capital on August 30, 2021. Arch LMI Pty Ltd. (“Arch LMI”) was authorized by APRA in January 2019 to conduct monoline lenders’ mortgage insurance business in Australia. Major regulatory requirements that are applicable to Arch LMI and Arch Indemnity as general as an insurance providers in Australia include requirements on minimum capital levels and compliance with corporate governance standards, including the risk management strategy for our Australian mortgage insurance business. At December 31, 2021 and 2020, these requirements were met. Arch Capital also conducts property and casualty insurance business in Australia through the Company’s Lloyd’s platform. This insurance business is managed by and distributed through local coverholders and is subject to Lloyd’s Supervision. In addition, the business is subject to local Australian prudential regulatory oversight by APRA, and additional separate financial services market conduct regulation by the Australian Securities and Investments Commission.

Subsequent Event

Subsequent Event	12 Months Ended
	Dec. 31, 2021
Subsequent Events [Abstract]
Subsequent event	Bellemeade Re 2022-1 Ltd . In January 2022, the Company announced that it has obtained over $315 million of indemnity reinsurance on a pool representing approximately $6.3 billion of mortgages from Bellemeade Re 2022-1 Ltd., a special purpose reinsurer. The coverage was obtained by issuing approximately $283.5 million in bonds and $33 million in direct reinsurance. This transaction largely covers a portfolio of policies issued from July through November 2021. Share Repurchases From January 1 to February 25, 2022, the Company repurchased 890,180 common shares for an aggregate purchase price of $41.5 million. At February 25, 2022 approximately $1.14 billion of repurchases were available under the share repurchase program.

Schedule II - Condensed Financi

Schedule II - Condensed Financial Information of Registrant	12 Months Ended
	Dec. 31, 2021
Condensed Financial Information Disclosure [Abstract]
Condensed Financial Information of Registrant	SCHEDULE II ARCH CAPITAL GROUP LTD. AND SUBSIDIARIES CONDENSED FINANCIAL INFORMATION OF REGISTRANT (U.S. dollars in thousands) Balance Sheet (Parent Company Only) December 31, 2021 2020 Assets Total investments $ 2,038 $ 172 Cash 16,317 18,932 Investments in subsidiaries 14,822,024 14,377,529 Investment in operating affiliates 6,877 7,731 Due from subsidiaries and affiliates 11 — Other assets 9,604 10,659 Total assets $ 14,856,871 $ 14,415,023 Liabilities Senior notes $ 1,286,208 $ 1,285,867 Due to subsidiaries and affiliates — — Other liabilities 24,767 23,270 Total liabilities 1,310,975 1,309,137 Shareholders' Equity Non-cumulative preferred shares 830,000 780,000 Common shares ($0.0011 par, shares issued: 583,289,850 and 579,000,841) 648 643 Additional paid-in capital 2,085,075 1,977,794 Retained earnings 14,455,868 12,362,463 Accumulated other comprehensive income (loss), net of deferred income tax (64,600) 488,895 Common shares held in treasury, at cost (shares: 204,365,956 and 172,280,199) (3,761,095) (2,503,909) Total shareholders' equity $ 13,545,896 $ 13,105,886 Total liabilities and shareholders' equity $ 14,856,871 $ 14,415,023 The financial information for the parent company (Arch Capital Group Ltd.) should be read in conjunction with the Consolidated Financial Statements and Notes thereto . Statement of Income (Parent Company Only) Year Ended December 31, 2021 2020 2019 Revenues Net investment income $ 1,524 $ 53 $ 212 Net realized gains (losses) — (2,110) — Total revenues 1,524 (2,057) 212 Expenses Corporate expenses 71,818 65,566 62,701 Interest expense 58,741 40,445 22,154 Net foreign exchange (gains) losses 7 3 1 Total expenses 130,566 106,014 84,856 Income (loss) before income taxes and income (loss) from operating affiliates (129,042) (108,071) (84,644) Income (loss) from operating affiliates (590) (437) (762) Income (loss) before equity in net income of subsidiaries (129,632) (108,508) (85,406) Equity in net income of subsidiaries 2,286,481 1,514,029 1,721,725 Net income available to Arch 2,156,849 1,405,521 1,636,319 Preferred dividends (48,343) (41,612) (41,612) Loss on redemption of preferred shares (15,101) — — Net income available to Arch common shareholders $ 2,093,405 $ 1,363,909 $ 1,594,707 The financial information for the parent company (Arch Capital Group Ltd.) should be read in conjunction with the Consolidated Financial Statements and Notes thereto . Statement of Cash Flows (Parent Company Only) Year Ended December 31, 2021 2020 2019 Operating Activities: Net Cash Provided By Operating Activities $ 1,727,529 $ 124,751 $ 52,487 Investing Activities: Net (purchases) sales of short-term investments (1,866) (130) 61 Capital contributed to subsidiaries (487,161) (988,975) (2,121) Purchase of fixed assets (783) (15) (162) Net Cash Used For Investing Activities (489,810) (989,120) (2,222) Financing Activities: Purchases of common shares under share repurchase program (1,234,294) (83,472) (2,871) Proceeds from common shares issued, net 6,418 1,876 6,203 Proceeds from issuance of preferred shares, net 485,821 — — Redemption of preferred shares (450,000) — — Proceeds from borrowings — 988,393 — Preferred dividends paid (48,280) (41,612) (41,612) Net Cash Used For Financing Activities (1,240,335) 865,185 (38,280) Increase (decrease) in cash and restricted cash (2,616) 816 11,985 Cash and restricted cash, beginning of year 18,960 18,144 6,159 Cash and restricted cash, end of period $ 16,344 $ 18,960 $ 18,144 The financial information for the parent company (Arch Capital Group Ltd.) should be read in conjunction with the Consolidated Financial Statements and Notes thereto .

Schedule III - Supplementary In

Schedule III - Supplementary Insurance Information	12 Months Ended
	Dec. 31, 2021
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, 2021 Insurance $378,265 $9,810,622 $2,937,664 $3,626,468 NM $2,344,365 $606,265 $558,906 $4,148,193 Reinsurance 424,390 6,878,721 2,263,264 2,840,443 NM 1,924,719 536,754 212,810 3,254,374 Mortgage 99,186 1,067,813 811,014 1,283,419 NM 56,677 97,418 194,010 1,261,068 Other 331,968 NM 259,042 62,741 32,869 354,702 Total $901,841 $17,757,156 $6,011,942 $8,082,298 NM $4,584,803 $1,303,178 $998,595 $9,018,337 December 31, 2020 Insurance $254,833 $8,989,930 $2,334,225 $2,871,420 NM $2,092,453 $418,483 $489,153 $3,162,907 Reinsurance 278,422 5,027,742 1,356,983 2,162,229 NM 1,628,320 354,048 168,011 2,457,370 Mortgage 203,748 976,673 740,043 1,397,935 NM 528,344 134,240 162,202 1,279,850 Other 53,705 1,519,583 407,714 560,351 NM 440,482 98,071 55,810 537,589 Total $790,708 $16,513,928 $4,838,965 $6,991,935 NM $4,689,599 $1,004,842 $875,176 $7,437,716 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 (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. 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, 2021
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, 2021 Premiums Written: Insurance $ 5,833,873 $ (1,719,541) $ 33,861 $ 4,148,193 0.8 % Reinsurance 408,520 (1,839,556) 4,685,410 3,254,374 144.0 % Mortgage 1,213,333 (246,757) 294,492 1,261,068 23.4 % Other 251,106 (102,763) 206,359 354,702 58.2 % Total $ 7,706,832 $ (3,734,150) $ 5,045,655 $ 9,018,337 55.9 % Year Ended December 31, 2020 Premiums Written: Insurance $ 4,659,416 $ (1,525,655) $ 29,146 $ 3,162,907 0.9 % Reinsurance 305,435 (1,014,716) 3,166,651 2,457,370 128.9 % Mortgage 1,192,316 (194,149) 281,683 1,279,850 22.0 % Other 396,743 (190,957) 331,803 537,589 61.7 % Total $ 6,553,910 $ (2,650,352) $ 3,534,158 $ 7,437,716 47.5 % 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 % (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, 2021
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) Consolidated Subsidiaries 2021 $ 901,841 $ 17,757,156 $ 55,575 $ 6,011,942 $ 8,082,298 $ 389,118 $ 4,940,987 $ (356,184) $ 1,303,178 $ 2,826,551 $ 9,018,337 2020 790,708 16,513,929 23,326 4,838,965 6,991,935 519,608 4,851,051 (161,452) 1,004,842 2,661,117 7,437,716 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

Significant Accounting Polici_2

Significant Accounting Policies (Policies)	12 Months Ended
	Dec. 31, 2021
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 Capital Group (U.S.) Inc.(“Arch-U.S.”), Arch Insurance Company, Arch Specialty Insurance Company, Arch Property & Casualty Insurance Company (“Arch P&C”), Arch Indemnity Insurance Company (“Arch Indemnity Insurance”), Arch Insurance Canada Ltd. (“Arch Insurance Canada”), Arch Reinsurance Europe Designated Activity Company (“Arch Re Europe”), Arch Mortgage Insurance Company (“AMIC”), Arch Mortgage Guaranty Company, United Guaranty Residential Insurance Company (“UGRIC”), Arch Indemnity, Arch Insurance (EU) Designated Activity Company (“Arch Insurance (EU)”), Arch Insurance (U.K.) Limited (“Arch Insurance (U.K.)”) and the Company’s participation on Lloyd’s of London syndicates 2012 (“Arch Syndicate 2012”) and 1955 (“Arch Syndicate 1955”). 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 allowance for credit losses; • 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 that 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. 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. 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. 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. Premiums receivable include amounts receivable from agents, brokers and insured that are both currently due and amounts not yet due on insurance, reinsurance and mortgage insurance policies. Premiums receivable balances are reported net of an allowance for expected credit losses. The Company monitors credit risk associated with premiums receivable through its ongoing review of amounts outstanding, aging of the receivable, historical loss data, and counterparty financial strength measures. The allowance also includes estimated uncollectible amounts related to dispute risk. In certain instances, credit risk may be reduced by the Company’s right to offset loss obligations or unearned premiums against premiums receivable. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses. See note 7, “Allowance for Expected Credit Losses” for additional information.
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 2021, 2020 or 2019.
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 8, “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. Reinsurance recoverables are recorded as assets, predicated on the reinsurers’ ability to meet their obligations under the reinsurance agreements. In certain instances, the Company obtains collateral, including letters of credit and trust accounts to further reduce the credit exposure on its reinsurance recoverables. The Company reports its reinsurance recoverables net of an allowance for expected credit loss. The allowance is based upon the Company’s ongoing review of amounts outstanding, the financial condition of its reinsurers, amounts and form of collateral obtained and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit loss. Any allowance for credit losses is charged to net realized gains (losses) in the period the recoverable is recorded and revised in s ubsequent periods to reflect changes in the Company’s estimate of expected credit losses . See note 7, “Allowance for Expected Credit Losses” for additional information.
Cash	Cash includes cash equivalents, which are investments with original maturities of three months or less which are not part of the investment portfolio.
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.
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. Prior to the termination of its program in 2021, the Company entered into securities lending agreements with financial institutions to enhance investment income whereby it loaned 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 maintained legal control over the securities it lent, retained the earnings and cash flows associated with the loaned securities and received a fee from the borrower for the temporary use of the securities. Collateral received was required at a rate of 102% or greater of the fair value of the loaned securities including accrued investment income and was 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 three 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, short-term investments 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 reverse repurchase agreements that are generally treated as collateralized receivables. Receivables for reverse repurchase agreements are reflected in “Other investments” or “Short-term investments” in the Company's consolidated balance sheet depending on their terms. These agreements are recorded at their contracted resale amount plus accrued interest, other than those that are accounted for at fair value. In reverse repurchase transactions, the Company obtains an interest in the purchased assets that are received as collateral. 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 and other investments. 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 conducts a periodic review to identify and evaluate credit based impairments related to the Company’s available for sale investments. The Company derives estimated credit losses by comparing expected future cash flows to be collected to the amortized cost of the security. Estimates of expected future cash flows consider among other things, macroeconomic conditions as well as the financial condition, near-term and long-term prospects for the issuer, and the likelihood of the recoverability of principal and interest. Effective January 1, 2020, credit losses are recognized through an allowance account subject to reversal, rather than a reduction in amortized cost. Declines in value attributable to factors other than credit are reported in other comprehensive income while the allowance for credit loss is charged to net realized gains (losses). For available for sale investments that the Company intends to sell or for which it is more likely than not that the Company would be required to sell before an anticipated recovery in value, the full amount of the impairment is included in net realized gains (losses). The new cost basis of the investment is the previous amortized cost basis reduced by the impairment recognized in net realized gains (losses). The new cost basis is not adjusted for any subsequent recoveries in fair value. The Company reports accrued investment income separately from investment balances and has elected not to measure an allowance for credit losses for accrued investment income . Any uncollectible accrued interest income is written off in the period it is deemed uncollectible. Prior to January 1, 2020, the Company performed quarterly reviews of its investments to determine whether declines in fair value below the cost basis were considered other-than-temporary in accordance with applicable accounting guidance regarding the recognition and presentation of OTTI. The process of determining whether a security was other-than-temporarily impaired required judgment and involved analyzing many factors. These factors included (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 were credit-related losses associated with debt securities for which the Company did not have an intent to sell and it was more likely than not that it would not be required to sell the security before recovery of its cost basis, the amount of the OTTI related to a credit loss was recognized in earnings and the amount of the OTTI related to other factors ( e.g. , interest rates, market conditions, etc.) was recorded as a component of other comprehensive income (loss). The amount of the credit loss of an impaired debt security was 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 existed but it was more likely than not that the Company would have to sell the debt security prior to the anticipated recovery, the decline in fair value below amortized cost was recognized as an OTTI in earnings. In periods after the recognition of an OTTI on debt securities, the Company accounted 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 would be accreted or amortized into net investment income. See note 9, “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 2021, 2020, and 2019, the Company did not designate any derivative instruments as hedges under the relevant accounting guidance. See note 11, “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 or more payments in arrears). 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
Contractholders receivables and payables	Certain insurance policies written by the Company’s U.S. insurance operations feature large deductibles, primarily in its construction and national accounts line 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 policy holder for the deductible amount. These amounts are included on a gross basis in the consolidated balance sheet as contractholder payables and contractholder receivables. 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.” Contractholder receivables are reported net of an allowance for expected credit losses. The allowance is based upon the Company’s ongoing review of amounts outstanding, changes in policyholder credit standing, amounts and form of collateral obtained, and other relevant factors. A ratings based probability-of-default and loss-given-default methodology is used to estimate the allowance for expected credit losses. Any allowance for credit losses is charged to net realized gains (losses) in the period the receivable is recorded and revised in subsequent periods to reflect changes in the Company’s estimate of expected credit losses . See note 7, “Allowance for Expected Credit Losses” for additional information.
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 15, “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 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 22, “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 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, including customer lists, trade name and IT platforms, 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.
Investment in operating affiliates	Investment in operating affiliates primarily represent the Company’s investments in which it has significant influence and which are accounted for under the equity method of accounting. In applying the equity method of accounting, investments in operating affiliates are initially recorded at cost and are subsequently adjusted based on the Company’s proportionate share of net income or loss of the operating affiliate. The Company records its proportionate share of other comprehensive income or loss of the operating affiliate as a component of other comprehensive income. Adjustments are based on the most recently available financial information from the operating affiliate. Changes in the carrying value of these investments are recorded in income (loss) from operating affiliates.
Recent accounting pronouncements	Recently Issued Accounting Standards Adopted The Company adopted ASU 2019-12, “Simplifying the Accounting for Income Taxes.” This ASU eliminates certain exceptions for recognizing deferred taxes for investments, performing intraperiod tax allocations and calculating income taxes in interim periods. The ASU also clarifies the accounting for transactions that result in a step-up in the tax basis of goodwill. The adoption of this guidance did not have a material effect on the Company’s consolidated financial statements. Recently Issued Accounting Standards Not Yet Adopted ASU 2020-04, “Facilitation of the Effects of Reference Rate Reform on Financial Reporting,” was issued in March 2020. This ASU provides optional expedients and exceptions for applying GAAP to investments, derivatives, or other transactions that reference the London Interbank Offered Rate (LIBOR) or another reference rate expected to be

Segment Information (Tables)

Segment Information (Tables)	12 Months Ended
	Dec. 31, 2021
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, 2021 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 5,867,734 $ 5,093,930 $ 1,507,825 $ 12,463,788 $ 457,465 $ 12,752,487 Premiums ceded (1,719,541) (1,839,556) (246,757) (3,800,153) (102,763) (3,734,150) Net premiums written 4,148,193 3,254,374 1,261,068 8,663,635 354,702 9,018,337 Change in unearned premiums (521,725) (413,931) 22,351 (913,305) (22,734) (936,039) Net premiums earned 3,626,468 2,840,443 1,283,419 7,750,330 331,968 8,082,298 Other underwriting income (loss) — 3,669 17,665 21,334 739 22,073 Losses and loss adjustment expenses (2,344,365) (1,924,719) (56,677) (4,325,761) (259,042) (4,584,803) Acquisition expenses (606,265) (536,754) (97,418) (1,240,437) (62,741) (1,303,178) Other operating expenses (558,906) (212,810) (194,010) (965,726) (32,869) (998,595) Underwriting income (loss) $ 116,932 $ 169,829 $ 952,979 1,239,740 (21,945) 1,217,795 Net investment income 346,808 42,310 389,118 Net realized gains (losses) 299,207 80,638 379,845 Equity in net income (loss) of investments accounted for using the equity method 366,402 — 366,402 Other income (loss) 10,244 — 10,244 Corporate expenses (77,119) — (77,119) Transaction costs and other (1,103) (935) (2,038) Amortization of intangible assets (82,057) (898) (82,955) Interest expense (131,060) (8,410) (139,470) Net foreign exchange gains (losses) 42,854 (1,325) 41,529 Income (loss) before income taxes and income (loss) from operating affiliates 2,013,916 89,435 2,103,351 Income tax expense (128,348) (234) (128,582) Income (loss) from operating affiliates 264,693 — 264,693 Net income (loss) 2,150,261 89,201 2,239,462 Amounts attributable to redeemable noncontrolling interests (2,346) (1,953) (4,299) Amounts attributable to nonredeemable noncontrolling interests — (78,314) (78,314) Net income (loss) available to Arch 2,147,915 8,934 2,156,849 Preferred dividends (48,343) — (48,343) Loss on redemption of preferred shares (15,101) — (15,101) Net income (loss) available to Arch common shareholders $ 2,084,471 $ 8,934 $ 2,093,405 Underwriting Ratios Loss ratio 64.6 % 67.8 % 4.4 % 55.8 % 78.0 % 56.7 % Acquisition expense ratio 16.7 % 18.9 % 7.6 % 16.0 % 18.9 % 16.1 % Other operating expense ratio 15.4 % 7.5 % 15.1 % 12.5 % 9.9 % 12.4 % Combined ratio 96.7 % 94.2 % 27.1 % 84.3 % 106.8 % 85.2 % Goodwill and intangible assets $ 256,434 $ 183,523 $ 505,026 $ 944,983 $ — $ 944,983 Total investable assets $ 27,442,153 $ — $ 27,442,153 Total assets 45,100,945 — 45,100,945 Total liabilities 31,545,816 — 31,545,816 (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, 2020 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 4,688,562 $ 3,472,086 $ 1,473,999 $ 9,632,691 $ 728,546 $ 10,088,068 Premiums ceded (1,525,655) (1,014,716) (194,149) (2,732,564) (190,957) (2,650,352) Net premiums written 3,162,907 2,457,370 1,279,850 6,900,127 537,589 7,437,716 Change in unearned premiums (291,487) (295,141) 118,085 (468,543) 22,762 (445,781) Net premiums earned 2,871,420 2,162,229 1,397,935 6,431,584 560,351 6,991,935 Other underwriting income (31) 4,454 20,316 24,739 2,045 26,784 Losses and loss adjustment expenses (2,092,453) (1,628,320) (528,344) (4,249,117) (440,482) (4,689,599) Acquisition expenses, net (418,483) (354,048) (134,240) (906,771) (98,071) (1,004,842) Other operating expenses (489,153) (168,011) (162,202) (819,366) (55,810) (875,176) Underwriting income (loss) $ (128,700) $ 16,304 $ 593,465 481,069 (31,967) 449,102 Net investment income 401,908 117,700 519,608 Net realized gains (losses) 813,781 9,679 823,460 Equity in net income (loss) of investments accounted for using the equity method 146,693 — 146,693 Other income (loss) 29 — 29 Corporate expenses (68,492) — (68,492) Transaction costs and other (9,456) (4,040) (13,496) Amortization of intangible assets (69,031) — (69,031) Interest expense (120,214) (23,242) (143,456) Net foreign exchange gains (losses) (80,161) (3,473) (83,634) Income (loss) before income taxes and income (loss) from operating affiliates 1,496,126 64,657 1,560,783 Income tax (expense) benefit (111,812) (26) (111,838) Income (loss) from operating affiliates 16,766 — 16,766 Net income (loss) 1,401,080 64,631 1,465,711 Amounts attributable to redeemable noncontrolling interests (2,997) (4,117) (7,114) Amounts attributable to nonredeemable noncontrolling interests — (53,076) (53,076) Net income (loss) available to Arch 1,398,083 7,438 1,405,521 Preferred dividends (41,612) — (41,612) Net income (loss) available to Arch common shareholders $ 1,356,471 $ 7,438 $ 1,363,909 Underwriting Ratios Loss ratio 72.9 % 75.3 % 37.8 % 66.1 % 78.6 % 67.1 % Acquisition expense ratio 14.6 % 16.4 % 9.6 % 14.1 % 17.5 % 14.4 % Other operating expense ratio 17.0 % 7.8 % 11.6 % 12.7 % 10.0 % 12.5 % Combined ratio 104.5 % 99.5 % 59.0 % 92.9 % 106.1 % 94.0 % Goodwill and intangible assets $ 280,978 $ 18,963 $ 385,272 $ 685,213 $ 7,650 $ 692,863 Total investable assets $ 26,856,295 $ 2,657,612 $ 29,513,907 Total assets 39,791,983 3,490,314 43,282,297 Total liabilities 26,789,149 2,505,707 29,294,856 (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, 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 — 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, net (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) 348,037 15,161 363,198 Equity in net income (loss) of investments accounted for using the equity method 123,672 — 123,672 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 and income (loss) from operating affiliates 1,785,204 61,673 1,846,877 Income tax benefit (155,790) (20) (155,810) Income (loss) from operating affiliates 2,233 — 2,233 Net income 1,631,647 61,653 1,693,300 Amounts 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) 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
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, 2021 2020 2019 Net premiums earned (1) Professional Lines (2) $ 942,817 $ 655,872 $ 499,224 Property, energy, marine and aviation 702,693 517,247 298,966 Programs 506,867 432,854 414,103 Construction and national accounts 381,306 387,934 325,687 Excess and surplus casualty (3) 318,027 270,620 200,615 Travel, accident and health 255,590 190,944 305,085 Lenders products 153,958 114,687 66,079 Other (4) 365,210 301,262 287,321 Total $ 3,626,468 $ 2,871,420 $ 2,397,080 Net premiums written by underwriting location (1) United States $ 2,813,039 $ 2,158,415 $ 1,983,476 Europe 1,125,192 856,572 559,214 Other 209,962 147,920 99,036 Total $ 4,148,193 $ 3,162,907 $ 2,641,726 (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, 2021 2020 2019 Net premiums earned (1) Property excluding property catastrophe $ 836,573 $ 562,208 $ 362,841 Other Specialty (2) 818,801 626,409 478,517 Casualty (3) 666,754 549,056 429,288 Property catastrophe 280,738 237,736 90,934 Marine and aviation 152,955 109,624 48,274 Other (4) 84,622 77,196 56,535 Total $ 2,840,443 $ 2,162,229 $ 1,466,389 Net premiums written by underwriting location (1) United States $ 828,504 $ 687,622 $ 529,943 Bermuda 1,557,294 1,001,990 578,618 Europe and other 868,576 767,758 494,162 Total $ 3,254,374 $ 2,457,370 $ 1,602,723 (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, 2021 2020 2019 Net premiums earned by underwriting location United States $ 970,507 $ 1,158,563 $ 1,134,849 Other 312,912 239,372 231,491 Total $ 1,283,419 $ 1,397,935 $ 1,366,340 Net premiums written by underwriting location United States $ 914,477 $ 1,021,950 $ 1,032,868 Other 346,591 257,900 228,888 Total $ 1,261,068 $ 1,279,850 $ 1,261,756 OTHER SEGMENT Year Ended December 31, 2021 2020 2019 Net premiums earned (1) Casualty (2) $ 138,551 $ 245,272 $ 246,894 Other specialty (3) 118,356 186,717 185,547 Property catastrophe 15,235 23,037 13,399 Property excluding property catastrophe 6,578 1,130 3,503 Marine and aviation 190 429 — Other (4) 53,058 103,766 107,346 Total $ 331,968 $ 560,351 $ 556,689 Net premiums written by underwriting location (1) United States $ 63,403 $ 115,471 $ 127,176 Europe 91,499 $ 97,753 $ 52,065 Bermuda 199,800 $ 324,365 $ 353,621 Total $ 354,702 $ 537,589 $ 532,862 (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, US programs and other.

Reserve for Losses and Loss A_2

Reserve for Losses and Loss Adjustment Expenses (Tables)	12 Months Ended
	Dec. 31, 2021
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, 2021 2020 2019 Reserve for losses and loss adjustment expenses at beginning of year $ 16,513,929 $ 13,891,842 $ 11,853,297 Unpaid losses and loss adjustment expenses recoverable 4,314,855 4,082,650 2,814,291 Net reserve for losses and loss adjustment expenses at beginning of year 12,199,074 9,809,192 9,039,006 Net incurred losses and loss adjustment expenses relating to losses occurring in: Current year 4,940,987 4,851,051 3,297,037 Prior years (356,184) (161,452) (163,585) Total net incurred losses and loss adjustment expenses 4,584,803 4,689,599 3,133,452 Net losses and loss adjustment expense reserves of acquired business (1) 104,176 — 209,486 Retroactive reinsurance transactions (2) (444,147) 182,210 (225,500) Impact of deconsolidation of Somers (3) (1,460,611) — — Foreign exchange (gains) losses and other 1,181 179,190 36,003 Net paid losses and loss adjustment expenses relating to losses occurring in: Current year (734,846) (661,529) (621,202) Prior years (2,091,705) (1,999,588) (1,762,053) Total net paid losses and loss adjustment expenses (2,826,551) (2,661,117) (2,383,255) Net reserve for losses and loss adjustment expenses at end of year 12,157,925 12,199,074 9,809,192 Unpaid losses and loss adjustment expenses recoverable 5,599,231 4,314,855 4,082,650 Reserve for losses and loss adjustment expenses at end of year $ 17,757,156 $ 16,513,929 $ 13,891,842 ( 1) Represents activity related to the Company’s acquisitions in the 2021 and the 2019 period. See Note 2 . (2) See ‘Retroactive Reinsurance Transactions’ section. (3) See note 12

Short Duration Contracts (Table

Short Duration Contracts (Tables)	12 Months Ended
	Dec. 31, 2021
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, 2021: December 31, 2021 Net outstanding liabilities Insurance Property, energy, marine and aviation $ 586,885 Third party occurrence business 2,885,557 Third party claims-made business 1,613,425 Multi-line and other specialty 1,125,841 Reinsurance Casualty 2,106,507 Property catastrophe 486,248 Property excluding property catastrophe 724,034 Marine and aviation 245,881 Other specialty 981,805 Mortgage U.S. primary 688,688 Other short duration lines not included in disclosures 441,459 Total for short duration lines 11,886,330 Unpaid losses and loss adjustment expenses recoverable Insurance Property, energy, marine and aviation 354,432 Third party occurrence business 1,537,549 Third party claims-made business 921,086 Multi-line and other specialty 199,485 Reinsurance Casualty 592,879 Property catastrophe 484,598 Property excluding property catastrophe 118,939 Marine and aviation 111,298 Other specialty 373,292 Mortgage U.S. primary 48,259 Other short duration lines not included in disclosures (1) 887,457 Intercompany eliminations (4,146) Total for short duration lines 5,625,128 Lines other than short duration 76,240 Discounting (55,575) Unallocated claims adjustment expenses 225,033 245,698 Total gross reserves for losses and loss adjustment expenses $ 17,757,156 (1) Includes unpaid loss and loss adjustment expenses recoverable of $390.1 million related to the loss portfolio transfer reinsurance agreements.
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, 2021 Total of IBNR liabilities plus expected development on reported claims Cumulative Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2012 $ 233,149 $ 232,498 $ 205,776 $ 199,469 $ 197,005 $ 192,993 $ 190,770 $ 178,616 $ 178,250 $ 178,343 $ 627 4,245 2013 159,102 156,785 149,199 143,400 134,952 133,869 128,624 127,290 126,276 25 4,243 2014 148,368 145,957 147,465 136,201 132,307 134,329 135,032 134,942 3,098 3,884 2015 112,409 109,865 103,995 102,515 97,852 91,830 91,892 3,804 4,536 2016 104,449 101,306 105,657 100,471 96,437 92,553 874 6,160 2017 280,715 246,291 235,951 230,439 231,228 8,248 6,426 2018 180,981 186,030 173,693 170,057 9,136 5,020 2019 179,056 178,564 165,477 6,667 5,080 2020 359,394 329,362 66,698 4,186 2021 426,870 158,163 2,951 Total $ 1,947,000 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 $ 20,638 $ 93,394 $ 138,977 $ 161,831 $ 167,540 $ 179,945 $ 181,307 $ 173,184 $ 174,032 $ 174,384 2013 32,292 84,936 110,808 120,111 122,244 125,475 123,356 124,688 124,841 2014 25,881 53,751 77,892 84,195 87,812 98,553 115,383 122,296 2015 23,580 64,953 76,338 86,253 87,926 86,246 87,316 2016 24,828 83,552 98,683 97,506 95,002 91,241 2017 30,228 139,867 195,532 211,708 215,895 2018 30,026 102,285 134,858 142,838 2019 26,130 105,380 133,911 2020 55,619 194,487 2021 90,423 Total 1,377,632 All outstanding liabilities before 2012, net of reinsurance 17,517 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 586,885 Third party occurrence business ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2021 Total of IBNR liabilities plus expected development on reported claims Cumulative Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2012 $ 241,368 $ 263,451 $ 269,204 $ 272,004 $ 258,371 $ 253,758 $ 243,863 $ 244,448 $ 242,332 $ 239,075 $ 43,924 65,731 2013 283,228 297,225 307,152 302,165 282,122 274,717 272,849 269,754 270,558 54,640 67,113 2014 330,015 336,019 338,890 343,113 339,701 344,197 342,934 343,569 66,498 75,904 2015 359,058 391,884 398,908 392,143 391,455 382,722 386,801 91,081 78,785 2016 389,832 394,485 406,082 399,571 374,896 367,818 115,303 79,005 2017 417,377 417,941 422,624 412,512 407,115 145,130 84,692 2018 430,415 453,190 450,937 451,459 189,965 77,700 2019 456,353 487,547 481,045 253,849 84,895 2020 607,249 616,910 428,750 89,560 2021 622,713 543,386 65,477 Total $ 4,187,063 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 $ 6,984 $ 30,915 $ 58,650 $ 83,637 $ 108,660 $ 130,098 $ 143,885 $ 155,085 $ 163,016 $ 168,119 2013 6,857 29,265 71,449 101,293 122,288 149,292 164,403 174,946 184,800 2014 9,228 40,346 71,624 112,702 162,123 191,305 211,643 224,101 2015 11,139 44,605 88,515 139,492 181,704 211,715 227,697 2016 11,709 41,979 87,616 136,870 164,662 194,773 2017 13,408 52,356 99,874 135,111 165,606 2018 17,025 63,848 115,137 154,248 2019 18,431 73,222 121,859 2020 24,509 76,743 2021 26,301 Total 1,544,247 All outstanding liabilities before 2012, net of reinsurance 242,741 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 2,885,557 Third party claims-made business ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2021 Total of IBNR liabilities plus expected development on reported claims Cumulative Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2012 $ 317,654 $ 320,207 $ 318,453 $ 313,907 $ 291,316 $ 275,665 $ 277,683 $ 285,163 $ 285,527 $ 286,118 $ 11,570 15,576 2013 301,956 320,659 324,442 320,524 294,674 291,205 281,996 271,501 273,948 11,739 15,696 2014 264,537 279,846 299,104 279,043 282,058 298,017 292,247 288,318 22,336 15,676 2015 258,989 277,615 276,492 260,063 255,432 252,478 267,925 20,617 14,724 2016 275,394 291,645 308,453 314,747 322,042 327,230 42,509 15,749 2017 271,088 286,565 312,554 308,917 323,854 60,718 16,404 2018 273,521 315,085 320,653 337,083 85,411 15,854 2019 290,217 318,469 318,498 119,673 12,982 2020 384,852 414,580 240,888 10,049 2021 516,420 435,910 8,550 Total $ 3,353,974 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 $ 17,718 $ 69,069 $ 121,211 $ 164,724 $ 190,395 $ 209,295 $ 227,389 $ 251,313 $ 255,337 $ 260,173 2013 19,032 87,458 137,963 179,395 198,008 217,132 238,951 245,687 247,078 2014 13,817 63,312 129,712 173,089 208,074 229,958 243,791 249,960 2015 9,066 52,046 100,089 126,499 174,161 193,186 216,986 2016 10,568 68,226 127,286 158,230 205,596 242,431 2017 9,306 67,669 113,208 143,340 196,125 2018 12,287 68,424 118,361 158,709 2019 12,418 65,477 122,362 2020 17,161 87,547 2021 23,349 Total 1,804,720 All outstanding liabilities before 2012, net of reinsurance 64,171 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 1,613,425 Multi-line and other specialty ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2021 Total of IBNR liabilities plus expected development on reported claims Cumulative Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2012 $ 254,684 $ 265,479 $ 259,582 $ 257,240 $ 256,379 $ 248,066 $ 248,310 $ 245,205 $ 245,260 $ 243,849 $ 2,057 55,219 2013 266,089 274,285 265,594 265,672 253,554 254,916 250,252 247,443 246,682 3,461 71,613 2014 303,053 327,098 319,706 319,418 318,297 314,300 311,097 310,097 5,770 109,575 2015 335,250 358,587 357,364 365,362 357,123 349,895 347,669 7,201 148,924 2016 409,367 431,760 428,579 416,724 410,610 408,621 11,032 175,261 2017 483,414 502,068 492,166 501,753 505,135 16,867 219,810 2018 513,466 565,717 563,969 566,283 32,467 247,052 2019 568,337 613,673 641,832 63,880 235,824 2020 622,241 572,265 192,056 149,004 2021 637,258 361,237 75,250 Total $ 4,479,691 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 $ 78,523 $ 166,414 $ 190,754 $ 209,916 $ 223,798 $ 232,640 $ 233,862 $ 237,221 $ 240,191 $ 239,928 2013 86,911 151,897 181,721 214,941 226,769 235,801 237,863 238,792 239,831 2014 108,003 197,609 235,079 267,959 282,104 292,638 294,049 295,551 2015 138,393 236,516 278,265 306,313 321,395 327,082 330,872 2016 176,238 305,250 342,345 363,392 379,885 385,890 2017 181,454 343,049 381,419 424,219 446,749 2018 212,316 390,009 443,644 480,852 2019 212,629 386,894 488,094 2020 173,123 311,112 2021 157,346 Total 3,376,225 All outstanding liabilities before 2012, net of reinsurance 22,375 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 1,125,841
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, 2021: 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 19.3 % 43.5 % 19.1 % 6.6 % 1.4 % 2.3 % 3.2 % 0.5 % 0.3 % 0.2 % Third party occurrence business 3.3 % 9.3 % 11.6 % 11.0 % 9.8 % 8.7 % 5.4 % 4.1 % 3.5 % 2.1 % Third party claims-made business 4.4 % 18.0 % 17.8 % 12.3 % 12.7 % 7.9 % 7.0 % 4.3 % 1.0 % 1.7 % Multi-line and other specialty 34.7 % 29.5 % 11.0 % 8.6 % 4.6 % 2.8 % 0.7 % 0.7 % 0.8 % (0.1) %
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, 2021 Total of IBNR liabilities plus expected development on reported claims Cumulative Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2012 $ 143,029 $ 141,202 $ 137,049 $ 125,104 $ 115,131 $ 109,788 $ 118,457 $ 121,721 $ 120,260 $ 119,222 $ 24,441 N/A 2013 166,016 159,257 155,066 148,784 136,717 135,155 131,475 135,762 135,959 30,873 N/A 2014 216,882 222,109 219,355 233,552 230,019 239,765 240,067 236,378 41,077 N/A 2015 223,208 221,922 230,830 238,126 242,180 249,029 252,809 57,345 N/A 2016 215,222 227,534 251,415 266,254 273,266 272,689 54,087 N/A 2017 270,728 257,088 273,166 301,616 313,605 66,450 N/A 2018 281,141 294,820 285,646 290,955 66,572 N/A 2019 336,062 348,015 374,002 120,045 N/A 2020 386,684 374,912 234,251 N/A 2021 445,047 392,885 N/A Total $ 2,815,578 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 $ 1,306 $ 8,486 $ 14,690 $ 25,523 $ 36,562 $ 47,807 $ 59,511 $ 69,877 $ 75,833 $ 79,364 2013 2,480 9,930 23,044 43,069 54,567 63,136 70,803 76,703 81,856 2014 3,920 16,061 40,804 63,441 91,098 114,456 134,529 145,376 2015 4,463 20,275 47,288 71,098 96,835 120,566 138,035 2016 5,739 25,649 51,684 86,798 113,835 132,814 2017 6,429 30,360 64,075 113,307 137,921 2018 7,580 31,218 106,571 129,196 2019 15,815 57,643 96,935 2020 17,730 50,603 2021 14,794 Total 1,006,894 All outstanding liabilities before 2012, net of reinsurance 297,823 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 2,106,507 Property catastrophe ($000’s) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2021 Total of IBNR liabilities plus expected development on reported claims Cumulative Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2012 $ 149,957 $ 122,942 $ 108,590 $ 102,114 $ 99,885 $ 99,071 $ 97,037 $ 97,145 $ 96,531 $ 96,447 $ 105 N/A 2013 67,257 47,780 36,401 31,902 29,345 28,617 27,727 27,865 27,657 (138) N/A 2014 45,159 30,877 25,296 22,412 20,652 19,945 19,841 19,615 (10) N/A 2015 33,579 18,075 11,580 5,585 3,775 3,130 2,920 67 N/A 2016 25,641 18,719 14,575 10,772 8,362 7,426 881 N/A 2017 87,504 54,768 50,553 36,846 25,121 (712) N/A 2018 77,868 60,418 41,642 27,657 4,783 N/A 2019 38,570 24,808 23,534 4,576 N/A 2020 267,750 334,185 40,561 N/A 2021 316,197 61,821 N/A Total $ 880,759 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 $ 25,850 $ 70,832 $ 83,822 $ 90,727 $ 92,886 $ 94,015 $ 94,625 $ 95,312 $ 95,414 $ 95,606 2013 12,200 19,201 24,038 25,894 27,652 27,891 27,892 28,597 28,346 2014 13,622 19,939 18,402 19,231 18,821 19,013 19,154 19,241 2015 (3,152) (2,518) 1,786 2,050 1,616 1,705 1,781 2016 (6,722) 2,521 2,796 4,082 3,312 3,668 2017 30,704 32,228 37,791 27,797 14,969 2018 27,497 12,506 24,259 (4,612) 2019 3,834 12,680 18,134 2020 53,275 155,063 2021 64,764 Total 396,960 All outstanding liabilities before 2012, net of reinsurance 2,449 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 486,248 Property excluding property catastrophe ($000’s) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2021 Total of IBNR liabilities plus expected development on reported claims Cumulative Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2012 $ 156,162 $ 121,808 $ 123,689 $ 119,124 $ 114,699 $ 112,477 $ 111,001 $ 108,436 $ 102,994 $ 103,367 $ 508 N/A 2013 115,473 76,905 70,558 66,208 64,486 63,702 62,504 63,269 62,782 384 N/A 2014 143,464 117,448 99,328 90,710 88,438 84,130 82,408 80,940 923 N/A 2015 215,095 189,109 184,774 189,045 188,343 177,281 173,659 8,482 N/A 2016 177,039 146,307 138,375 136,868 140,681 137,579 12,700 N/A 2017 271,713 253,859 240,749 233,153 216,358 13,045 N/A 2018 225,638 242,069 238,052 214,942 11,593 N/A 2019 216,653 206,997 196,840 17,777 N/A 2020 371,752 343,078 51,075 N/A 2021 552,066 255,343 N/A Total $ 2,081,611 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 $ 26,153 $ 78,080 $ 93,198 $ 101,868 $ 102,844 $ 103,480 $ 102,658 $ 102,598 $ 102,504 $ 102,525 2013 25,993 42,737 49,816 52,997 53,796 55,676 61,183 62,113 62,139 2014 23,496 62,800 71,692 76,634 78,274 78,657 78,567 78,268 2015 75,622 119,237 149,814 160,848 166,025 159,675 159,925 2016 33,400 95,616 99,428 104,984 112,838 115,102 2017 27,569 125,768 158,066 166,087 181,628 2018 30,047 108,863 153,944 169,054 2019 43,230 124,222 150,931 2020 101,969 208,888 2021 136,712 Total 1,365,172 All outstanding liabilities before 2012, net of reinsurance 7,595 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 724,034 Marine and aviation ($000’s) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2021 Total of IBNR liabilities plus expected development on reported claims Cumulative Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2012 $ 58,992 $ 58,868 $ 55,053 $ 52,286 $ 51,079 $ 49,727 $ 46,046 $ 43,028 $ 41,182 $ 40,016 $ 1,005 N/A 2013 38,881 37,668 36,653 35,251 35,157 34,415 33,970 30,316 27,605 2,394 N/A 2014 30,958 29,159 27,373 25,674 23,677 23,310 22,031 21,984 4,909 N/A 2015 33,646 37,505 31,790 31,736 30,789 28,464 27,680 3,867 N/A 2016 27,351 22,747 23,567 19,273 16,969 15,019 6,708 N/A 2017 28,800 26,346 23,830 20,827 19,903 6,387 N/A 2018 28,017 26,084 24,615 24,756 6,452 N/A 2019 48,929 55,307 60,983 15,112 N/A 2020 83,457 76,598 36,671 N/A 2021 111,046 89,459 N/A Total $ 425,590 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 $ 2,658 $ 11,433 $ 27,528 $ 33,313 $ 35,055 $ 36,257 $ 37,746 $ 38,038 $ 38,131 $ 38,116 2013 4,945 13,731 18,415 21,388 22,398 23,672 24,049 23,786 23,753 2014 4,177 7,985 11,590 12,469 14,645 15,080 15,956 16,036 2015 7 13,418 19,023 20,861 22,629 22,306 22,445 2016 (7,333) (1,687) 521 3,261 5,864 6,767 2017 1,660 6,541 9,367 11,030 11,632 2018 2,005 6,968 11,236 13,585 2019 10,756 21,580 29,068 2020 9,220 26,519 2021 8,643 Total 196,564 All outstanding liabilities before 2012, net of reinsurance 16,855 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 245,881 Other specialty ($000’s) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2021 Total of IBNR liabilities plus expected development on reported claims Cumulative Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2012 $ 222,558 $ 211,839 $ 202,046 $ 196,138 $ 193,882 $ 196,539 $ 194,726 $ 189,193 $ 181,246 $ 179,364 $ 2,392 N/A 2013 252,744 226,032 216,250 212,721 213,614 211,261 210,825 204,894 201,830 6,409 N/A 2014 274,826 256,332 258,114 251,474 246,393 248,083 243,652 237,478 7,857 N/A 2015 209,764 201,057 199,468 196,521 196,840 193,626 182,162 8,549 N/A 2016 223,191 220,661 215,078 209,564 215,614 210,344 13,182 N/A 2017 269,254 258,419 247,203 245,505 241,598 30,855 N/A 2018 320,538 316,231 308,190 324,536 40,807 N/A 2019 360,854 341,409 326,168 51,165 N/A 2020 533,861 460,084 102,130 N/A 2021 582,446 300,667 N/A Total $ 2,946,010 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 $ 45,663 $ 121,679 $ 144,429 $ 155,445 $ 163,160 $ 167,164 $ 171,519 $ 173,305 $ 173,606 $ 173,494 2013 57,317 119,445 145,521 161,608 171,189 176,483 183,772 184,111 186,956 2014 68,869 146,652 182,184 195,433 201,974 212,991 215,597 219,060 2015 54,359 114,382 138,350 145,419 154,369 162,314 164,471 2016 65,055 138,648 162,661 174,403 186,247 189,411 2017 73,366 164,829 192,274 199,051 205,998 2018 71,167 201,732 231,358 245,330 2019 79,718 158,132 216,647 2020 97,617 243,980 2021 126,635 Total 1,971,982 All outstanding liabilities before 2012, net of reinsurance 7,777 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 981,805
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, 2021: 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 2.5 % 7.3 % 11.6 % 11.3 % 9.6 % 8.4 % 7.7 % 5.9 % 4.4 % 3.0 % Property catastrophe 21.6 % 30.0 % 32.8 % (14.2) % (11.6) % 2.2 % 1.0 % 1.2 % (0.4) % 0.2 % Property excluding property catastrophe 26.7 % 38.9 % 13.3 % 5.8 % 3.4 % 0.4 % 2.0 % 0.4 % — % — % Marine and aviation 4.9 % 26.9 % 19.0 % 10.3 % 7.4 % 2.9 % 2.4 % — % 0.1 % — % Other specialty 26.3 % 34.2 % 12.9 % 5.2 % 4.2 % 3.1 % 2.1 % 0.9 % 0.8 % (0.1) %
Mortgage
Claims Development [Line Items]
Claims development tables	The following table presents information on the mortgage segment’s short-duration insurance contracts: U.S. primary mortgage insurance ($000’s except claim count) Incurred losses and allocated loss adjustment expenses, net of reinsurance December 31, 2021 Total of IBNR liabilities plus expected development on reported claims Cumulative Year ended December 31, Accident year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2012 $ 520,835 $ 480,592 $ 475,317 $ 469,238 $ 467,296 $ 459,467 $ 458,065 $ 456,286 $ 456,331 $ 456,362 1 15,080 2013 469,311 419,668 411,793 405,809 395,693 393,149 390,987 391,062 391,324 1 9,468 2014 316,095 297,151 279,434 266,027 265,992 261,091 262,682 262,829 4 6,299 2015 222,790 197,238 198,001 194,677 189,235 190,913 190,560 1 4,554 2016 183,556 170,532 148,715 140,608 142,392 141,657 1 3,424 2017 179,376 132,220 107,255 108,181 109,242 1 2,474 2018 132,318 96,357 89,120 87,962 60 1,635 2019 108,424 119,253 110,362 181 851 2020 420,003 373,533 2,686 189 2021 144,375 2,246 11 Total $ 2,268,206 Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance 2012 (106,065) 186,605 327,605 395,695 426,024 441,577 448,151 452,348 453,587 453,986 2013 41,447 203,957 308,956 353,189 373,909 382,200 386,853 387,894 387,879 2014 20,099 129,159 201,925 233,879 247,038 254,175 256,285 256,875 2015 16,159 92,431 151,222 171,337 180,321 183,472 184,025 2016 11,462 72,201 113,357 127,286 131,161 131,717 2017 8,622 48,112 78,650 87,317 89,756 2018 3,966 31,478 50,135 55,853 2019 2,899 20,105 29,102 2020 1,040 4,144 2021 469 1,593,806 All outstanding liabilities before 2012, net of reinsurance 14,288 Liabilities for losses and loss adjustment expenses, net of reinsurance $ 688,688
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, 2021: 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 U.S. Primary 2.7 % 34.9 % 25.3 % 10.5 % 4.4 % 2.1 % 0.9 % 0.5 % 0.1 % 0.1 %

Allowance for Expected Credit_2

Allowance for Expected Credit Losses (Tables)	12 Months Ended
	Dec. 31, 2021
Credit Loss [Abstract]
Allowance for credit losses on premiums receivable	Premiums Receivable The following table provides a roll forward of the allowance for expected credit losses of the Company’s premium receivables: Year Ended December 31, 2021 Premium Receivables, Net of Allowance Allowance for Expected Credit Losses Balance at beginning of period $ 2,064,586 $ 37,781 Change for provision of expected credit losses (2) 2,177 Balance at end of period $ 2,633,280 $ 39,958 Year Ended December 31, 2020 Balance at beginning of period $ 1,778,717 $ 21,003 Cumulative effect of accounting change (1) 6,539 Change for provision of expected credit losses (2) 10,239 Balance at end of period $ 2,064,586 $ 37,781 (1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”. (2) Amounts deemed uncollectible are written-off in operating expenses. For the 2021 and 2020 periods, amounts written off totaled $3.8 million and $2.8 million, respectively.
Allowance for credit losses on reinsurance recoverable	The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables: Year Ended December 31, 2021 Reinsurance Recoverables, Net of Allowance Allowance for Expected Credit Losses Balance at beginning of period $ 4,500,802 $ 11,636 Change for provision of expected credit losses 1,594 Balance at end of period $ 5,880,735 $ 13,230 Year Ended December 31, 2020 Balance at beginning of period $ 4,346,816 $ 1,364 Cumulative effect of accounting change (1) 12,010 Change for provision of expected credit losses (1,738) Balance at end of period 4,500,802 $ 11,636 (1) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”.
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, 2021 and 2020: December 31, 2021 2020 Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses $ 5,880,735 $ 4,500,802 % due from carriers with A.M. Best rating of “A-” or better 69.7 % 63.9 % % due from all other rated carriers 0.1 % 0.1 % % due from all other carriers with no A.M. Best rating (1) 30.2 % 36.0 % Largest balance due from any one carrier as % of total shareholders’ equity (2) 6.7 % 1.8 % (1) At December 31, 2021 and 2020 period, over 91% and 94% of such amount is collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively. (2) The 2021 period included impact of deconsolidation of Somers. See note 12.
Allowance for credit losses on contractholder receivables	The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables: Year Ended December 31, 2021 Contractholder Receivables, Net of Allowance Allowance for Expected Credit Losses Balance at beginning of period $ 1,986,924 $ 8,638 Change for provision of expected credit losses (5,201) Balance at end of period $ 1,828,691 $ 3,437 Year Ended December 31, 2020 Balance at beginning of period $ 2,119,460 $ — Cumulative effect of accounting change (1) 6,663 Change for provision of expected credit losses 1,975 Balance at end of period 1,986,924 $ 8,638

Reinsurance (Tables)

Reinsurance (Tables)	12 Months Ended
	Dec. 31, 2021
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, 2021 2020 2019 Premiums Written Direct $ 7,706,832 $ 6,553,910 $ 5,681,523 Assumed 5,045,655 3,534,158 2,457,437 Ceded (3,734,150) (2,650,352) (2,099,893) Net $ 9,018,337 $ 7,437,716 $ 6,039,067 Premiums Earned Direct $ 7,149,794 $ 6,361,451 $ 5,447,829 Assumed 4,333,873 3,213,873 2,337,950 Ceded (3,401,369) (2,583,389) (1,999,281) Net $ 8,082,298 $ 6,991,935 $ 5,786,498 Losses and Loss Adjustment Expenses Direct $ 4,266,758 $ 4,392,392 $ 2,953,072 Assumed 2,826,820 2,204,323 1,602,528 Ceded (2,508,775) (1,907,116) (1,422,148) Net $ 4,584,803 $ 4,689,599 $ 3,133,452
Coverage and retention	The following table summarizes the respective coverages and retentions at December 31, 2021: December 31, 2021 Initial Coverage at Issuance Current Remaining Retention, Net Bellemeade 2017-1 Ltd. (1) $ 368,114 $ 108,368 $ 125,926 Bellemeade 2018-1 Ltd. (2) 374,460 181,136 122,118 Bellemeade 2018-3 Ltd. (3) 506,110 302,563 128,020 Bellemeade 2019-1 Ltd. (4) 341,790 181,324 97,845 Bellemeade 2019-2 Ltd. (5) 621,022 398,316 156,419 Bellemeade 2019-3 Ltd. (6) 700,920 409,859 181,583 Bellemeade 2019-4 Ltd. (7) 577,267 411,954 116,292 Bellemeade 2020-2 Ltd. (8) 449,167 218,877 222,567 Bellemeade 2020-3 Ltd. (9) 451,816 365,141 154,732 Bellemeade 2020-4 Ltd. (10) 337,013 186,065 129,824 Bellemeade 2021-1 Ltd. (11) 643,577 630,163 149,189 Bellemeade 2021-2 Ltd. (12) 616,017 616,017 139,763 Bellemeade 2021-3 Ltd. (13) 639,391 639,391 140,545 Total $ 6,626,664 $ 4,649,174 $ 1,864,823 (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. (8) Issued in September 2020, covering in-force policies issued between January 1, 2020 and May 31, 2020. $423 million was directly funded by Bellemeade 2020-2 Ltd. with an additional $26 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers. (9) Issued in November 2020, covering in-force policies issued between June 1, 2020 and August 31, 2020. $418 million was directly funded by Bellemeade 2020-3 Ltd. with an additional $34 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers. (10) Issued in December 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $321 million was directly funded by Bellemeade 2020-4 Ltd. with an additional $16 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers. (11) Issued in March 2021, covering in-force policies issued between September 1, 2020 and November 30, 2020. $580 million was directly funded by Bellemeade Re 2021-1 Ltd. with an additional $64 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers. (12) Issued in June 2021, covering in-force policies issued between December 1, 2020 and March 31, 2021. $523 million was directly funded by Bellemeade Re 2021-2 Ltd. via insurance-linked notes, with an additional $93 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers. (13) Issued in September 2021, covering in-force policies issued between April 1, 2021 and June 30, 2021. $508 million was directly funded by Bellemeade Re 2021-3 Ltd. via insurance-linked notes, with an additional $131 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.

Investment Information (Tables)

Investment Information (Tables)	12 Months Ended
	Dec. 31, 2021
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 Gross Unrealized Gains Gross Unrealized Losses Allowance for Expected Credit Losses (2) Cost or December 31, 2021 Fixed maturities: Corporate bonds $ 6,553,333 $ 104,170 $ (69,194) $ (2,037) $ 6,520,394 Mortgage backed securities 408,477 2,825 (5,410) (48) 411,110 Municipal bonds 404,666 18,724 (1,409) (2) 387,353 Commercial mortgage backed securities 1,046,484 1,740 (3,117) (6) 1,047,867 U.S. government and government agencies 4,772,764 10,076 (45,967) — 4,808,655 Non-U.S. government securities 2,120,294 54,048 (34,749) (82) 2,101,077 Asset backed securities 2,692,091 6,540 (11,108) (708) 2,697,367 Total 17,998,109 198,123 (170,954) (2,883) 17,973,823 Short-term investments 1,734,716 568 (590) — 1,734,738 Total $ 19,732,825 $ 198,691 $ (171,544) $ (2,883) $ 19,708,561 December 31, 2020 Fixed maturities (1): Corporate bonds $ 7,856,571 $ 414,247 $ (34,388) $ (896) $ 7,477,608 Mortgage backed securities 630,001 8,939 (5,028) (278) 626,368 Municipal bonds 494,522 27,291 (3,835) (11) 471,077 Commercial mortgage backed securities 389,900 8,722 (2,954) (122) 384,254 U.S. government and government agencies 5,557,077 22,612 (12,611) — 5,547,076 Non-U.S. government securities 2,433,733 153,891 (8,060) — 2,287,902 Asset backed securities 1,634,804 19,225 (10,715) (1,090) 1,627,384 Total 18,996,608 654,927 (77,591) (2,397) 18,421,669 Short-term investments 1,924,922 2,693 (2,063) — 1,924,292 Total $ 20,921,530 $ 657,620 $ (79,654) $ (2,397) $ 20,345,961 (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.” In 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions.
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 Gross Unrealized Losses Estimated Fair Gross Unrealized Losses Estimated Fair Gross Unrealized Losses December 31, 2021 Fixed maturities: Corporate bonds $ 3,639,582 $ (63,938) $ 98,867 $ (5,256) $ 3,738,449 $ (69,194) Mortgage backed securities 222,176 (3,545) 46,809 (1,865) 268,985 (5,410) Municipal bonds 26,665 (385) 16,361 (1,024) 43,026 (1,409) Commercial mortgage backed securities 675,603 (2,805) 5,908 (312) 681,511 (3,117) U.S. government and government agencies 4,211,621 (44,180) 33,373 (1,787) 4,244,994 (45,967) Non-U.S. government securities 1,511,301 (31,983) 62,957 (2,766) 1,574,258 (34,749) Asset backed securities 1,667,002 (9,853) 33,082 (1,255) 1,700,084 (11,108) Total 11,953,950 (156,689) 297,357 (14,265) 12,251,307 (170,954) Short-term investments 284,733 (590) — — 284,733 (590) Total $ 12,238,683 $ (157,279) $ 297,357 $ (14,265) $ 12,536,040 $ (171,544) December 31, 2020 Fixed maturities (1): Corporate bonds $ 747,442 $ (33,086) $ 3,934 $ (1,302) $ 751,376 $ (34,388) Mortgage backed securities 284,619 (4,788) 3,637 (240) 288,256 (5,028) Municipal bonds 67,937 (3,835) — — 67,937 (3,835) Commercial mortgage backed securities 126,624 (2,916) 2,655 (38) 129,279 (2,954) U.S. government and government agencies 1,285,907 (12,611) — — 1,285,907 (12,611) Non-U.S. government securities 543,844 (7,658) 2,441 (402) 546,285 (8,060) Asset backed securities 634,470 (9,110) 57,737 (1,605) 692,207 (10,715) Total 3,690,843 (74,004) 70,404 (3,587) 3,761,247 (77,591) Short-term investments 97,920 (2,063) — — 97,920 (2,063) Total $ 3,788,763 $ (76,067) $ 70,404 $ (3,587) $ 3,859,167 $ (79,654) (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.” In 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions.
Contractual maturities of the Company's fixed maturities and fixed maturities pledged under securities lending arrangements	December 31, 2021 December 31, 2020 Maturity Estimated Fair Value Amortized Cost Estimated Fair Value Amortized Cost Due in one year or less $ 300,889 $ 299,772 $ 348,200 $ 339,951 Due after one year through five years 8,355,255 8,339,387 10,629,959 10,340,819 Due after five years through 10 years 4,689,155 4,684,393 4,881,564 4,654,754 Due after 10 years 505,758 493,927 482,180 448,139 13,851,057 13,817,479 16,341,903 15,783,663 Mortgage backed securities 408,477 411,110 630,001 626,368 Commercial mortgage backed securities 1,046,484 1,047,867 389,900 384,254 Asset backed securities 2,692,091 2,697,367 1,634,804 1,627,384 Total (1) $ 17,998,109 $ 17,973,823 $ 18,996,608 $ 18,421,669 (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.” In 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions.
Summary of securities lending transactions accounted for as secured borrowings, with significant investment categories	The carrying value of collateral held under the Company’s securities lending transactions by significant investment category and remaining contractual maturity of the underlying agreements was as follows at December 31, 2020 (no balances at December 31, 2021 due to the termination of the program): Remaining Contractual Maturity of the Agreements Overnight and Continuous Less than 30 Days 30-90 Days 90 Days or More Total December 31, 2020 U.S. government and government agencies $ 142,317 $ — $ 139,290 $ — $ 281,607 Corporate bonds 3,021 — — — 3,021 Equity securities 16,461 — — — 16,461 Total $ 161,799 $ — $ 139,290 $ — $ 301,089 Gross amount of recognized liabilities for securities lending in offsetting disclosure in Note 11 — Amounts related to securities lending not included in offsetting disclosure in Note 11 $ 301,089
Components of net investment income	The components of net investment income were derived from the following sources: Year Ended December 31, 2021 2020 2019 Fixed maturities $ 330,061 $ 412,481 $ 505,399 Term loans 34,843 84,149 98,949 Equity securities 42,396 28,958 15,857 Short-term investments 6,928 10,840 15,820 Other (1) 62,895 72,395 80,618 Gross investment income 477,123 608,823 716,643 Investment expenses (88,005) (89,215) (88,905) Net investment income $ 389,118 $ 519,608 $ 627,738 (1) Includes income distributions from investment funds and other items
Summary of net realized gains (losses)	Net realized gains (losses) were as follows: Year Ended December 31, 2021 2020 2019 Available for sale securities: Gross gains on investment sales $ 313,886 $ 595,941 $ 235,655 Gross losses on investment sales (156,791) (117,282) (104,612) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities 7,953 15,881 41,910 Other investments 116,781 13,656 (35,734) Equity securities 13,028 14,629 15,869 Short-term investments 601 2,279 3,801 Equity securities, at fair value : Net realized gains (losses) on securities sold 122,606 26,849 11,313 Net unrealized gains (losses) on equity securities still held at reporting date 48,746 102,394 97,768 Allowance for credit losses: Investments related (2,100) (3,597) — Underwriting related 1,062 (10,007) — Net impairment losses — (533) (3,165) Derivative instruments (1) (32,390) 179,675 119,741 Other (2) (53,537) 3,575 (19,348) Net realized gains (losses) $ 379,845 $ 823,460 $ 363,198 (1) See Note 11 for information on the Company’s derivative instruments. (2) 2021 periods reflected $33.1 million of losses related to the Company’s deconsolidation of Somers.
Other investments	The following table summarizes the Company’s other investments and other investable assets: December 31, 2021 2020 Fixed maturities $ 416,698 $ 843,354 Other investments 1,432,553 2,331,885 Short-term investments 97,806 557,008 Equity securities 26,493 92,549 Investments accounted for using the fair value option 1,973,550 3,824,796 Other investable assets (1) — 500,000 Total other investments $ 1,973,550 $ 4,324,796 (1) Participation interests in a receivable of a reverse repurchase agreement. The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy: December 31, 2021 2020 Lending 536,345 572,636 Term loan investments 484,950 1,231,731 Investment grade fixed income 147,810 138,646 Private equity 91,126 48,750 Energy 81,692 65,813 Credit related funds 70,278 90,780 Infrastructure 20,352 165,516 Real estate — 18,013 Total $ 1,432,553 $ 2,331,885
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, 2021 2020 Credit related funds $ 1,022,334 $ 740,060 Private equity 436,042 235,289 Real estate 396,395 258,518 Equities 395,090 343,058 Lending 376,649 179,629 Infrastructure 230,070 175,882 Energy 119,141 115,453 Fixed income 101,890 — Total $ 3,077,611 $ 2,047,889 A summary of financial information for the Company’s investment funds and operating affiliates accounted for using the equity method is as follows: December 31, 2021 2020 Invested assets $ 58,508,009 $ 44,131,377 Total assets 69,648,905 49,078,464 Total liabilities 17,944,325 6,054,189 Net assets $ 51,704,580 $ 43,024,275 Year Ended December 31, 2021 2020 2019 Total revenues $ 11,785,949 $ 5,762,098 $ 164,669 Total expenses 3,238,606 1,656,029 528,762 Net income (loss) $ 8,547,343 $ 4,106,069 $ (364,093)
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, 2021 2020 Investments accounted for using the equity method (1) $ 3,077,611 $ 2,047,889 Investments accounted for using the fair value option (2) 170,595 184,720 Total $ 3,248,206 $ 2,232,609 (1) Aggregate unfunded commitments were $2.6 billion at December 31, 2021, compared to $1.8 billion at December 31, 2020.
Roll forward of the allowance for expected credit losses of securities classified as available for sale	The following table provides a roll forward of the allowance for expected credit losses of the Company’s securities classified as available for sale: Year Ended December 31, 2021 Structured Securities (1) Municipal Corporate Total Balance at beginning of period $ 1,490 $ 11 $ 896 $ 2,397 Additions for current-period provision for expected credit losses 602 — 2,858 3,460 Additions (reductions) for previously recognized expected credit losses (847) (9) (320) (1,176) Reductions due to disposals (3) (443) — (1,355) (1,798) Balance at end of period $ 802 $ 2 $ 2,079 $ 2,883 Year Ended December 31, 2020 Balance at beginning of period $ — $ — $ — $ — Cumulative effect of accounting change (2) 517 — 117 634 Additions for current-period provision for expected credit losses 2,942 67 7,644 10,653 Additions (reductions) for previously recognized expected credit losses (1,398) 6 (5,638) (7,030) Reductions due to disposals (571) (62) (1,227) (1,860) Balance at end of period $ 1,490 $ 11 $ 896 $ 2,397 (1) Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities. (2) Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”. (3) Reduction for the 2021 periods primarily related to the Company’s deconsolidation of Somers.
Summary of restricted assets	The following table details the value of the Company’s restricted assets: December 31, 2021 2020 Assets used for collateral or guarantees: Affiliated transactions $ 4,223,955 $ 4,643,334 Third party agreements 2,721,160 3,083,324 Deposits with U.S. regulatory authorities 798,100 827,552 Deposits with non-U.S. regulatory authorities 506,517 179,099 Total restricted assets (1) $ 8,249,732 $ 8,733,309 (1) 2020 balances included $1.036 billion related to Somers. See note 12 .
Reconciliation of cash and restricted cash	The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets: December 31, 2021 2020 2019 Cash $ 858,668 $ 906,448 $ 726,230 Restricted cash (included in ‘other assets’) 456,103 384,096 177,468 Cash and restricted cash $ 1,314,771 $ 1,290,544 $ 903,698

Fair Value (Tables)

Fair Value (Tables)	12 Months Ended
	Dec. 31, 2021
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, 2021: Fair Value Measurement Using: Estimated Quoted Prices in Active Markets for Identical Assets Significant Other Observable Inputs Significant Unobservable Inputs Assets measured at fair value: Available for sale securities: Fixed maturities: Corporate bonds $ 6,553,333 $ — $ 6,553,320 $ 13 Mortgage backed securities 408,477 — 408,477 — Municipal bonds 404,666 — 404,666 — Commercial mortgage backed securities 1,046,484 — 1,046,484 — U.S. government and government agencies 4,772,764 4,744,517 28,247 — Non-U.S. government securities 2,120,294 — 2,120,294 — Asset backed securities 2,692,091 — 2,688,744 3,347 Total 17,998,109 4,744,517 13,250,232 3,360 Short-term investments 1,734,716 1,052,822 681,894 — Equity securities, at fair value 1,804,170 1,762,864 38,388 2,918 Derivative instruments (3) 127,121 — 127,121 — Residential mortgage loans 49,847 — 49,847 — Fair value option: Corporate bonds 388,546 — 388,546 — Non-U.S. government bonds 23,785 — 23,785 — Asset backed securities 4,367 — 4,367 — Short-term investments 97,806 528 97,278 — Equity securities 26,493 21,745 — 4,748 Other investments 310,798 20,352 262,465 27,981 Other investments measured at net asset value (1) 1,121,755 Total 1,973,550 42,625 776,441 32,729 Total assets measured at fair value $ 23,687,513 $ 7,602,828 $ 14,923,923 $ 39,007 Liabilities measured at fair value: Contingent consideration liabilities $ (16,960) $ — $ — $ (16,960) Securities sold but not yet purchased (2) — — — — Derivative instruments (3) (54,224) — (54,224) — Total liabilities measured at fair value $ (71,184) $ — $ (54,224) $ (16,960) (1) 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. (2) 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. (3) See Note 11. The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2020: Fair Value Measurement Using: Estimated Quoted Prices in Active Markets for Identical Assets Significant Other Observable Inputs Significant Unobservable Inputs Assets measured at fair value (1): Available for sale securities: Fixed maturities: Corporate bonds $ 7,856,571 $ — $ 7,856,558 $ 13 Mortgage backed securities 630,001 — 630,001 — Municipal bonds 494,522 — 494,522 — Commercial mortgage backed securities 389,900 — 389,900 — U.S. government and government agencies 5,557,077 5,463,356 93,721 — Non-U.S. government securities 2,433,733 — 2,433,733 — Asset backed securities 1,634,804 — 1,631,378 3,426 Total 18,996,608 5,463,356 13,529,813 3,439 Equity securities, at fair value 1,460,959 1,401,653 17,291 42,015 Short-term investments 1,924,922 1,920,565 4,357 — Derivative instruments (4) 177,383 — 177,383 — Fair value option: Corporate bonds 651,294 — 650,309 985 Non-U.S. government bonds 35,263 — 35,263 — Mortgage backed securities 3,282 — 3,282 — Commercial mortgage backed securities 1,090 — 1,090 — Asset backed securities 152,151 — 152,151 — U.S. government and government agencies 274 164 110 — Short-term investments 557,008 420,131 136,877 — Equity securities 92,549 23,373 188 68,988 Other investments 1,134,229 51,149 1,015,977 67,103 Other investments measured at net asset value (2) 1,197,656 Total 3,824,796 494,817 1,995,247 137,076 Total assets measured at fair value $ 26,384,668 $ 9,280,391 $ 15,724,091 $ 182,530 Liabilities measured at fair value: Contingent consideration liabilities $ (461) $ — $ — $ (461) Securities sold but not yet purchased (3) (21,679) — (21,679) — Derivative instruments (4) (108,705) — (108,705) — Total liabilities measured at fair value $ (130,845) $ — $ (130,384) $ (461) (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 9. (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 11.
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 2021 and 2020: Assets Liabilities Available For Sale Fair Value Option Fair Value Structured Securities (1) Corporate Bonds Corporate Bonds Other Investments Equity Securities Equity Securities Contingent Year Ended December 31, 2021 Balance at beginning of year $ 3,426 $ 13 $ 985 $ 67,103 $ 68,988 $ 42,015 $ (461) Total gains or (losses) (realized/unrealized) Included in earnings (2) (135) — 13 868 4,941 1,958 — Included in other comprehensive income 133 — — — — — — Purchases, issuances, sales and settlements Purchases — — — 13,213 — 5,718 (16,494) Issuances — — — — — — — Sales (3) — — (998) (53,203) (69,181) (46,773) — Settlements (77) — — — — — (5) Transfers in and/or out of Level 3 — — — — — — — Balance at end of year $ 3,347 $ 13 $ — $ 27,981 $ 4,748 $ 2,918 $ (16,960) Year Ended December 31, 2020 Balance at beginning of year $ 5,216 $ 8,851 $ 932 $ 68,817 $ 58,094 $ 55,889 $ (7,998) Total gains or (losses) (realized/unrealized) Included in earnings (2) — (5,865) (13) (314) 10,894 8,214 (72) Included in other comprehensive income (169) 397 — — — — — Purchases, issuances, sales and settlements Purchases — — 66 52,449 — 4,030 — Issuances — — — — — — — Sales — — — (56,833) — (26,118) — Settlements (1,413) (1,462) — — — — 7,609 Transfers in and/or out of Level 3 (208) (1,908) — 2,984 — — — Balance at end of year $ 3,426 $ 13 $ 985 $ 67,103 $ 68,988 $ 42,015 $ (461) (1) Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities. (2) Gains or losses were included in net realized gains (losses). (3) Sales for the 2021 period primarily relates to the Company’s deconsolidation of Somers.

Derivative Instruments (Tables)

Derivative Instruments (Tables)	12 Months Ended
	Dec. 31, 2021
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 December 31, 2021 Futures contracts (2) $ 34,999 $ (9,808) $ 2,826,564 Foreign currency forward contracts (2) 7,734 (11,390) 915,962 TBAs 11,227 — 11,227 Other (2) 73,161 (33,026) 3,736,773 Total $ 127,121 $ (54,224) December 31, 2020 Futures contracts (2) $ 11,046 $ (4,496) $ 3,099,796 Foreign currency forward contracts (2) 52,716 (6,202) 1,656,729 TBAs — — — Other (2) 113,621 (98,007) 5,763,919 Total $ 177,383 $ (108,705) (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.’
Summary of net realized gains (losses) recorded in the consolidated statements of income	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, 2021 2020 2019 Net realized gains (losses): Futures contracts $ (15,262) $ 114,987 $ 114,123 Foreign currency forward contracts (39,755) 49,974 (9,499) TBAs (233) 1,129 463 Other 22,860 13,585 14,654 Total $ (32,390) $ 179,675 $ 119,741

Variable Interest Entity and _2

Variable Interest Entity and Noncontrolling Interests (Tables)	12 Months Ended
	Dec. 31, 2021
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 Somers were reported: December 31, 2020 Assets Investments accounted for using the fair value option (1) $ 1,790,385 Fixed maturities available for sale, at fair value 655,249 Equity securities, at fair value 52,410 Cash 211,451 Accrued investment income 14,679 Premiums receivable 224,377 Reinsurance recoverable on unpaid and paid losses and LAE 286,590 Ceded unearned premiums 122,339 Deferred acquisition costs, net 53,705 Receivable for securities sold 37,423 Goodwill and intangible assets 7,650 Other assets 75,801 Total assets of consolidated VIE $ 3,532,059 Liabilities Reserves for losses and loss adjustment expenses $ 1,519,583 Unearned premiums 407,714 Reinsurance balances payable 63,269 Revolving credit agreement borrowings 155,687 Senior notes 172,689 Payable for securities purchased 25,881 Other liabilities 193,494 Total liabilities of consolidated VIE $ 2,538,317 Redeemable noncontrolling interests $ 52,398 (1) Included in “other investments” on the Company’s balance sheet.
Summary of VIE cash flows	The following table summarizes Somers’ cash flow from operating, investing and financing activities. Year Ended December 31, 2021 2020 2019 Total cash provided by (used for): Operating activities 46,991 181,736 239,284 Investing activities 96,325 258,589 (140,620) Financing activities (2,042) (335,776) (61,433)
Activity in non-redeemable noncontrolling interests	The following table sets forth activity in the non-redeemable noncontrolling interests: December 31, 2021 2020 Balance, beginning of year $ 823,007 $ 762,777 Impact of deconsolidation of Somers (918,874) — Additional paid in capital attributable to noncontrolling interests 22,113 1,334 Repurchases attributable to non-redeemable noncontrolling interests — (2,867) Amounts attributable to noncontrolling interests 78,314 53,076 Other amounts attributable to noncontrolling interests — (375) Other comprehensive (income) loss attributable to noncontrolling interests (4,560) 9,062 Balance, end of year $ — $ 823,007
Activity in redeemable noncontrolling interest	The following table sets forth activity in the redeemable noncontrolling interests: December 31, 2021 2020 2019 Balance, beginning of year $ 58,548 $ 55,404 $ 206,292 Impact of deconsolidation of Somers (48,919) — — Redemption of noncontrolling interests — — (157,709) Accretion of preference share issuance costs — 93 244 Other (396) 3,051 6,577 Balance, end of year $ 9,233 $ 58,548 $ 55,404
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, 2021 2020 2019 Amounts attributable to non-redeemable noncontrolling interests $ (78,314) $ (53,076) $ (40,072) Amounts attributable to redeemable noncontrolling interests (4,299) (7,114) (16,909) Net (income) loss attributable to noncontrolling interests $ (82,613) $ (60,190) $ (56,981)
Total assets and maximum loss exposure of VIE	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 benchmark index for each respective transaction and short term invested trust asset yields. The benchmark index for agreements effective prior to 2021 is based on one-month LIBOR, while the 2021 agreements benchmark index is based on the Secured Overnight Financing Rate (“SOFR”). SOFR is a measure of the cost of borrowing cash overnight, collateralized by U.S. Treasury securities, and is based on directly observable U.S. Treasury-backed repurchase transactions. Dec 31, 2021 Dec 31, 2020 Maximum Exposure to Loss Maximum Exposure to Loss Bellemeade Entities (Issue Date) Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total Bellemeade 2017-1 Ltd. (Oct-17) $ 108,368 $ (159) $ 424 $ 265 $ 145,573 $ (245) $ 844 $ 599 Bellemeade 2018-1 Ltd. (Apr-18) 181,136 (528) 1,268 740 250,095 (903) 2,245 1,342 Bellemeade 2018-2 Ltd. (Aug-18) — — — — 108,395 (138) 280 142 Bellemeade 2018-3 Ltd. (Oct-18) 302,563 (1,018) 2,496 1,478 302,563 (1,320) 3,262 1,942 Bellemeade 2019-1 Ltd. (Mar-19) 181,324 (380) 5,807 5,427 219,256 (1,361) 8,461 7,100 Bellemeade 2019-2 Ltd. (Apr-19) 398,316 (515) 3,998 3,483 398,316 (730) 5,201 4,471 Bellemeade 2019-3 Ltd. (Jul-19) 409,859 (584) 3,190 2,606 528,084 (861) 5,079 4,218 Bellemeade 2019-4 Ltd. (Oct-19) 411,954 (462) 4,759 4,297 468,737 (890) 6,676 5,786 Bellemeade 2020-1 Ltd. (Jun-20) — — — — 275,068 (178) 1,012 834 Bellemeade 2020-2 Ltd. (Sep-20) (1) 217,766 (177) 1,984 1,807 423,420 (556) 6,839 6,283 Bellemeade 2020-3 Ltd. (Nov-20) (2) 348,818 (128) 5,793 5,665 418,158 (631) 9,605 8,974 Bellemeade 2020-4 Ltd. (Dec-20) (3) 176,826 (50) 1,630 1,580 321,393 (156) 6,816 6,660 Bellemeade 2021-1 Ltd. (Mar-21) (4) 568,986 (303) 3,283 2,980 — — — — Bellemeade 2021-2 Ltd. (Jun-21) (5) 522,807 281 4,124 4,405 — — — — Bellemeade 2021-3 Ltd. (Sep-21) (6) 507,873 (411) 3,446 3,035 — — — — Total $ 4,336,596 $ (4,434) $ 42,202 $ 37,768 $ 3,859,058 $ (7,969) $ 56,320 $ 48,351 (1) At December 31, 2021, $1 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table). (2) At December 31, 2021, $16 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table). (3) At December 31, 2021, $9 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table). (4) At December 31, 2021, $61 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table). (5) At December 31, 2021, $93 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table). (6) At December 31, 2021, $131 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table).

Other Comprehensive Income (Tab

Other Comprehensive Income (Tables)	12 Months Ended
	Dec. 31, 2021
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, 2021 Beginning balance $ 501,295 $ (12,400) $ 488,895 Other comprehensive income (loss) before reclassifications (371,741) (65,686) (437,427) Amounts reclassified from accumulated other comprehensive income (116,068) — (116,068) Net current period other comprehensive income (loss) (487,809) (65,686) (553,495) Ending balance $ 13,486 $ (78,086) $ (64,600) Year Ended December 31, 2020 Beginning balance $ 258,486 $ (46,395) $ 212,091 Other comprehensive income (loss) before reclassifications 668,996 33,995 702,991 Amounts reclassified from accumulated other comprehensive income (426,187) — (426,187) Net current period other comprehensive income (loss) 242,809 33,995 276,804 Ending balance $ 501,295 $ (12,400) $ 488,895 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
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 2021 2020 2019 Unrealized appreciation on available-for-sale investments Net realized gains (losses) $ 157,095 $ 478,659 $ 131,043 Provision for credit losses (2,099) (3,597) — Other-than-temporary impairment losses — (533) (3,165) Total before tax 154,996 474,529 127,878 Income tax (expense) benefit (38,928) (48,342) (8,937) Net of tax $ 116,068 $ 426,187 $ 118,941
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, 2021 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (406,774) $ (19,845) $ (386,929) Less reclassification of net realized gains (losses) included in net income 154,996 38,928 116,068 Foreign currency translation adjustments (64,423) 59 (64,482) Other comprehensive income (loss) $ (626,193) $ (58,714) $ (567,479) Year Ended December 31, 2020 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ 754,572 $ 75,855 $ 678,717 Less reclassification of net realized gains (losses) included in net income 474,529 48,342 426,187 Foreign currency translation adjustments 33,706 370 33,336 Other comprehensive income (loss) $ 313,749 $ 27,883 $ 285,866 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

Earnings Per Common Share (Tabl

Earnings Per Common Share (Tables)	12 Months Ended
	Dec. 31, 2021
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, 2021 2020 2019 Numerator: Net income $ 2,239,462 $ 1,465,711 $ 1,693,300 Amounts attributable to noncontrolling interests (82,613) (60,190) (56,981) Net income available to Arch 2,156,849 1,405,521 1,636,319 Preferred dividends (48,343) (41,612) (41,612) Loss on redemption of preferred shares (15,101) — — Net income available to Arch common shareholders $ 2,093,405 $ 1,363,909 $ 1,594,707 Denominator: Weighted average common shares outstanding 391,748,715 403,062,179 401,802,815 Effect of dilutive common share equivalents: Nonvested restricted shares 1,996,524 1,682,309 1,673,770 Stock options (1) 6,600,697 5,514,967 8,132,893 Weighted average common shares and common share equivalents outstanding – diluted 400,345,936 410,259,455 411,609,478 Earnings per common share: Basic $ 5.34 $ 3.38 $ 3.97 Diluted $ 5.23 $ 3.32 $ 3.87 (1) 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 2021, 2020 and 2019, the number of stock options excluded were 2,398,608, 2,249,821 and 1,302,017, respectively.

Income Taxes (Tables)

Income Taxes (Tables)	12 Months Ended
	Dec. 31, 2021
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, 2021 2020 2019 Current expense (benefit): United States $ 284,274 $ 181,571 $ 139,407 Non-U.S. 11,259 16,091 4,954 295,533 197,662 144,361 Deferred expense (benefit): United States (123,261) (89,170) 11,849 Non-U.S. (43,690) 3,346 (400) (166,951) (85,824) 11,449 Income tax expense $ 128,582 $ 111,838 $ 155,810
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, 2021 2020 2019 Income (Loss) Before Income Taxes: Bermuda $ 1,518,616 $ 1,114,117 $ 1,122,952 United States 643,239 409,893 701,480 Other 206,187 53,539 24,678 Total $ 2,368,042 $ 1,577,549 $ 1,849,110
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, 2021 2020 2019 Expected income tax expense (benefit) computed on pre-tax income at weighted average income tax rate $ 158,269 $ 111,947 $ 149,799 Addition (reduction) in income tax expense (benefit) resulting from: Tax-exempt investment income (23,572) (1,824) (3,091) Meals and entertainment 379 547 1,134 State taxes, net of U.S. federal tax benefit 20,978 5,027 3,314 Foreign branch taxes 1,998 2,094 1,231 Prior year adjustment (1,432) 3,983 632 Foreign exchange gains & losses 1,190 (1,736) 436 Changes in applicable tax rate 447 — — Dividend withholding taxes 12,211 7,105 6,510 Change in valuation allowance (40,425) 13,190 1,628 Contingent consideration — 9 190 Share based compensation (5,339) (2,533) (6,592) Intercompany loan write-off — (22,083) — Other 3,878 (3,888) 619 Income tax expense (benefit) $ 128,582 $ 111,838 $ 155,810
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, 2021 2020 Deferred income tax assets: Net operating loss $ 87,960 $ 67,142 Uncrystallized losses — 2,926 Discounting of net loss reserves 72,001 74,247 Net unearned premium reserve 75,483 66,368 Compensation liabilities 28,062 27,351 Foreign tax credit carryforward 20,058 19,160 Interest expense 755 622 Goodwill and intangible assets — 14,450 Bad debt reserves 10,252 10,842 Depreciation and amortization 115,041 — Lease liability 21,453 23,604 Net unrealized foreign exchange gains 166 165 Other, net — 2,318 Deferred tax assets before valuation allowance 431,231 309,195 Valuation allowance (43,953) (88,255) Deferred tax assets net of valuation allowance 387,278 220,940 Deferred income tax liabilities: Depreciation and amortization — (495) Deposit accounting liability (1,578) (1,751) Goodwill and intangibles (70,549) — Lloyds year of account deferral (12,514) — Contingency reserve (49,486) (64,593) Deferred policy acquisition costs (25,612) (42,045) Investment related (7,492) (9,571) Net unrealized appreciation of investments (8,377) (66,681) Right-of-use asset (17,406) (19,239) Other, net (218) (843) Total deferred tax liabilities (193,232) (205,218) Net deferred income tax assets $ 194,046 $ 15,722
Summary of operating loss carryforwards	At December 31, 2021, the Company’s net operating loss carryforwards and tax credits were as follows: Year Ended December 31, 2021 Expiration Operating Loss Carryforwards United Kingdom $ 259,235 No expiration Ireland 9,032 No expiration Australia 39,981 No expiration Hong Kong 23,203 No expiration United States (1) 29,508 2029 - 2038 Tax Credits U.K. foreign tax credits 20,058 No expiration (1) 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 $7.6 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, 2021, the Company’s net operating loss carryforwards and tax credits were as follows: Year Ended December 31, 2021 Expiration Operating Loss Carryforwards United Kingdom $ 259,235 No expiration Ireland 9,032 No expiration Australia 39,981 No expiration Hong Kong 23,203 No expiration United States (1) 29,508 2029 - 2038 Tax Credits U.K. foreign tax credits 20,058 No expiration (1) 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 $7.6 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, 2021 2020 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 2015-2021 United Kingdom 2020-2021 Ireland 2017-2021 Canada 2017-2021 Switzerland 2018-2021 Denmark 2017-2021 Australia 2017-2021

Leases (Tables)

Leases (Tables)	12 Months Ended
	Dec. 31, 2021
Leases [Abstract]
Additional information regarding operating leases	Additional information regarding the Company’s operating leases is as follows: December 31, 2021 2020 Operating lease costs $ 31,691 $ 31,826 Cash payments included in the measurement of lease liabilities reported in operating cash flows $ 32,094 $ 30,365 Right-of-use assets obtained in exchange for new lease liabilities $ 22,686 $ 12,060 Right-of-use assets (1) $ 106,836 $ 115,911 Operating lease liability (1) $ 126,711 $ 136,015 Weighted average discount rate 3.9 % 3.9 % Weighted average remaining lease term 5.9 years 5.8 years (1) The right-of-use assets are included in ‘ other assets
Contractual maturities of operating lease liabilities	The following table presents the contractual maturities of the Company's operating lease liabilities at December 31, 2021: Years Ending December 31, 2022 $ 31,682 2023 25,288 2024 22,102 2025 16,253 2026 13,430 2027 and thereafter 34,173 Total undiscounted lease liability 142,928 Less: present value adjustment (16,217) Operating lease liability 126,711

Commitments and Contingencies (

Commitments and Contingencies (Tables)	12 Months Ended
	Dec. 31, 2021
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, 2021 2020 2019 Marsh & McLennan Companies and its subsidiaries 18.3 % 13.3 % 9.6 % Aon Corporation and its subsidiaries 12.2 % 12.0 % 12.2 %

Debt and Financing Arrangemen_2

Debt and Financing Arrangements - (Tables)	12 Months Ended
	Dec. 31, 2021
Debt Disclosure [Abstract]
Schedule of senior notes	The Company’s senior notes payable at December 31, 2021 and 2020 were as follows: Carrying Amount at Interest Principal December 31, (Fixed) Amount 2021 2020 2034 notes (1) 7.350 % 300,000 297,488 297,367 2043 notes (2) 5.144 % 500,000 495,063 494,944 2026 notes (3) 4.011 % 500,000 497,633 497,211 2046 notes (4) 5.031 % 450,000 445,490 445,402 2050 notes (5) 3.635 % 1,000,000 988,720 988,500 Somers notes (6) 137,689 $ 2,750,000 $ 2,724,394 $ 2,861,113 (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 Arch Capital issued on June 30, 2020 and due June 30, 2050 (“2050 notes”). (6) Senior notes of Somers issued on July 2, 2019 and due July 2, 2029 (“Somers Senior Notes”), reflecting the elimination of amounts owned by Arch-U.S. Effective July 1, 2021, the Company no longer consolidates Somers in its financials. See note 12.
Schedule of outstanding revolving credit agreement borrowings	The Company’s outstanding revolving credit agreement borrowings were as follows: Year Ended December 31, 2021 2020 Arch Capital $ — $ — Somers 155,687 Total $ — $ 155,687

Goodwill and Intangible Assets

Goodwill and Intangible Assets (Tables)	12 Months Ended
	Dec. 31, 2021
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, 2019 $ 326,551 $ 85,911 $ 325,621 $ 738,083 Acquisitions — — 39,178 39,178 Amortization — — (69,031) (69,031) Foreign currency movements and other adjustments (11,922) (6,692) 3,247 (15,367) Net balance at Dec. 31, 2020 314,629 79,219 299,015 692,863 Acquisitions (1) 31,677 — 318,459 350,136 Amortization — — (82,955) (82,955) Impact of deconsolidation of Somers (2) — (7,650) — (7,650) Foreign currency movements and other adjustments (1,441) (212) (5,758) (7,411) Net balance at Dec. 31, 2021 $ 344,865 $ 71,357 $ 528,761 $ 944,983 Gross balance at Dec. 31, 2021 $ 342,842 $ 70,246 $ 1,102,298 $ 1,515,386 Accumulated amortization — — (571,839) (571,839) Foreign currency movements and other adjustments 2,023 1,111 (1,698) 1,436 Net balance at Dec. 31, 2021 $ 344,865 $ 71,357 $ 528,761 $ 944,983 (1) Certain amounts for the Company’s 2021 acquisitions are considered provisional. (2) See note 12 .
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 Dec. 31, 2021 Acquired insurance contracts $ 451,505 $ (409,592) $ 339 $ 42,252 Operating platform 52,674 (48,838) 56 3,892 Distribution relationships 602,518 (120,302) (2,207) 480,009 Goodwill 342,842 — 2,023 344,865 Insurance licenses 48,331 — — 48,331 Syndicate capacity 21,915 — 1,111 23,026 Unfavorable service contract (9,533) 9,435 — (98) Other 5,134 (2,542) 114 2,706 Total $ 1,515,386 $ (571,839) $ 1,436 $ 944,983 Dec. 31, 2020 Acquired insurance contracts $ 451,505 $ (381,349) $ 284 $ 70,440 Operating platform 52,674 (44,347) 60 8,387 Distribution relationships 285,141 (71,383) 3,450 217,208 Goodwill 318,043 — (3,414) 314,629 Insurance licenses 55,981 — — 55,981 Syndicate capacity 21,915 — 1,324 23,239 Unfavorable service contract (9,533) 9,147 — (386) Other 5,134 (1,896) 127 3,365 Total $ 1,180,860 $ (489,828) $ 1,831 $ 692,863
Estimated future amortization expense	The estimated remaining amortization expense for the Company’s intangible assets with finite lives is as follows: 2022 $ 109,144 2023 99,620 2024 79,410 2025 44,523 2026 35,252 2027 and thereafter 160,812 Total $ 528,761

Shareholders' Equity (Tables)

Shareholders' Equity (Tables)	12 Months Ended
	Dec. 31, 2021
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, 2021 2020 2019 Common Shares: Shares issued and outstanding, beginning of year 579,000,841 574,617,195 570,737,283 Shares issued (1) 2,669,229 2,646,164 2,835,994 Restricted shares issued, net of cancellations 1,619,780 1,737,482 1,043,918 Shares issued and outstanding, end of year 583,289,850 579,000,841 574,617,195 Common shares in treasury, end of year (204,365,956) (172,280,199) (168,997,994) Shares issued and outstanding, end of year 378,923,894 406,720,642 405,619,201
Schedule of share repurchases	The Company’s repurchases under the share repurchase program were as follows: Year Ended December 31, 2021 2020 2019 Aggregate cost of shares repurchased $ 1,234,294 $ 83,472 $ 2,871 Shares repurchased 31,486,830 2,850,102 110,598 Average price per share repurchased $ 39.20 $ 29.29 $ 25.96

Share-Based Compensation (Table

Share-Based Compensation (Tables)	12 Months Ended
	Dec. 31, 2021
Share-based Payment Arrangement [Abstract]
Valuation assumptions	Year Ended December 31, 2021 2020 2019 Dividend yield — % — % — % Expected volatility 24.2 % 16.6 % 18.1 % Risk free interest rate 1.0 % 1.2 % 2.5 % 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 2021 is presented below: Year Ended December 31, 2021 Number of Weighted Average Exercise Price Weighted Average Contractual Term Aggregate Intrinsic Value Outstanding, beginning of year 17,839,333 $ 23.32 Granted 1,243,984 $ 35.90 Exercised (1,931,320) $ 15.57 Forfeited or expired (68,837) $ 35.39 Outstanding, end of year 17,083,160 $ 25.06 4.41 $ 331,214 Exercisable, end of year 14,730,147 $ 23.20 3.78 $ 312,966
Weighted average grant date fair value	Year Ended December 31, 2021 2020 2019 Weighted average grant date fair value $ 9.22 $ 8.14 $ 7.90 Aggregate intrinsic value of Options/SARs exercised $ 47,074 $ 59,723 $ 51,350
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 2021 is presented below: Restricted Common Shares Restricted Unit Awards Unvested Shares: Unvested balance, beginning of year 1,635,845 1,121,719 Granted 1,085,811 175,962 Vested (549,892) (555,870) Forfeited (100,927) (41,945) Unvested balance, end of year 2,070,837 699,866 Weighted Average Grant Date Fair Value: Unvested balance, beginning of year $ 36.34 $ 31.43 Granted $ 36.14 $ 35.94 Vested $ 35.94 $ 30.46 Forfeited $ 36.28 $ 32.23 Unvested balance, end of year $ 36.35 $ 33.29
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Performance shares and units, valuation assumptions	Year Ended December 31, 2021 2020 2019 Expected volatility 37.5 % 18.1 % 17.1 % Risk free interest rate 0.3 % 1.1 % 2.5 %
Unvested performance share and unit activity	Performance Shares Performance Units Unvested Shares: Unvested balance, beginning of year 1,851,382 32,065 Granted 674,406 10,698 Performance adjustment (1) (2) (39,510) 11,447 Vested (624,518) (24,440) Unvested balance, end of year 1,861,760 29,770 Weighted Average Grant Date Fair Value: Unvested balance, beginning of year $ 34.42 $ 33.48 Granted $ 37.38 $ 37.38 Performance adjustment (1) (2) 24.78 24.71 Vested $ 24.78 $ 24.71 Unvested balance, end of year $ 38.93 $ 38.71 (1) The performance adjustment represents the difference between the number of performance shares granted and earned, which vested following the end of the performance period. The performance shares were granted at the maximum level of achievement. (2) The performance adjustment represents the change in PSUs, which vested following the end of the performance period. The performance units were granted at the target level of achievement.
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, 2021 2020 2019 Pre-Tax Stock options and SARs $ 12,316 $ 11,744 $ 12,866 Restricted share and unit awards 46,817 41,284 38,988 Performance awards 23,696 14,729 8,949 ESPP 3,751 2,135 3,045 Total $ 86,580 $ 69,892 $ 63,848 After-Tax Stock options and SARs $ 10,927 $ 10,388 $ 11,450 Restricted share and unit awards 39,349 34,599 32,999 Performance awards 21,920 13,380 8,295 ESPP 3,471 1,978 2,758 Total $ 75,667 $ 60,345 $ 55,502
Unrecognized compensation cost	December 31, 2021 Stock Options and SARs Restricted Common Performance Common Shares and Units Unrecognized compensation cost related to unvested awards $ 8,233 $ 45,936 $ 7,635 Weighted average recognition period (years) 0.91 1.23 0.52
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, 2021 2020 2019 Restricted shares and restricted unit awards granted 1,261,773 1,535,330 1,195,741 Weighted average grant date fair value $ 36.12 $ 37.55 $ 32.89 Aggregate fair value of vested restricted share and unit awards $ 65,477 $ 39,703 $ 46,262
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, 2021 2020 2019 Performance awards 685,104 557,204 696,360 Weighted average grant date fair value $ 37.38 $ 44.17 $ 36.05

Statutory Information (Tables)

Statutory Information (Tables)	12 Months Ended
	Dec. 31, 2021
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, 2021 and 2020: December 31, 2021 2020 Actual capital and surplus (1): Bermuda $ 17,528,510 $ 17,390,943 Ireland 958,200 883,337 United States 5,600,652 4,904,840 United Kingdom 902,002 967,440 Canada 70,063 64,286 Australia 283,693 64,507 Required capital and surplus: Bermuda $ 5,661,301 $ 5,234,121 Ireland 794,933 701,161 United States 1,717,646 1,644,324 United Kingdom 563,164 601,662 Canada 42,513 37,441 Australia 214,022 19,370 (1) Such amounts include ownership interests in affiliated insurance and reinsurance subsidiaries. The statutory net income (loss) for the Company’s principal operating subsidiaries for 2021, 2020 and 2019 was as follows: Year Ended December 31, 2021 2020 2019 Statutory net income (loss): Bermuda $ 2,370,746 $ 1,579,889 $ 1,801,486 Ireland 25,191 18,397 26,367 United States 345,790 143,271 481,188 United Kingdom 35,286 4,078 (17,423) Canada 6,985 (1,049) (1,023) Australia 11,874 (8,601) (6,199)

General (Details)

General (Details)	Jul. 01, 2021
Greysbridge Holdings Ltd | Kelso And Company
Schedule of Equity Method Investments [Line Items]
Percentage ownership	30.00%
Greysbridge Holdings Ltd | Warburg Pincus
Schedule of Equity Method Investments [Line Items]
Percentage ownership	30.00%
Greysbridge Holdings Ltd
Schedule of Equity Method Investments [Line Items]
Percentage ownership	40.00%

Acquisitions (Details)

Acquisitions (Details) - USD ($) $ in Thousands	Aug. 31, 2021	Aug. 06, 2021	Dec. 31, 2021	[1]	Dec. 31, 2020
Business Acquisition [Line Items]
Goodwill and intangible assets, acquisitions			$ 350,136		$ 39,178
Westpac Lenders Mortgage Insurance Limited
Business Acquisition [Line Items]
Term of business exclusivity agreement	10 years
Somerset
Business Acquisition [Line Items]
Goodwill and intangible assets, acquisitions		$ 350,100
[1]	Certain amounts for the Company’s 2021 acquisitions are considered provisional.

Significant Accounting Polici_3

Significant Accounting Policies (Details)	12 Months Ended
	Dec. 31, 2021
Significant Accounting Policies [Line Items]
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
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

Segment Information - Analysis

Segment Information - Analysis of underwriting income by segment and reconciliation to net income available to common shareholders (Details) $ in Thousands		12 Months Ended
		Dec. 31, 2021USD ($)segment	Dec. 31, 2020USD ($)	Dec. 31, 2019USD ($)
Segment Reporting Information [Line Items]
Gross premiums written		$ 12,752,487	$ 10,088,068	$ 8,138,960
Premiums ceded		(3,734,150)	(2,650,352)	(2,099,893)
Net premiums written		9,018,337	7,437,716	6,039,067
Change in unearned premiums		(936,039)	(445,781)	(252,569)
Net premiums earned		8,082,298	6,991,935	5,786,498
Other underwriting income		22,073	26,784	24,861
Losses and loss adjustment expenses		(4,584,803)	(4,689,599)	(3,133,452)
Acquisition expenses, net		(1,303,178)	(1,004,842)	(840,945)
Other operating expenses		(998,595)	(875,176)	(800,997)
Underwriting income (loss)		1,217,795	449,102	1,035,965
Net investment income		389,118	519,608	627,738
Net realized gains (losses)		379,845	823,460	363,198
Equity in net income (loss) of investment funds accounted for using the equity method		366,402	146,693	123,672
Other income (loss)		10,244	29	0
Corporate expenses		(77,119)	(68,492)	(65,667)
Transaction costs and other		(2,038)	(13,496)	(14,444)
Amortization of intangible assets		(82,955)	(69,031)	(82,104)
Interest expense		(139,470)	(143,456)	(120,872)
Net foreign exchange gains (losses)		41,529	(83,634)	(20,609)
Income (loss) before income taxes and income (loss) from operating affiliates		2,103,351	1,560,783	1,846,877
Income tax (expense) benefit		(128,582)	(111,838)	(155,810)
Income (loss) from operating affiliates		264,693	16,766	2,233
Net income (loss)		2,239,462	1,465,711	1,693,300
Amounts attributable to redeemable noncontrolling interests		(4,299)	(7,114)	(16,909)
Amounts attributable to nonredeemable noncontrolling interests		(78,314)	(53,076)	(40,072)
Net income available to Arch		2,156,849	1,405,521	1,636,319
Preferred share dividends		(48,343)	(41,612)	(41,612)
Loss on redemption of preferred shares		(15,101)	0	0
Net income (loss) available to Arch common shareholders		$ 2,093,405	$ 1,363,909	$ 1,594,707
Underwriting Ratios
Loss ratio		56.70%	67.10%	54.20%
Acquisition expense ratio		16.10%	14.40%	14.50%
Other operating expense ratio		12.40%	12.50%	13.80%
Combined ratio		85.20%	94.00%	82.50%
Goodwill and intangible assets		$ 944,983	$ 692,863	$ 738,083
Total investable assets		27,442,153	29,513,907	24,990,265
Total assets		45,100,945	43,282,297	37,885,361
Total liabilities		$ 31,545,816	29,294,856	25,569,809
Operating segments | Underwriting Segments
Segment Reporting Information [Line Items]
Number of segments | segment		3
Gross premiums written	[1]	$ 12,463,788	9,632,691	7,695,645
Premiums ceded		(3,800,153)	(2,732,564)	(2,189,440)
Net premiums written		8,663,635	6,900,127	5,506,205
Change in unearned premiums		(913,305)	(468,543)	(276,396)
Net premiums earned		7,750,330	6,431,584	5,229,809
Other underwriting income		21,334	24,739	22,449
Losses and loss adjustment expenses		(4,325,761)	(4,249,117)	(2,680,317)
Acquisition expenses, net		(1,240,437)	(906,771)	(734,965)
Other operating expenses		(965,726)	(819,366)	(749,346)
Underwriting income (loss)		1,239,740	481,069	1,087,630
Net investment income		346,808	401,908	491,067
Net realized gains (losses)		299,207	813,781	348,037
Equity in net income (loss) of investment funds accounted for using the equity method		366,402	146,693	123,672
Other income (loss)		10,244	29
Corporate expenses		(77,119)	(68,492)	(65,667)
Transaction costs and other		(1,103)	(9,456)	(14,444)
Amortization of intangible assets		(82,057)	(69,031)	(82,104)
Interest expense		(131,060)	(120,214)	(93,735)
Net foreign exchange gains (losses)		42,854	(80,161)	(9,252)
Income (loss) before income taxes and income (loss) from operating affiliates		2,013,916	1,496,126	1,785,204
Income tax (expense) benefit		(128,348)	(111,812)	(155,790)
Income (loss) from operating affiliates		264,693	16,766	2,233
Net income (loss)		2,150,261	1,401,080	1,631,647
Amounts attributable to redeemable noncontrolling interests		(2,346)	(2,997)	0
Amounts attributable to nonredeemable noncontrolling interests		0	0	0
Net income available to Arch		2,147,915	1,398,083	1,631,647
Preferred share dividends		(48,343)	(41,612)	(41,612)
Loss on redemption of preferred shares		(15,101)
Net income (loss) available to Arch common shareholders		$ 2,084,471	$ 1,356,471	$ 1,590,035
Underwriting Ratios
Loss ratio		55.80%	66.10%	51.30%
Acquisition expense ratio		16.00%	14.10%	14.10%
Other operating expense ratio		12.50%	12.70%	14.30%
Combined ratio		84.30%	92.90%	79.70%
Goodwill and intangible assets		$ 944,983	$ 685,213	$ 730,433
Total investable assets		27,442,153	26,856,295	22,285,676
Total assets		45,100,945	39,791,983	34,374,468
Total liabilities		31,545,816	26,789,149	22,977,636
Operating segments | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	5,867,734	4,688,562	3,907,993
Premiums ceded	[2]	(1,719,541)	(1,525,655)	(1,266,267)
Net premiums written		4,148,193	3,162,907	2,641,726
Change in unearned premiums		(521,725)	(291,487)	(244,646)
Net premiums earned		3,626,468	2,871,420	2,397,080
Other underwriting income		0	(31)	0
Losses and loss adjustment expenses		(2,344,365)	(2,092,453)	(1,615,475)
Acquisition expenses, net		(606,265)	(418,483)	(361,614)
Other operating expenses		(558,906)	(489,153)	(454,770)
Underwriting income (loss)		$ 116,932	$ (128,700)	$ (34,779)
Underwriting Ratios
Loss ratio		64.60%	72.90%	67.40%
Acquisition expense ratio		16.70%	14.60%	15.10%
Other operating expense ratio		15.40%	17.00%	19.00%
Combined ratio		96.70%	104.50%	101.50%
Goodwill and intangible assets		$ 256,434	$ 280,978	$ 289,021
Operating segments | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	5,093,930	3,472,086	2,323,223
Premiums ceded	[2]	(1,839,556)	(1,014,716)	(720,500)
Net premiums written		3,254,374	2,457,370	1,602,723
Change in unearned premiums		(413,931)	(295,141)	(136,334)
Net premiums earned		2,840,443	2,162,229	1,466,389
Other underwriting income		3,669	4,454	6,444
Losses and loss adjustment expenses		(1,924,719)	(1,628,320)	(1,011,329)
Acquisition expenses, net		(536,754)	(354,048)	(239,032)
Other operating expenses		(212,810)	(168,011)	(141,484)
Underwriting income (loss)		$ 169,829	$ 16,304	$ 80,988
Underwriting Ratios
Loss ratio		67.80%	75.30%	69.00%
Acquisition expense ratio		18.90%	16.40%	16.30%
Other operating expense ratio		7.50%	7.80%	9.60%
Combined ratio		94.20%	99.50%	94.90%
Goodwill and intangible assets		$ 183,523	$ 18,963	$ 2,516
Operating segments | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,507,825	1,473,999	1,466,265
Premiums ceded	[2]	(246,757)	(194,149)	(204,509)
Net premiums written		1,261,068	1,279,850	1,261,756
Change in unearned premiums		22,351	118,085	104,584
Net premiums earned		1,283,419	1,397,935	1,366,340
Other underwriting income		17,665	20,316	16,005
Losses and loss adjustment expenses		(56,677)	(528,344)	(53,513)
Acquisition expenses, net		(97,418)	(134,240)	(134,319)
Other operating expenses		(194,010)	(162,202)	(153,092)
Underwriting income (loss)		$ 952,979	$ 593,465	$ 1,041,421
Underwriting Ratios
Loss ratio		4.40%	37.80%	3.90%
Acquisition expense ratio		7.60%	9.60%	9.80%
Other operating expense ratio		15.10%	11.60%	11.20%
Combined ratio		27.10%	59.00%	24.90%
Goodwill and intangible assets		$ 505,026	$ 385,272	$ 438,896
Operating segments | Other
Segment Reporting Information [Line Items]
Number of segments | segment		2
Gross premiums written	[1]	$ 457,465	728,546	754,881
Premiums ceded	[2]	(102,763)	(190,957)	(222,019)
Net premiums written		354,702	537,589	532,862
Change in unearned premiums		(22,734)	22,762	23,827
Net premiums earned		331,968	560,351	556,689
Other underwriting income		739	2,045	2,412
Losses and loss adjustment expenses		(259,042)	(440,482)	(453,135)
Acquisition expenses, net		(62,741)	(98,071)	(105,980)
Other operating expenses		(32,869)	(55,810)	(51,651)
Underwriting income (loss)		(21,945)	(31,967)	(51,665)
Net investment income		42,310	117,700	136,671
Net realized gains (losses)		80,638	9,679	15,161
Equity in net income (loss) of investment funds accounted for using the equity method		0	0	0
Other income (loss)		0	0
Corporate expenses		0	0	0
Transaction costs and other		(935)	(4,040)	0
Amortization of intangible assets		(898)	0	0
Interest expense		(8,410)	(23,242)	(27,137)
Net foreign exchange gains (losses)		(1,325)	(3,473)	(11,357)
Income (loss) before income taxes and income (loss) from operating affiliates		89,435	64,657	61,673
Income tax (expense) benefit		(234)	(26)	(20)
Income (loss) from operating affiliates		0	0	0
Net income (loss)		89,201	64,631	61,653
Amounts attributable to redeemable noncontrolling interests		(1,953)	(4,117)	(16,909)
Amounts attributable to nonredeemable noncontrolling interests		(78,314)	(53,076)	(40,072)
Net income available to Arch		8,934	7,438	4,672
Preferred share dividends		0	0	0
Loss on redemption of preferred shares		0
Net income (loss) available to Arch common shareholders		$ 8,934	$ 7,438	$ 4,672
Underwriting Ratios
Loss ratio		78.00%	78.60%	81.40%
Acquisition expense ratio		18.90%	17.50%	19.00%
Other operating expense ratio		9.90%	10.00%	9.30%
Combined ratio		106.80%	106.10%	109.70%
Goodwill and intangible assets		$ 0	$ 7,650	$ 7,650
Total investable assets		0	2,657,612	2,704,589
Total assets		0	3,490,314	3,510,893
Total liabilities		$ 0	$ 2,505,707	$ 2,592,173
[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		12 Months Ended
		Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Segment Reporting Information [Line Items]
Net premiums earned		$ 8,082,298	$ 6,991,935	$ 5,786,498
Net premiums written		9,018,337	7,437,716	6,039,067
Operating segments | Insurance
Segment Reporting Information [Line Items]
Net premiums earned		3,626,468	2,871,420	2,397,080
Net premiums written		4,148,193	3,162,907	2,641,726
Operating segments | Insurance | United States
Segment Reporting Information [Line Items]
Net premiums written	[1]	2,813,039	2,158,415	1,983,476
Operating segments | Insurance | Europe
Segment Reporting Information [Line Items]
Net premiums written	[1]	1,125,192	856,572	559,214
Operating segments | Insurance | Other geographic location
Segment Reporting Information [Line Items]
Net premiums written	[1]	209,962	147,920	99,036
Operating segments | Insurance | Professional lines
Segment Reporting Information [Line Items]
Net premiums earned	[1],[2]	942,817	655,872	499,224
Operating segments | Insurance | Property, energy, marine and aviation
Segment Reporting Information [Line Items]
Net premiums earned	[1]	702,693	517,247	298,966
Operating segments | Insurance | Programs
Segment Reporting Information [Line Items]
Net premiums earned	[1]	506,867	432,854	414,103
Operating segments | Insurance | Construction and national accounts
Segment Reporting Information [Line Items]
Net premiums earned	[1]	381,306	387,934	325,687
Operating segments | Insurance | Excess and surplus casualty
Segment Reporting Information [Line Items]
Net premiums earned	[1],[3]	318,027	270,620	200,615
Operating segments | Insurance | Travel, accident and health
Segment Reporting Information [Line Items]
Net premiums earned	[1]	255,590	190,944	305,085
Operating segments | Insurance | Lenders products
Segment Reporting Information [Line Items]
Net premiums earned	[1]	153,958	114,687	66,079
Operating segments | Insurance | Other
Segment Reporting Information [Line Items]
Net premiums earned	[1],[4]	365,210	301,262	287,321
Operating segments | Reinsurance
Segment Reporting Information [Line Items]
Net premiums earned		2,840,443	2,162,229	1,466,389
Net premiums written		3,254,374	2,457,370	1,602,723
Operating segments | Reinsurance | United States
Segment Reporting Information [Line Items]
Net premiums written	[5]	828,504	687,622	529,943
Operating segments | Reinsurance | Bermuda
Segment Reporting Information [Line Items]
Net premiums written	[5]	1,557,294	1,001,990	578,618
Operating segments | Reinsurance | Europe and other
Segment Reporting Information [Line Items]
Net premiums written	[5]	868,576	767,758	494,162
Operating segments | Reinsurance | Property excluding property catastrophe
Segment Reporting Information [Line Items]
Net premiums earned	[5],[6]	836,573	562,208	362,841
Operating segments | Reinsurance | Other specialty
Segment Reporting Information [Line Items]
Net premiums earned	[5],[6]	818,801	626,409	478,517
Operating segments | Reinsurance | Casualty
Segment Reporting Information [Line Items]
Net premiums earned	[5],[7]	666,754	549,056	429,288
Operating segments | Reinsurance | Property catastrophe
Segment Reporting Information [Line Items]
Net premiums earned	[5],[7]	280,738	237,736	90,934
Operating segments | Reinsurance | Marine and aviation
Segment Reporting Information [Line Items]
Net premiums earned	[5]	152,955	109,624	48,274
Operating segments | Reinsurance | Other
Segment Reporting Information [Line Items]
Net premiums earned	[5],[8]	84,622	77,196	56,535
Operating segments | Mortgage
Segment Reporting Information [Line Items]
Net premiums earned		1,283,419	1,397,935	1,366,340
Net premiums written		1,261,068	1,279,850	1,261,756
Operating segments | Mortgage | United States
Segment Reporting Information [Line Items]
Net premiums earned		970,507	1,158,563	1,134,849
Net premiums written		914,477	1,021,950	1,032,868
Operating segments | Mortgage | Other geographic location
Segment Reporting Information [Line Items]
Net premiums earned		312,912	239,372	231,491
Net premiums written		346,591	257,900	228,888
Operating segments | Other
Segment Reporting Information [Line Items]
Net premiums earned		331,968	560,351	556,689
Net premiums written		354,702	537,589	532,862
Operating segments | Other | United States
Segment Reporting Information [Line Items]
Net premiums written	[9]	63,403	115,471	127,176
Operating segments | Other | Europe
Segment Reporting Information [Line Items]
Net premiums written	[9]	91,499	97,753	52,065
Operating segments | Other | Bermuda
Segment Reporting Information [Line Items]
Net premiums written	[9]	199,800	324,365	353,621
Operating segments | Other | Property excluding property catastrophe
Segment Reporting Information [Line Items]
Net premiums earned	[9]	6,578	1,130	3,503
Operating segments | Other | Other specialty
Segment Reporting Information [Line Items]
Net premiums earned	[9],[10]	118,356	186,717	185,547
Operating segments | Other | Casualty
Segment Reporting Information [Line Items]
Net premiums earned	[9],[11]	138,551	245,272	246,894
Operating segments | Other | Property catastrophe
Segment Reporting Information [Line Items]
Net premiums earned	[9]	15,235	23,037	13,399
Operating segments | Other | Marine and aviation
Segment Reporting Information [Line Items]
Net premiums earned	[9]	190	429	0
Operating segments | Other | Other
Segment Reporting Information [Line Items]
Net premiums earned	[9],[12]	$ 53,058	$ 103,766	$ 107,346
[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.
[5]	Reinsurance segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.
[6]	Includes proportional motor, surety, accident and health, workers’ compensation catastrophe, agriculture, trade credit and other.
[7]	Includes executive assurance, professional liability, workers’ compensation, excess motor, healthcare and other.
[8]	Includes life, casualty clash and other.
[9]	Other segment results include premiums assumed through intersegment transactions and exclude premiums ceded through intersegment transactions.
[10]	Includes proportional motor and other.
[11]	Includes professional liability, excess motor, programs and other.
[12]	Includes mortgage, US programs 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, 2021	Dec. 31, 2020	Dec. 31, 2019
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]
Reserve for losses and loss adjustment expenses at beginning of year		$ 16,513,929	$ 13,891,842	$ 11,853,297
Unpaid losses and loss adjustment expenses recoverable		4,314,855	4,082,650	2,814,291
Net reserve for losses and loss adjustment expenses at beginning of year		12,199,074	9,809,192	9,039,006
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year		4,940,987	4,851,051	3,297,037
Prior years		(356,184)	(161,452)	(163,585)
Total net incurred losses and loss adjustment expenses		4,584,803	4,689,599	3,133,452
Net losses and loss adjustment expense reserves of acquired business	[1]	104,176	0	209,486
Retroactive reinsurance transaction	[2]	(444,147)	182,210	(225,500)
Impact of deconsolidation of Somers		(1,460,611)	0	0
Foreign exchange (gains) losses and other		1,181	179,190	36,003
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year		(734,846)	(661,529)	(621,202)
Prior years		(2,091,705)	(1,999,588)	(1,762,053)
Total net paid losses and loss adjustment expenses		(2,826,551)	(2,661,117)	(2,383,255)
Net reserve for losses and loss adjustment expenses at end of year		12,157,925	12,199,074	9,809,192
Unpaid losses and loss adjustment expenses recoverable		5,599,231	4,314,855	4,082,650
Reserve for losses and loss adjustment expenses at end of year		$ 17,757,156	$ 16,513,929	$ 13,891,842
[1]	Represents activity related to the Company’s acquisitions in the 2021 and the 2019 period.
[2]	See ‘Retroactive Reinsurance Transactions’ section.

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, 2021	Dec. 31, 2020	Dec. 31, 2019
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 356,184	$ 161,452	$ 163,585
Operating segments | Insurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 16,200	$ 7,800	$ 15,800
Prior year reserve development (points)	0.40%	0.30%	0.70%
Operating segments | Insurance | Short-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 81,700	$ 33,600	$ 54,900
Operating segments | Insurance | Short-tailed lines | Property
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	38,900	21,600
Operating segments | Insurance | Short-tailed lines | Lenders products
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	26,700
Operating 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 development favorable (unfavorable)	16,200	8,400
Operating segments | Insurance | Medium-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(93,500)	(75,200)
Operating segments | Insurance | Medium-tailed lines | Programs
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		(16,000)
Operating segments | Insurance | Medium-tailed lines | Professional liability
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(30,800)
Operating segments | Insurance | Medium-tailed lines | Surety
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		(37,900)
Operating segments | Insurance | Medium-tailed lines | Contract binding
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(57,600)	(23,100)
Operating segments | Insurance | Long-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	28,100	49,400
Operating segments | Insurance | Long-tailed lines | Other business
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		38,800
Operating segments | Insurance | Long-tailed lines | Construction and national accounts
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		9,300
Operating 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 development favorable (unfavorable)			(39,100)
Operating 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 development favorable (unfavorable)			(30,100)
Operating 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 development favorable (unfavorable)			19,300
Operating 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 development favorable (unfavorable)			15,800
Operating 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 development favorable (unfavorable)			(33,600)
Operating segments | Insurance | Short Tailed And Long Tailed Lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	109,800	83,000
Operating segments | Reinsurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 178,800	$ 134,000	$ 46,400
Prior year reserve development (points)	6.30%	6.20%	3.20%
Operating segments | Reinsurance | Short-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 175,500	$ 144,000	$ 70,500
Operating 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 development favorable (unfavorable)		87,700	33,700
Operating segments | Reinsurance | Short-tailed lines | Property catastrophe
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(36,400)
Operating segments | Reinsurance | Short-tailed lines | Property other than property catastrophe
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	88,600
Operating 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 development favorable (unfavorable)	123,300	53,600	40,800
Operating segments | Reinsurance | Medium-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)			16,000
Operating segments | Reinsurance | Long-tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(5,300)	(21,900)	(40,100)
Operating segments | Reinsurance | Long-tailed lines | Casualty
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)			(44,500)
Operating segments | Reinsurance | Short Tailed And Medium Tailed Lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	184,100	155,900
Operating segments | Mortgage
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 169,600	$ 19,000	$ 125,200
Prior year reserve development (points)	13.20%	1.40%	9.20%
Operating segments | Mortgage | Primary mortgage business
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		$ 16,200	$ 117,100
Operating segments | Other
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ (8,400)	$ 700	$ (23,800)

Short Duration Contracts - Clai

Short Duration Contracts - Claims development - Insurance (Details) $ in Thousands	Dec. 31, 2021USD ($)claims	Dec. 31, 2020USD ($)	Dec. 31, 2019USD ($)	Dec. 31, 2018USD ($)	Dec. 31, 2017USD ($)	Dec. 31, 2016USD ($)	Dec. 31, 2015USD ($)	Dec. 31, 2014USD ($)	Dec. 31, 2013USD ($)	Dec. 31, 2012USD ($)
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance	$ 11,886,330
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	1,947,000
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,377,632
All outstanding liabilities before 2012, net of reinsurance	17,517
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	178,343	$ 178,250	$ 178,616	$ 190,770	$ 192,993	$ 197,005	$ 199,469	$ 205,776	$ 232,498	$ 233,149
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	174,384	174,032	173,184	181,307	179,945	167,540	161,831	138,977	93,394	20,638
Total of IBNR liabilities plus expected development on reported claims	$ 627
Cumulative number of reported claims | claims	4,245
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	$ 126,276	127,290	128,624	133,869	134,952	143,400	149,199	156,785	159,102
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	124,841	124,688	123,356	125,475	122,244	120,111	110,808	84,936	32,292
Total of IBNR liabilities plus expected development on reported claims	$ 25
Cumulative number of reported claims | claims	4,243
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	$ 134,942	135,032	134,329	132,307	136,201	147,465	145,957	148,368
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	122,296	115,383	98,553	87,812	84,195	77,892	53,751	25,881
Total of IBNR liabilities plus expected development on reported claims	$ 3,098
Cumulative number of reported claims | claims	3,884
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	$ 91,892	91,830	97,852	102,515	103,995	109,865	112,409
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	87,316	86,246	87,926	86,253	76,338	64,953	23,580
Total of IBNR liabilities plus expected development on reported claims	$ 3,804
Cumulative number of reported claims | claims	4,536
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	$ 92,553	96,437	100,471	105,657	101,306	104,449
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	91,241	95,002	97,506	98,683	83,552	24,828
Total of IBNR liabilities plus expected development on reported claims	$ 874
Cumulative number of reported claims | claims	6,160
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	$ 231,228	230,439	235,951	246,291	280,715
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	215,895	211,708	195,532	139,867	30,228
Total of IBNR liabilities plus expected development on reported claims	$ 8,248
Cumulative number of reported claims | claims	6,426
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	$ 170,057	173,693	186,030	180,981
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	142,838	134,858	102,285	30,026
Total of IBNR liabilities plus expected development on reported claims	$ 9,136
Cumulative number of reported claims | claims	5,020
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	$ 165,477	178,564	179,056
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	133,911	105,380	26,130
Total of IBNR liabilities plus expected development on reported claims	$ 6,667
Cumulative number of reported claims | claims	5,080
Insurance | Property, energy, marine and aviation | 2020
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 329,362	359,394
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	194,487	55,619
Total of IBNR liabilities plus expected development on reported claims	$ 66,698
Cumulative number of reported claims | claims	4,186
Insurance | Property, energy, marine and aviation | 2021
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 426,870
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	90,423
Total of IBNR liabilities plus expected development on reported claims	$ 158,163
Cumulative number of reported claims | claims	2,951
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	$ 4,187,063
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,544,247
All outstanding liabilities before 2012, net of reinsurance	242,741
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	239,075	242,332	244,448	243,863	253,758	258,371	272,004	269,204	263,451	241,368
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	168,119	163,016	155,085	143,885	130,098	108,660	83,637	58,650	30,915	6,984
Total of IBNR liabilities plus expected development on reported claims	$ 43,924
Cumulative number of reported claims | claims	65,731
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	$ 270,558	269,754	272,849	274,717	282,122	302,165	307,152	297,225	283,228
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	184,800	174,946	164,403	149,292	122,288	101,293	71,449	29,265	6,857
Total of IBNR liabilities plus expected development on reported claims	$ 54,640
Cumulative number of reported claims | claims	67,113
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	$ 343,569	342,934	344,197	339,701	343,113	338,890	336,019	330,015
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	224,101	211,643	191,305	162,123	112,702	71,624	40,346	9,228
Total of IBNR liabilities plus expected development on reported claims	$ 66,498
Cumulative number of reported claims | claims	75,904
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	$ 386,801	382,722	391,455	392,143	398,908	391,884	359,058
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	227,697	211,715	181,704	139,492	88,515	44,605	11,139
Total of IBNR liabilities plus expected development on reported claims	$ 91,081
Cumulative number of reported claims | claims	78,785
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	$ 367,818	374,896	399,571	406,082	394,485	389,832
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	194,773	164,662	136,870	87,616	41,979	11,709
Total of IBNR liabilities plus expected development on reported claims	$ 115,303
Cumulative number of reported claims | claims	79,005
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	$ 407,115	412,512	422,624	417,941	417,377
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	165,606	135,111	99,874	52,356	13,408
Total of IBNR liabilities plus expected development on reported claims	$ 145,130
Cumulative number of reported claims | claims	84,692
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	$ 451,459	450,937	453,190	430,415
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	154,248	115,137	63,848	17,025
Total of IBNR liabilities plus expected development on reported claims	$ 189,965
Cumulative number of reported claims | claims	77,700
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	$ 481,045	487,547	456,353
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	121,859	73,222	18,431
Total of IBNR liabilities plus expected development on reported claims	$ 253,849
Cumulative number of reported claims | claims	84,895
Insurance | Third party occurrence business | 2020
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 616,910	607,249
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	76,743	24,509
Total of IBNR liabilities plus expected development on reported claims	$ 428,750
Cumulative number of reported claims | claims	89,560
Insurance | Third party occurrence business | 2021
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 622,713
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	26,301
Total of IBNR liabilities plus expected development on reported claims	$ 543,386
Cumulative number of reported claims | claims	65,477
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	$ 3,353,974
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,804,720
All outstanding liabilities before 2012, net of reinsurance	64,171
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	286,118	285,527	285,163	277,683	275,665	291,316	313,907	318,453	320,207	317,654
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	260,173	255,337	251,313	227,389	209,295	190,395	164,724	121,211	69,069	17,718
Total of IBNR liabilities plus expected development on reported claims	$ 11,570
Cumulative number of reported claims | claims	15,576
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	$ 273,948	271,501	281,996	291,205	294,674	320,524	324,442	320,659	301,956
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	247,078	245,687	238,951	217,132	198,008	179,395	137,963	87,458	19,032
Total of IBNR liabilities plus expected development on reported claims	$ 11,739
Cumulative number of reported claims | claims	15,696
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	$ 288,318	292,247	298,017	282,058	279,043	299,104	279,846	264,537
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	249,960	243,791	229,958	208,074	173,089	129,712	63,312	13,817
Total of IBNR liabilities plus expected development on reported claims	$ 22,336
Cumulative number of reported claims | claims	15,676
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	$ 267,925	252,478	255,432	260,063	276,492	277,615	258,989
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	216,986	193,186	174,161	126,499	100,089	52,046	9,066
Total of IBNR liabilities plus expected development on reported claims	$ 20,617
Cumulative number of reported claims | claims	14,724
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	$ 327,230	322,042	314,747	308,453	291,645	275,394
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	242,431	205,596	158,230	127,286	68,226	10,568
Total of IBNR liabilities plus expected development on reported claims	$ 42,509
Cumulative number of reported claims | claims	15,749
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	$ 323,854	308,917	312,554	286,565	271,088
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	196,125	143,340	113,208	67,669	9,306
Total of IBNR liabilities plus expected development on reported claims	$ 60,718
Cumulative number of reported claims | claims	16,404
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	$ 337,083	320,653	315,085	273,521
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	158,709	118,361	68,424	12,287
Total of IBNR liabilities plus expected development on reported claims	$ 85,411
Cumulative number of reported claims | claims	15,854
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	$ 318,498	318,469	290,217
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	122,362	65,477	12,418
Total of IBNR liabilities plus expected development on reported claims	$ 119,673
Cumulative number of reported claims | claims	12,982
Insurance | Third party claims-made business | 2020
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 414,580	384,852
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	87,547	17,161
Total of IBNR liabilities plus expected development on reported claims	$ 240,888
Cumulative number of reported claims | claims	10,049
Insurance | Third party claims-made business | 2021
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 516,420
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	23,349
Total of IBNR liabilities plus expected development on reported claims	$ 435,910
Cumulative number of reported claims | claims	8,550
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	$ 4,479,691
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	3,376,225
All outstanding liabilities before 2012, net of reinsurance	22,375
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	243,849	245,260	245,205	248,310	248,066	256,379	257,240	259,582	265,479	254,684
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	239,928	240,191	237,221	233,862	232,640	223,798	209,916	190,754	166,414	$ 78,523
Total of IBNR liabilities plus expected development on reported claims	$ 2,057
Cumulative number of reported claims | claims	55,219
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	$ 246,682	247,443	250,252	254,916	253,554	265,672	265,594	274,285	266,089
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	239,831	238,792	237,863	235,801	226,769	214,941	181,721	151,897	$ 86,911
Total of IBNR liabilities plus expected development on reported claims	$ 3,461
Cumulative number of reported claims | claims	71,613
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	$ 310,097	311,097	314,300	318,297	319,418	319,706	327,098	303,053
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	295,551	294,049	292,638	282,104	267,959	235,079	197,609	$ 108,003
Total of IBNR liabilities plus expected development on reported claims	$ 5,770
Cumulative number of reported claims | claims	109,575
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	$ 347,669	349,895	357,123	365,362	357,364	358,587	335,250
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	330,872	327,082	321,395	306,313	278,265	236,516	$ 138,393
Total of IBNR liabilities plus expected development on reported claims	$ 7,201
Cumulative number of reported claims | claims	148,924
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	$ 408,621	410,610	416,724	428,579	431,760	409,367
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	385,890	379,885	363,392	342,345	305,250	$ 176,238
Total of IBNR liabilities plus expected development on reported claims	$ 11,032
Cumulative number of reported claims | claims	175,261
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	$ 505,135	501,753	492,166	502,068	483,414
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	446,749	424,219	381,419	343,049	$ 181,454
Total of IBNR liabilities plus expected development on reported claims	$ 16,867
Cumulative number of reported claims | claims	219,810
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	$ 566,283	563,969	565,717	513,466
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	480,852	443,644	390,009	$ 212,316
Total of IBNR liabilities plus expected development on reported claims	$ 32,467
Cumulative number of reported claims | claims	247,052
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	$ 641,832	613,673	568,337
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	488,094	386,894	$ 212,629
Total of IBNR liabilities plus expected development on reported claims	$ 63,880
Cumulative number of reported claims | claims	235,824
Insurance | Multi-line and other specialty | 2020
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 572,265	622,241
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	311,112	$ 173,123
Total of IBNR liabilities plus expected development on reported claims	$ 192,056
Cumulative number of reported claims | claims	149,004
Insurance | Multi-line and other specialty | 2021
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 637,258
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	157,346
Total of IBNR liabilities plus expected development on reported claims	$ 361,237
Cumulative number of reported claims | claims	75,250

Short Duration Contracts - Cl_2

Short Duration Contracts - Claims development - Reinsurance (Details) - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017	Dec. 31, 2016	Dec. 31, 2015	Dec. 31, 2014	Dec. 31, 2013	Dec. 31, 2012
Claims Development [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance	$ 11,886,330
Reinsurance | Casualty
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	2,815,578
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,006,894
All outstanding liabilities before 2012, net of reinsurance	297,823
Reinsurance | Casualty | 2012
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	119,222	$ 120,260	$ 121,721	$ 118,457	$ 109,788	$ 115,131	$ 125,104	$ 137,049	$ 141,202	$ 143,029
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	79,364	75,833	69,877	59,511	47,807	36,562	25,523	14,690	8,486	1,306
Total of IBNR liabilities plus expected development on reported claims	24,441
Reinsurance | Casualty | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	135,959	135,762	131,475	135,155	136,717	148,784	155,066	159,257	166,016
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	81,856	76,703	70,803	63,136	54,567	43,069	23,044	9,930	2,480
Total of IBNR liabilities plus expected development on reported claims	30,873
Reinsurance | Casualty | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	236,378	240,067	239,765	230,019	233,552	219,355	222,109	216,882
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	145,376	134,529	114,456	91,098	63,441	40,804	16,061	3,920
Total of IBNR liabilities plus expected development on reported claims	41,077
Reinsurance | Casualty | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	252,809	249,029	242,180	238,126	230,830	221,922	223,208
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	138,035	120,566	96,835	71,098	47,288	20,275	4,463
Total of IBNR liabilities plus expected development on reported claims	57,345
Reinsurance | Casualty | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	272,689	273,266	266,254	251,415	227,534	215,222
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	132,814	113,835	86,798	51,684	25,649	5,739
Total of IBNR liabilities plus expected development on reported claims	54,087
Reinsurance | Casualty | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	313,605	301,616	273,166	257,088	270,728
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	137,921	113,307	64,075	30,360	6,429
Total of IBNR liabilities plus expected development on reported claims	66,450
Reinsurance | Casualty | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	290,955	285,646	294,820	281,141
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	129,196	106,571	31,218	7,580
Total of IBNR liabilities plus expected development on reported claims	66,572
Reinsurance | Casualty | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	374,002	348,015	336,062
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	96,935	57,643	15,815
Total of IBNR liabilities plus expected development on reported claims	120,045
Reinsurance | Casualty | 2020
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	374,912	386,684
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	50,603	17,730
Total of IBNR liabilities plus expected development on reported claims	234,251
Reinsurance | Casualty | 2021
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	445,047
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	14,794
Total of IBNR liabilities plus expected development on reported claims	392,885
Reinsurance | Property catastrophe
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	880,759
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	396,960
All outstanding liabilities before 2012, net of reinsurance	2,449
Reinsurance | Property catastrophe | 2012
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	96,447	96,531	97,145	97,037	99,071	99,885	102,114	108,590	122,942	149,957
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	95,606	95,414	95,312	94,625	94,015	92,886	90,727	83,822	70,832	25,850
Total of IBNR liabilities plus expected development on reported claims	105
Reinsurance | Property catastrophe | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	27,657	27,865	27,727	28,617	29,345	31,902	36,401	47,780	67,257
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	28,346	28,597	27,892	27,891	27,652	25,894	24,038	19,201	12,200
Total of IBNR liabilities plus expected development on reported claims	(138)
Reinsurance | Property catastrophe | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	19,615	19,841	19,945	20,652	22,412	25,296	30,877	45,159
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	19,241	19,154	19,013	18,821	19,231	18,402	19,939	13,622
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	2,920	3,130	3,775	5,585	11,580	18,075	33,579
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,781	1,705	1,616	2,050	1,786	(2,518)	(3,152)
Total of IBNR liabilities plus expected development on reported claims	67
Reinsurance | Property catastrophe | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	7,426	8,362	10,772	14,575	18,719	25,641
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	3,668	3,312	4,082	2,796	2,521	(6,722)
Total of IBNR liabilities plus expected development on reported claims	881
Reinsurance | Property catastrophe | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	25,121	36,846	50,553	54,768	87,504
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	14,969	27,797	37,791	32,228	30,704
Total of IBNR liabilities plus expected development on reported claims	(712)
Reinsurance | Property catastrophe | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	27,657	41,642	60,418	77,868
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	(4,612)	24,259	12,506	27,497
Total of IBNR liabilities plus expected development on reported claims	4,783
Reinsurance | Property catastrophe | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	23,534	24,808	38,570
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	18,134	12,680	3,834
Total of IBNR liabilities plus expected development on reported claims	4,576
Reinsurance | Property catastrophe | 2020
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	334,185	267,750
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	155,063	53,275
Total of IBNR liabilities plus expected development on reported claims	40,561
Reinsurance | Property catastrophe | 2021
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	316,197
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	64,764
Total of IBNR liabilities plus expected development on reported claims	61,821
Reinsurance | Property excluding property catastrophe
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	2,081,611
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,365,172
All outstanding liabilities before 2012, net of reinsurance	7,595
Reinsurance | Property excluding property catastrophe | 2012
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	103,367	102,994	108,436	111,001	112,477	114,699	119,124	123,689	121,808	156,162
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	102,525	102,504	102,598	102,658	103,480	102,844	101,868	93,198	78,080	26,153
Total of IBNR liabilities plus expected development on reported claims	508
Reinsurance | Property excluding property catastrophe | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	62,782	63,269	62,504	63,702	64,486	66,208	70,558	76,905	115,473
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	62,139	62,113	61,183	55,676	53,796	52,997	49,816	42,737	25,993
Total of IBNR liabilities plus expected development on reported claims	384
Reinsurance | Property excluding property catastrophe | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	80,940	82,408	84,130	88,438	90,710	99,328	117,448	143,464
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	78,268	78,567	78,657	78,274	76,634	71,692	62,800	23,496
Total of IBNR liabilities plus expected development on reported claims	923
Reinsurance | Property excluding property catastrophe | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	173,659	177,281	188,343	189,045	184,774	189,109	215,095
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	159,925	159,675	166,025	160,848	149,814	119,237	75,622
Total of IBNR liabilities plus expected development on reported claims	8,482
Reinsurance | Property excluding property catastrophe | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	137,579	140,681	136,868	138,375	146,307	177,039
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	115,102	112,838	104,984	99,428	95,616	33,400
Total of IBNR liabilities plus expected development on reported claims	12,700
Reinsurance | Property excluding property catastrophe | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	216,358	233,153	240,749	253,859	271,713
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	181,628	166,087	158,066	125,768	27,569
Total of IBNR liabilities plus expected development on reported claims	13,045
Reinsurance | Property excluding property catastrophe | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	214,942	238,052	242,069	225,638
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	169,054	153,944	108,863	30,047
Total of IBNR liabilities plus expected development on reported claims	11,593
Reinsurance | Property excluding property catastrophe | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	196,840	206,997	216,653
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	150,931	124,222	43,230
Total of IBNR liabilities plus expected development on reported claims	17,777
Reinsurance | Property excluding property catastrophe | 2020
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	343,078	371,752
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	208,888	101,969
Total of IBNR liabilities plus expected development on reported claims	51,075
Reinsurance | Property excluding property catastrophe | 2021
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	552,066
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	136,712
Total of IBNR liabilities plus expected development on reported claims	255,343
Reinsurance | Marine and aviation
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	425,590
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	196,564
All outstanding liabilities before 2012, net of reinsurance	16,855
Reinsurance | Marine and aviation | 2012
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	40,016	41,182	43,028	46,046	49,727	51,079	52,286	55,053	58,868	58,992
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	38,116	38,131	38,038	37,746	36,257	35,055	33,313	27,528	11,433	2,658
Total of IBNR liabilities plus expected development on reported claims	1,005
Reinsurance | Marine and aviation | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	27,605	30,316	33,970	34,415	35,157	35,251	36,653	37,668	38,881
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	23,753	23,786	24,049	23,672	22,398	21,388	18,415	13,731	4,945
Total of IBNR liabilities plus expected development on reported claims	2,394
Reinsurance | Marine and aviation | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	21,984	22,031	23,310	23,677	25,674	27,373	29,159	30,958
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	16,036	15,956	15,080	14,645	12,469	11,590	7,985	4,177
Total of IBNR liabilities plus expected development on reported claims	4,909
Reinsurance | Marine and aviation | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	27,680	28,464	30,789	31,736	31,790	37,505	33,646
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	22,445	22,306	22,629	20,861	19,023	13,418	7
Total of IBNR liabilities plus expected development on reported claims	3,867
Reinsurance | Marine and aviation | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	15,019	16,969	19,273	23,567	22,747	27,351
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	6,767	5,864	3,261	521	(1,687)	(7,333)
Total of IBNR liabilities plus expected development on reported claims	6,708
Reinsurance | Marine and aviation | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	19,903	20,827	23,830	26,346	28,800
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	11,632	11,030	9,367	6,541	1,660
Total of IBNR liabilities plus expected development on reported claims	6,387
Reinsurance | Marine and aviation | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	24,756	24,615	26,084	28,017
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	13,585	11,236	6,968	2,005
Total of IBNR liabilities plus expected development on reported claims	6,452
Reinsurance | Marine and aviation | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	60,983	55,307	48,929
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	29,068	21,580	10,756
Total of IBNR liabilities plus expected development on reported claims	15,112
Reinsurance | Marine and aviation | 2020
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	76,598	83,457
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	26,519	9,220
Total of IBNR liabilities plus expected development on reported claims	36,671
Reinsurance | Marine and aviation | 2021
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	111,046
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	8,643
Total of IBNR liabilities plus expected development on reported claims	89,459
Reinsurance | Other specialty
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	2,946,010
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,971,982
All outstanding liabilities before 2012, net of reinsurance	7,777
Reinsurance | Other specialty | 2012
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	179,364	181,246	189,193	194,726	196,539	193,882	196,138	202,046	211,839	222,558
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	173,494	173,606	173,305	171,519	167,164	163,160	155,445	144,429	121,679	$ 45,663
Total of IBNR liabilities plus expected development on reported claims	2,392
Reinsurance | Other specialty | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	201,830	204,894	210,825	211,261	213,614	212,721	216,250	226,032	252,744
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	186,956	184,111	183,772	176,483	171,189	161,608	145,521	119,445	$ 57,317
Total of IBNR liabilities plus expected development on reported claims	6,409
Reinsurance | Other specialty | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	237,478	243,652	248,083	246,393	251,474	258,114	256,332	274,826
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	219,060	215,597	212,991	201,974	195,433	182,184	146,652	$ 68,869
Total of IBNR liabilities plus expected development on reported claims	7,857
Reinsurance | Other specialty | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	182,162	193,626	196,840	196,521	199,468	201,057	209,764
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	164,471	162,314	154,369	145,419	138,350	114,382	$ 54,359
Total of IBNR liabilities plus expected development on reported claims	8,549
Reinsurance | Other specialty | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	210,344	215,614	209,564	215,078	220,661	223,191
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	189,411	186,247	174,403	162,661	138,648	$ 65,055
Total of IBNR liabilities plus expected development on reported claims	13,182
Reinsurance | Other specialty | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	241,598	245,505	247,203	258,419	269,254
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	205,998	199,051	192,274	164,829	$ 73,366
Total of IBNR liabilities plus expected development on reported claims	30,855
Reinsurance | Other specialty | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	324,536	308,190	316,231	320,538
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	245,330	231,358	201,732	$ 71,167
Total of IBNR liabilities plus expected development on reported claims	40,807
Reinsurance | Other specialty | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	326,168	341,409	360,854
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	216,647	158,132	$ 79,718
Total of IBNR liabilities plus expected development on reported claims	51,165
Reinsurance | Other specialty | 2020
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	460,084	533,861
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	243,980	$ 97,617
Total of IBNR liabilities plus expected development on reported claims	102,130
Reinsurance | Other specialty | 2021
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	582,446
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	126,635
Total of IBNR liabilities plus expected development on reported claims	$ 300,667

Short Duration Contracts - Cl_3

Short Duration Contracts - Claims development - Mortgage (Details) $ in Thousands	Dec. 31, 2021USD ($)claims	Dec. 31, 2020USD ($)	Dec. 31, 2019USD ($)	Dec. 31, 2018USD ($)	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	$ 11,886,330
Mortgage
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	2,268,206
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	1,593,806
All outstanding liabilities before 2012, net of reinsurance	14,288
Mortgage | 2012
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	456,362	$ 456,331	$ 456,286	$ 458,065	$ 459,467	$ 467,296	$ 469,238	$ 475,317	$ 480,592	$ 520,835
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	453,986	453,587	452,348	448,151	441,577	426,024	395,695	327,605	186,605	$ (106,065)
Total of IBNR liabilities plus expected development on reported claims	$ 1
Cumulative number of paid claims | claims	15,080
Mortgage | 2013
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 391,324	391,062	390,987	393,149	395,693	405,809	411,793	419,668	469,311
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	387,879	387,894	386,853	382,200	373,909	353,189	308,956	203,957	$ 41,447
Total of IBNR liabilities plus expected development on reported claims	$ 1
Cumulative number of paid claims | claims	9,468
Mortgage | 2014
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 262,829	262,682	261,091	265,992	266,027	279,434	297,151	316,095
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	256,875	256,285	254,175	247,038	233,879	201,925	129,159	$ 20,099
Total of IBNR liabilities plus expected development on reported claims	$ 4
Cumulative number of paid claims | claims	6,299
Mortgage | 2015
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 190,560	190,913	189,235	194,677	198,001	197,238	222,790
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	184,025	183,472	180,321	171,337	151,222	92,431	$ 16,159
Total of IBNR liabilities plus expected development on reported claims	$ 1
Cumulative number of paid claims | claims	4,554
Mortgage | 2016
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 141,657	142,392	140,608	148,715	170,532	183,556
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	131,717	131,161	127,286	113,357	72,201	$ 11,462
Total of IBNR liabilities plus expected development on reported claims	$ 1
Cumulative number of paid claims | claims	3,424
Mortgage | 2017
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 109,242	108,181	107,255	132,220	179,376
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	89,756	87,317	78,650	48,112	$ 8,622
Total of IBNR liabilities plus expected development on reported claims	$ 1
Cumulative number of paid claims | claims	2,474
Mortgage | 2018
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 87,962	89,120	96,357	132,318
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	55,853	50,135	31,478	$ 3,966
Total of IBNR liabilities plus expected development on reported claims	$ 60
Cumulative number of paid claims | claims	1,635
Mortgage | 2019
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 110,362	119,253	108,424
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	29,102	20,105	$ 2,899
Total of IBNR liabilities plus expected development on reported claims	$ 181
Cumulative number of paid claims | claims	851
Mortgage | 2020
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 373,533	420,003
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	4,144	$ 1,040
Total of IBNR liabilities plus expected development on reported claims	$ 2,686
Cumulative number of paid claims | claims	189
Mortgage | 2021
Claims Development [Line Items]
Incurred losses and allocated loss adjustment expenses, net of reinsurance	$ 144,375
Cumulative paid losses and allocated loss adjustment expenses, net of reinsurance	469
Total of IBNR liabilities plus expected development on reported claims	$ 2,246
Cumulative number of paid claims | claims	11

Short Duration Contracts - Perc

Short Duration Contracts - Percentage annual payout - all segments (Details)	Dec. 31, 2021
Insurance | Property, energy, marine and aviation
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	19.30%
Year Two	43.50%
Year Three	19.10%
Year Four	6.60%
Year Five	1.40%
Year Six	2.30%
Year Seven	3.20%
Year Eight	0.50%
Year Nine	0.30%
Year Ten	0.20%
Insurance | Third party occurrence business
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	3.30%
Year Two	9.30%
Year Three	11.60%
Year Four	11.00%
Year Five	9.80%
Year Six	8.70%
Year Seven	5.40%
Year Eight	4.10%
Year Nine	3.50%
Year Ten	2.10%
Insurance | Third party claims-made business
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	4.40%
Year Two	18.00%
Year Three	17.80%
Year Four	12.30%
Year Five	12.70%
Year Six	7.90%
Year Seven	7.00%
Year Eight	4.30%
Year Nine	1.00%
Year Ten	1.70%
Insurance | Multi-line and other specialty
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	34.70%
Year Two	29.50%
Year Three	11.00%
Year Four	8.60%
Year Five	4.60%
Year Six	2.80%
Year Seven	0.70%
Year Eight	0.70%
Year Nine	0.80%
Year Ten	(0.10%)
Reinsurance | Casualty
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	2.50%
Year Two	7.30%
Year Three	11.60%
Year Four	11.30%
Year Five	9.60%
Year Six	8.40%
Year Seven	7.70%
Year Eight	5.90%
Year Nine	4.40%
Year Ten	3.00%
Reinsurance | Property catastrophe
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	21.60%
Year Two	30.00%
Year Three	32.80%
Year Four	(14.20%)
Year Five	(11.60%)
Year Six	2.20%
Year Seven	1.00%
Year Eight	1.20%
Year Nine	(0.40%)
Year Ten	0.20%
Reinsurance | Property catastrophe and property other than property catastrophe
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	26.70%
Year Two	38.90%
Year Three	13.30%
Year Four	5.80%
Year Five	3.40%
Year Six	0.40%
Year Seven	2.00%
Year Eight	0.40%
Year Nine	0.00%
Year Ten	0.00%
Reinsurance | Marine and aviation
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	4.90%
Year Two	26.90%
Year Three	19.00%
Year Four	10.30%
Year Five	7.40%
Year Six	2.90%
Year Seven	2.40%
Year Eight	0.00%
Year Nine	0.10%
Year Ten	0.00%
Reinsurance | Other specialty
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	26.30%
Year Two	34.20%
Year Three	12.90%
Year Four	5.20%
Year Five	4.20%
Year Six	3.10%
Year Seven	2.10%
Year Eight	0.90%
Year Nine	0.80%
Year Ten	(0.10%)
Mortgage
Short-duration Insurance Contracts, Historical Claims Duration [Line Items]
Year One	2.70%
Year Two	34.90%
Year Three	25.30%
Year Four	10.50%
Year Five	4.40%
Year Six	2.10%
Year Seven	0.90%
Year Eight	0.50%
Year Nine	0.10%
Year Ten	0.10%

Short Duration Contracts - Reco

Short Duration Contracts - Reconciliation of claims development to liability (Details) - USD ($) $ in Thousands		Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		$ 11,886,330
Unpaid losses and loss adjustment expenses recoverable		5,599,231	$ 4,314,855	$ 4,082,650	$ 2,814,291
Lines other than short duration		76,240
Discounting		(55,575)
Unallocated claims adjustment expenses		225,033
Total reconciling items		245,698
Reserve for losses and loss adjustment expenses		17,757,156	$ 16,513,929	$ 13,891,842	$ 11,853,297
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	[1]	390,100
Total for short duration lines
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Unpaid losses and loss adjustment expenses recoverable		5,625,128
Operating segments | 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		441,459
Unpaid losses and loss adjustment expenses recoverable	[1]	887,457
Operating segments | 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		586,885
Unpaid losses and loss adjustment expenses recoverable		354,432
Operating segments | 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		2,885,557
Unpaid losses and loss adjustment expenses recoverable		1,537,549
Operating segments | 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		1,613,425
Unpaid losses and loss adjustment expenses recoverable		921,086
Operating segments | 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		1,125,841
Unpaid losses and loss adjustment expenses recoverable		199,485
Operating segments | Reinsurance | Casualty
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		2,106,507
Unpaid losses and loss adjustment expenses recoverable		592,879
Operating segments | 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		486,248
Unpaid losses and loss adjustment expenses recoverable		484,598
Operating segments | 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		724,034
Unpaid losses and loss adjustment expenses recoverable		118,939
Operating segments | 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		245,881
Unpaid losses and loss adjustment expenses recoverable		111,298
Operating segments | 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		981,805
Unpaid losses and loss adjustment expenses recoverable		373,292
Operating segments | Mortgage
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Liabilities for losses and loss adjustment expenses, net of reinsurance		688,688
Unpaid losses and loss adjustment expenses recoverable		48,259
Consolidating adjustments and eliminations
Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Line Items]
Unpaid losses and loss adjustment expenses recoverable		$ (4,146)
[1]	Includes unpaid loss and loss adjustment expenses recoverable of $390.1 million related to the loss portfolio transfer reinsurance agreements.

Short Duration Contracts (Detai

Short Duration Contracts (Details)	12 Months Ended
	Dec. 31, 2021USD ($)
Mortgage
Claims Development [Line Items]
Large claim size threshold	$ 250,000

Allowance for Expected Credit_3

Allowance for Expected Credit Losses - Premiums receivable (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2021	Dec. 31, 2020
Credit Loss [Abstract]
Balance at beginning of period		$ 2,064,586	$ 1,778,717
Balance at end of period		2,633,280	2,064,586
Allowance for Expected Credit Losses
Balance at beginning of period		37,781	21,003
Cumulative effect of accounting change	[1]		6,539
Change for provision of expected credit losses	[2]	2,177	10,239
Balance at end of period		39,958	37,781
Write-offs charged against the allowance		$ 3,800	$ 2,800
[1]	Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”
[2]	Amounts deemed uncollectible are written-off in operating expenses. For the 2021 and 2020 periods, amounts written off totaled $3.8 million and $2.8 million, respectively

Allowance for Expected Credit_4

Allowance for Expected Credit Losses - Reinsurance recoverables (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2021	Dec. 31, 2020
Credit Loss [Abstract]
Balance at beginning of period		$ 4,500,802	$ 4,346,816
Balance at end of period		5,880,735	4,500,802
Allowance for Expected Credit Losses
Balance at beginning of period		11,636	1,364
Cumulative effect of accounting change	[1]		12,010
Change for provision of expected credit losses		1,594	(1,738)
Balance at end of period		$ 13,230	$ 11,636
[1]	Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”

Allowance for Expected Credit_5

Allowance for Expected Credit Losses - Ceded credit risk (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Concentration Risk [Line Items]
Reinsurance recoverable for paid and unpaid claims and claims adjustments		$ 5,880,735	$ 4,500,802	$ 4,346,816
Shareholders' equity | Reinsurer concentration risk | Largest balance due from any one carrier
Concentration Risk [Line Items]
Concentration risk percentage	[1]	6.70%	1.80%
AM Best "A-" Or Better Rating | Reinsurance recoverable | Reinsurer concentration risk
Concentration Risk [Line Items]
Concentration risk percentage		69.70%	63.90%
Rating Below A- | Reinsurance recoverable | Reinsurer concentration risk | All Other Carriers
Concentration Risk [Line Items]
Concentration risk percentage		0.10%	0.10%
No AM Best rating | Reinsurance recoverable | Reinsurer concentration risk | All Other Carriers
Concentration Risk [Line Items]
Concentration risk percentage	[2]	30.20%	36.00%
No AM Best rating | Reinsurance recoverable | Reinsurer concentration risk | Reinsurance trusts or letters of credit
Concentration Risk [Line Items]
Concentration risk percentage		91.00%	94.00%
[1]	The 2021 period included impact of deconsolidation of Somers.
[2]	At December 31, 2021 and 2020 period, over 91% and 94% of such amount is collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively

Allowance for Expected Credit_6

Allowance for Expected Credit Losses - Contractholder receivables (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2021	Dec. 31, 2020
Credit Loss [Abstract]
Balance at beginning of period		$ 1,986,924	$ 2,119,460
Balance at end of period		1,828,691	1,986,924
Allowance for Expected Credit Losses
Balance at beginning of period		8,638	0
Cumulative effect of accounting change	[1]		6,663
Change for provision of expected credit losses		(5,201)	1,975
Balance at end of period		$ 3,437	$ 8,638
[1]	Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”

Reinsurance - Effects of reinsu

Reinsurance - Effects of reinsurance (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Premiums Written
Direct	$ 7,706,832	$ 6,553,910	$ 5,681,523
Assumed	5,045,655	3,534,158	2,457,437
Ceded	(3,734,150)	(2,650,352)	(2,099,893)
Net premiums written	9,018,337	7,437,716	6,039,067
Premiums Earned
Direct	7,149,794	6,361,451	5,447,829
Assumed	4,333,873	3,213,873	2,337,950
Ceded	(3,401,369)	(2,583,389)	(1,999,281)
Net premiums earned	8,082,298	6,991,935	5,786,498
Losses and Loss Adjustment Expenses
Direct	4,266,758	4,392,392	2,953,072
Assumed	2,826,820	2,204,323	1,602,528
Ceded	(2,508,775)	(1,907,116)	(1,422,148)
Net	$ 4,584,803	$ 4,689,599	$ 3,133,452

Reinsurance - Coverage and rete

Reinsurance - Coverage and retention (Details) - Variable Interest Entity, Not Primary Beneficiary $ in Thousands	12 Months Ended
	Dec. 31, 2021USD ($)
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	$ 6,626,664
Current Coverage	4,649,174
Remaining Retention, Net	$ 1,864,823
Amortization period	10 years
Bellemeade 2017-1 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	$ 368,114	[1]
Current Coverage	108,368	[1]
Remaining Retention, Net	125,926	[1]
Bellemeade 2018-1 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	374,460	[2]
Current Coverage	181,136	[2]
Remaining Retention, Net	122,118	[2]
Bellemeade 2018-3 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	506,110	[3]
Current Coverage	302,563	[3]
Remaining Retention, Net	128,020	[3]
Bellemeade 2019-1 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	341,790	[4]
Current Coverage	181,324	[4]
Remaining Retention, Net	97,845	[4]
Bellemeade 2019-2 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	621,022	[5]
Current Coverage	398,316	[5]
Remaining Retention, Net	156,419	[5]
Bellemeade 2019-3 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	700,920	[6]
Current Coverage	409,859	[6]
Remaining Retention, Net	181,583	[6]
Bellemeade 2019-4 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	577,267	[7]
Current Coverage	411,954	[7]
Remaining Retention, Net	116,292	[7]
Bellemeade 2020-2 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	449,167	[8]
Current Coverage	218,877	[8]
Remaining Retention, Net	222,567	[8]
Bellemeade 2020-2 Ltd | Funded By VIE
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	423,000
Bellemeade 2020-2 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	26,000
Bellemeade 2020-3 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	451,816	[9]
Current Coverage	365,141	[9]
Remaining Retention, Net	154,732	[9]
Bellemeade 2020-3 Ltd | Funded By VIE
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	418,000
Bellemeade 2020-3 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	34,000
Bellemeade 2020-4 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	337,013	[10]
Current Coverage	186,065	[10]
Remaining Retention, Net	129,824	[10]
Bellemeade 2020-4 Ltd | Funded By VIE
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	321,000
Bellemeade 2020-4 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	16,000
Bellemeade 2021-1 Ltd Member
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	643,577	[11]
Current Coverage	630,163	[11]
Remaining Retention, Net	149,189	[11]
Bellemeade 2021-1 Ltd Member | Funded By VIE
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	580,000
Bellemeade 2021-1 Ltd Member | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	64,000
Bellemeade 2021-2 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	616,017	[12]
Current Coverage	616,017	[12]
Remaining Retention, Net	139,763	[12]
Bellemeade 2021-2 Ltd | Funded By VIE
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	523,000
Bellemeade 2021-2 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	93,000
Bellemeade 2021-3 Ltd
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	639,391	[13]
Current Coverage	639,391	[13]
Remaining Retention, Net	140,545	[13]
Bellemeade 2021-3 Ltd | Funded By VIE
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	508,000
Bellemeade 2021-3 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance	$ 131,000
[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.
[8]	Issued in September 2020, covering in-force policies issued between January 1, 2020 and May 31, 2020. $423 million was directly funded by Bellemeade 2020-2 Ltd. with an additional $26 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers
[9]	Issued in November 2020, covering in-force policies issued between June 1, 2020 and August 31, 2020. $418 million was directly funded by Bellemeade 2020-3 Ltd. with an additional $34 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.
[10]	Issued in December 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $321 million was directly funded by Bellemeade 2020-4 Ltd. with an additional $16 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers
[11]	Issued in March 2021, covering in-force policies issued between September 1, 2020 and November 30, 2020. $580 million was directly funded by Bellemeade Re 2021-1 Ltd. with an additional $64 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.
[12]	Issued in June 2021, covering in-force policies issued between December 1, 2020 and March 31, 2021. $523 million was directly funded by Bellemeade Re 2021-2 Ltd. via insurance-linked notes, with an additional $93 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers
[13]	Issued in September 2021, covering in-force policies issued between April 1, 2021 and June 30, 2021. $508 million was directly funded by Bellemeade Re 2021-3 Ltd. via insurance-linked notes, with an additional $131 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers

Investment Information - Summar

Investment Information - Summary of available for sale securities (Details) - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020		Dec. 31, 2019
Available for sale securities:
Estimated fair value	$ 17,998,109	$ 18,717,825
Gross Unrealized Gains	198,691	657,620
Gross Unrealized Losses	(171,544)	(79,654)
Allowance for Expected Credit Losses	(2,883)	(2,397)
Cost or Amortized Cost	17,973,823	18,143,305
Short-term investments	1,734,716	1,924,922
Fair value of securities classified as available for sale	19,732,825	20,921,530
Short-term investments available for sale, at amortized cost	1,734,738	1,924,292
Cost or amortized cost of securities classified as available for sale	19,708,561	20,345,961
Fixed maturities and fixed maturities pledged under securities lending agreements
Available for sale securities:
Estimated fair value	17,998,109	18,996,608
Gross Unrealized Gains	198,123	654,927
Gross Unrealized Losses	(170,954)	(77,591)
Allowance for Expected Credit Losses	(2,883)	(2,397)		$ 0
Cost or Amortized Cost	17,973,823	18,421,669
Fixed maturities and fixed maturities pledged under securities lending agreements | Corporate bonds
Available for sale securities:
Estimated fair value	6,553,333	7,856,571
Gross Unrealized Gains	104,170	414,247	[1]
Gross Unrealized Losses	(69,194)	(34,388)	[1]
Allowance for Expected Credit Losses	(2,037)	(896)	[1],[2]
Cost or Amortized Cost	6,520,394	7,477,608
Fixed maturities and fixed maturities pledged under securities lending agreements | Mortgage backed securities
Available for sale securities:
Estimated fair value	408,477	630,001
Gross Unrealized Gains	2,825	8,939	[1]
Gross Unrealized Losses	(5,410)	(5,028)	[1]
Allowance for Expected Credit Losses	(48)	(278)	[1],[2]
Cost or Amortized Cost	411,110	626,368
Fixed maturities and fixed maturities pledged under securities lending agreements | Municipal bonds
Available for sale securities:
Estimated fair value	404,666	494,522
Gross Unrealized Gains	18,724	27,291	[1]
Gross Unrealized Losses	(1,409)	(3,835)	[1]
Allowance for Expected Credit Losses	(2)	(11)	[1],[2]	$ 0
Cost or Amortized Cost	387,353	471,077
Fixed maturities and fixed maturities pledged under securities lending agreements | Commercial mortgage backed securities
Available for sale securities:
Estimated fair value	1,046,484	389,900
Gross Unrealized Gains	1,740	8,722	[1]
Gross Unrealized Losses	(3,117)	(2,954)	[1]
Allowance for Expected Credit Losses	(6)	(122)	[1],[2]
Cost or Amortized Cost	1,047,867	384,254
Fixed maturities and fixed maturities pledged under securities lending agreements | US government and government agencies
Available for sale securities:
Estimated fair value	4,772,764	5,557,077
Gross Unrealized Gains	10,076	22,612	[1]
Gross Unrealized Losses	(45,967)	(12,611)	[1]
Allowance for Expected Credit Losses	0	0	[1],[2]
Cost or Amortized Cost	4,808,655	5,547,076
Fixed maturities and fixed maturities pledged under securities lending agreements | Non-US government securities
Available for sale securities:
Estimated fair value	2,120,294	2,433,733
Gross Unrealized Gains	54,048	153,891	[1]
Gross Unrealized Losses	(34,749)	(8,060)	[1]
Allowance for Expected Credit Losses	(82)	0	[1],[2]
Cost or Amortized Cost	2,101,077	2,287,902
Fixed maturities and fixed maturities pledged under securities lending agreements | Asset backed securities
Available for sale securities:
Estimated fair value	2,692,091	1,634,804
Gross Unrealized Gains	6,540	19,225	[1]
Gross Unrealized Losses	(11,108)	(10,715)	[1]
Allowance for Expected Credit Losses	(708)	(1,090)	[1],[2]
Cost or Amortized Cost	2,697,367	1,627,384
Short-term investments
Available for sale securities:
Gross Unrealized Gains	568	2,693
Gross Unrealized Losses	(590)	(2,063)
Allowance for Expected Credit Losses	0	0
Short-term investments	1,734,716	1,924,922
Short-term investments available for sale, at amortized cost	$ 1,734,738	$ 1,924,292
[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.” In 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions.
[2]	Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.

Investment Information - Aging

Investment Information - Aging of available for sale securities in an unrealized loss position (Details) - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020
Available for sale securities:
Estimated Fair Value - Less than 12 Months	$ 12,238,683	$ 3,788,763
Gross Unrealized Losses - Less than 12 Months	(157,279)	(76,067)
Estimated Fair Value - 12 Months or More	297,357	70,404
Gross Unrealized Losses - 12 Months or More	(14,265)	(3,587)
Estimated Fair Value - Total	12,536,040	3,859,167
Gross Unrealized Losses - Total	(171,544)	(79,654)
Fixed maturities and fixed maturities pledged under securities lending agreements
Available for sale securities:
Estimated Fair Value - Less than 12 Months	11,953,950	3,690,843
Gross Unrealized Losses - Less than 12 Months	(156,689)	(74,004)
Estimated Fair Value - 12 Months or More	297,357	70,404
Gross Unrealized Losses - 12 Months or More	(14,265)	(3,587)
Estimated Fair Value - Total	12,251,307	3,761,247
Gross Unrealized Losses - Total	(170,954)	(77,591)
Fixed maturities and fixed maturities pledged under securities lending agreements | Corporate bonds
Available for sale securities:
Estimated Fair Value - Less than 12 Months	3,639,582	747,442	[1]
Gross Unrealized Losses - Less than 12 Months	(63,938)	(33,086)	[1]
Estimated Fair Value - 12 Months or More	98,867	3,934	[1]
Gross Unrealized Losses - 12 Months or More	(5,256)	(1,302)	[1]
Estimated Fair Value - Total	3,738,449	751,376	[1]
Gross Unrealized Losses - Total	(69,194)	(34,388)	[1]
Fixed maturities and fixed maturities pledged under securities lending agreements | Mortgage backed securities
Available for sale securities:
Estimated Fair Value - Less than 12 Months	222,176	284,619	[1]
Gross Unrealized Losses - Less than 12 Months	(3,545)	(4,788)	[1]
Estimated Fair Value - 12 Months or More	46,809	3,637	[1]
Gross Unrealized Losses - 12 Months or More	(1,865)	(240)	[1]
Estimated Fair Value - Total	268,985	288,256	[1]
Gross Unrealized Losses - Total	(5,410)	(5,028)	[1]
Fixed maturities and fixed maturities pledged under securities lending agreements | Municipal bonds
Available for sale securities:
Estimated Fair Value - Less than 12 Months	26,665	67,937	[1]
Gross Unrealized Losses - Less than 12 Months	(385)	(3,835)	[1]
Estimated Fair Value - 12 Months or More	16,361	0	[1]
Gross Unrealized Losses - 12 Months or More	(1,024)	0	[1]
Estimated Fair Value - Total	43,026	67,937	[1]
Gross Unrealized Losses - Total	(1,409)	(3,835)	[1]
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	675,603	126,624	[1]
Gross Unrealized Losses - Less than 12 Months	(2,805)	(2,916)	[1]
Estimated Fair Value - 12 Months or More	5,908	2,655	[1]
Gross Unrealized Losses - 12 Months or More	(312)	(38)	[1]
Estimated Fair Value - Total	681,511	129,279	[1]
Gross Unrealized Losses - Total	(3,117)	(2,954)	[1]
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	4,211,621	1,285,907	[1]
Gross Unrealized Losses - Less than 12 Months	(44,180)	(12,611)	[1]
Estimated Fair Value - 12 Months or More	33,373	0	[1]
Gross Unrealized Losses - 12 Months or More	(1,787)	0	[1]
Estimated Fair Value - Total	4,244,994	1,285,907	[1]
Gross Unrealized Losses - Total	(45,967)	(12,611)	[1]
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	1,511,301	543,844	[1]
Gross Unrealized Losses - Less than 12 Months	(31,983)	(7,658)	[1]
Estimated Fair Value - 12 Months or More	62,957	2,441	[1]
Gross Unrealized Losses - 12 Months or More	(2,766)	(402)	[1]
Estimated Fair Value - Total	1,574,258	546,285	[1]
Gross Unrealized Losses - Total	(34,749)	(8,060)	[1]
Fixed maturities and fixed maturities pledged under securities lending agreements | Asset backed securities
Available for sale securities:
Estimated Fair Value - Less than 12 Months	1,667,002	634,470	[1]
Gross Unrealized Losses - Less than 12 Months	(9,853)	(9,110)	[1]
Estimated Fair Value - 12 Months or More	33,082	57,737	[1]
Gross Unrealized Losses - 12 Months or More	(1,255)	(1,605)	[1]
Estimated Fair Value - Total	1,700,084	692,207	[1]
Gross Unrealized Losses - Total	(11,108)	(10,715)	[1]
Short-term investments
Available for sale securities:
Estimated Fair Value - Less than 12 Months	284,733	97,920
Gross Unrealized Losses - Less than 12 Months	(590)	(2,063)
Estimated Fair Value - 12 Months or More	0	0
Gross Unrealized Losses - 12 Months or More	0	0
Estimated Fair Value - Total	284,733	97,920
Gross Unrealized Losses - Total	$ (590)	$ (2,063)
[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.” In 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions.

Investment Information - Maturi

Investment Information - Maturity profile of available for sale securities (Details) - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020
Estimated Fair Value:
Estimated fair value	$ 17,998,109	$ 18,717,825
Amortized Cost:
Amortized cost	17,973,823	18,143,305
Fixed maturities and fixed maturities pledged under securities lending agreements
Estimated Fair Value:
Due in one year or less	300,889	348,200	[1]
Due after one year through five years	8,355,255	10,629,959	[1]
Due after five years through 10 years	4,689,155	4,881,564	[1]
Due after 10 years	505,758	482,180	[1]
Single maturity date	13,851,057	16,341,903	[1]
Estimated fair value	17,998,109	18,996,608
Amortized Cost:
Due in one year or less	299,772	339,951	[1]
Due after one year through five years	8,339,387	10,340,819	[1]
Due after five years through 10 years	4,684,393	4,654,754	[1]
Due after 10 years	493,927	448,139	[1]
Single maturity date	13,817,479	15,783,663	[1]
Amortized cost	17,973,823	18,421,669
Fixed maturities and fixed maturities pledged under securities lending agreements | Mortgage backed securities
Estimated Fair Value:
Securities without single maturity date	408,477	630,001	[1]
Estimated fair value	408,477	630,001
Amortized Cost:
Securities without single maturity date	411,110	626,368	[1]
Amortized cost	411,110	626,368
Fixed maturities and fixed maturities pledged under securities lending agreements | Commercial mortgage backed securities
Estimated Fair Value:
Securities without single maturity date	1,046,484	389,900	[1]
Estimated fair value	1,046,484	389,900
Amortized Cost:
Securities without single maturity date	1,047,867	384,254	[1]
Amortized cost	1,047,867	384,254
Fixed maturities and fixed maturities pledged under securities lending agreements | Asset backed securities
Estimated Fair Value:
Securities without single maturity date	2,692,091	1,634,804	[1]
Estimated fair value	2,692,091	1,634,804
Amortized Cost:
Securities without single maturity date	2,697,367	1,627,384	[1]
Amortized cost	$ 2,697,367	$ 1,627,384
[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.” In 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions.

Investment Information - Securi

Investment Information - Securities lending arrangements (Details) - USD ($)	Dec. 31, 2021	Dec. 31, 2020
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable	$ 0	$ 301,089,000
Gross amount of recognized liabilities for securities lending in offsetting disclosure in Note 11		0
Amounts related to securities lending not included in offsetting disclosure in Note 11		301,089,000
Collateral received under securities lending, at fair value	0	301,096,000
Cash and Cash Equivalents
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Collateral received under securities lending, at fair value	0	0
Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Collateral received under securities lending, at fair value	$ 0	301,100,000
US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		281,607,000
Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		3,021,000
Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		16,461,000
Overnight and Continuous
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		161,799,000
Overnight and Continuous | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		142,317,000
Overnight and Continuous | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		3,021,000
Overnight and Continuous | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		16,461,000
Less than 30 Days
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		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
Less than 30 Days | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		0
Less than 30 Days | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		0
30-90 Days
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		139,290,000
30-90 Days | US government and government agencies
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		139,290,000
30-90 Days | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		0
30-90 Days | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		0
90 Days or More
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		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
90 Days or More | Corporate bonds
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		0
90 Days or More | Equity securities
Transfer of Certain Financial Assets Accounted for as Secured Borrowings [Line Items]
Securities lending payable		$ 0

Investment Information - Net in

Investment Information - Net investment Income (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Net investment income:
Gross investment income		$ 477,123	$ 608,823	$ 716,643
Investment expenses		(88,005)	(89,215)	(88,905)
Net investment income		389,118	519,608	627,738
Fixed maturities
Net investment income:
Gross investment income		330,061	412,481	505,399
Term loan investments
Net investment income:
Gross investment income		34,843	84,149	98,949
Equity securities
Net investment income:
Gross investment income		42,396	28,958	15,857
Short-term investments
Net investment income:
Gross investment income		6,928	10,840	15,820
Other
Net investment income:
Gross investment income	[1]	$ 62,895	$ 72,395	$ 80,618
[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		12 Months Ended
		Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Net realized gains and losses:
Available for sale securities, gross gains on investment sales		$ 313,886	$ 595,941	$ 235,655
Available for sale securities, gross losses on investment sales		(156,791)	(117,282)	(104,612)
Equity securities at fair value, net realized gains (losses) on sales during the period		122,606	26,849	11,313
Equity securities at fair value, net unrealized gains (losses) on equity securities still held at reporting date		48,746	102,394	97,768
Allowance for credit losses - investment related		(2,100)	(3,597)	0
Allowance for credit losses - underwriting related		1,062	(10,007)	0
Net impairment losses		0	533
Net impairment losses				(3,165)
Derivative instruments		(32,390)	179,675	119,741
Other	[1]	(53,537)	3,575	(19,348)
Net realized gains (losses)		379,845	823,460	363,198
Greysbridge Holdings Ltd
Net realized gains and losses:
Gain (loss) on deconsolidation		(33,100)
Fixed maturities
Net realized gains and losses:
Change in fair value of assets and liabilities accounted for using the fair value option		7,953	15,881	41,910
Other investments
Net realized gains and losses:
Change in fair value of assets and liabilities accounted for using the fair value option		116,781	13,656	(35,734)
Equity securities
Net realized gains and losses:
Change in fair value of assets and liabilities accounted for using the fair value option		13,028	14,629	15,869
Short-term investments
Net realized gains and losses:
Change in fair value of assets and liabilities accounted for using the fair value option		$ 601	$ 2,279	$ 3,801
[1]	2021 periods reflected $33.1 million of losses related to the Company’sdeconsolidation of Somers

Investment Information - Other

Investment Information - Other investments and other investable assets (Details) - USD ($) $ in Thousands		Dec. 31, 2021	Dec. 31, 2020
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option		$ 1,973,550	$ 3,824,796
Other investable assets	[1]	0	500,000
Total other investments		1,973,550	4,324,796
Fixed maturities
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option		416,698	843,354
Other investments
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option		1,432,553	2,331,885
Short-term investments
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option		97,806	557,008
Equity securities
Fair Value, Option, Quantitative Disclosures [Line Items]
Investments accounted for using the fair value option		$ 26,493	$ 92,549
[1]	Participation interests in a receivable of a reverse repurchase agreement.

Investment Information - Othe_2

Investment Information - Other investments by strategy (Details) - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020
Schedule Of Other Investments [Line Items]
Investments accounted for using the fair value option	$ 1,973,550	$ 3,824,796
Other investments
Schedule Of Other Investments [Line Items]
Investments accounted for using the fair value option	1,432,553	2,331,885
Other investments | Lending
Schedule Of Other Investments [Line Items]
Investments accounted for using the fair value option	536,345	572,636
Other investments | Term loan investments
Schedule Of Other Investments [Line Items]
Investments accounted for using the fair value option	484,950	1,231,731
Other investments | Investment grade fixed income
Schedule Of Other Investments [Line Items]
Investments accounted for using the fair value option	147,810	138,646
Other investments | Private equity
Schedule Of Other Investments [Line Items]
Investments accounted for using the fair value option	91,126	48,750
Other investments | Energy
Schedule Of Other Investments [Line Items]
Investments accounted for using the fair value option	81,692	65,813
Other investments | Credit related funds
Schedule Of Other Investments [Line Items]
Investments accounted for using the fair value option	70,278	90,780
Other investments | Infrastructure
Schedule Of Other Investments [Line Items]
Investments accounted for using the fair value option	20,352	165,516
Other investments | Real estate
Schedule Of Other Investments [Line Items]
Investments accounted for using the fair value option	$ 0	$ 18,013

Investment Information - Equity

Investment Information - Equity method investments and investments in affiliates (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Balance sheet:
Total assets	$ 45,100,945	$ 43,282,297	$ 37,885,361
Total liabilities	31,545,816	29,294,856	25,569,809
Income statement:
Total revenues	9,249,980	8,508,509	6,925,967
Net income	2,239,462	1,465,711	1,693,300
Investments accounted for using the equity method	3,077,611	2,047,889
Equity in net income (loss) of investment funds accounted for using the equity method	366,402	146,693	123,672
Credit related funds
Income statement:
Investments accounted for using the equity method	1,022,334	740,060
Private equity
Income statement:
Investments accounted for using the equity method	436,042	235,289
Real estate
Income statement:
Investments accounted for using the equity method	396,395	258,518
Equity Funds
Income statement:
Investments accounted for using the equity method	395,090	343,058
Lending
Income statement:
Investments accounted for using the equity method	376,649	179,629
Infrastructure
Income statement:
Investments accounted for using the equity method	230,070	175,882
Energy
Income statement:
Investments accounted for using the equity method	119,141	115,453
Fixed income
Income statement:
Investments accounted for using the equity method	101,890	0
Equity Method Investment, Nonconsolidated Investee or Group of Investees [Member]
Balance sheet:
Invested assets	58,508,009	44,131,377
Total assets	69,648,905	49,078,464
Total liabilities	17,944,325	6,054,189
Net assets	51,704,580	43,024,275
Income statement:
Total revenues	11,785,949	5,762,098	164,669
Total expenses	3,238,606	1,656,029	528,762
Net income	$ 8,547,343	$ 4,106,069	$ (364,093)

Investment Information - Limite

Investment Information - Limited partnership interests (Details) - USD ($) $ in Thousands		Dec. 31, 2021	Dec. 31, 2020
Schedule of Equity Method Investments [Line Items]
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		$ 3,248,206	$ 2,232,609
Aggregate commitments		3,000,000	2,100,000
Equity method investments
Schedule of Equity Method Investments [Line Items]
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount	[1]	3,077,611	2,047,889
Aggregate commitments		2,600,000	1,800,000
Fair value option
Schedule of Equity Method Investments [Line Items]
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount	[2]	170,595	184,720
Aggregate commitments		$ 18,800	$ 35,600
[1]	Aggregate unfunded commitments were $2.6 billion at December 31, 2021, compared to $1.8 billion at December 31, 2020.
[2]	Aggregate unfunded commitments were $18.8 million at December 31, 2021, compared to $35.6 million at December 31, 2020.

Investment Information - Operat

Investment Information - Operating affiliates (Details) € / shares in Units, $ / shares in Units, $ in Thousands, € in Millions	12 Months Ended
	Dec. 31, 2021USD ($)	Dec. 31, 2020USD ($)	Dec. 31, 2019USD ($)	Dec. 31, 2021EUR (€)€ / shares	Dec. 30, 2021	Jul. 01, 2021$ / shares
Schedule of Equity Method Investments [Line Items]
Investment in operating affiliates	$ 1,135,655	$ 129,291
Income (loss) from operating affiliates	$ 264,693	$ 16,766	$ 2,233
Greysbridge Holdings Ltd | Kelso And Company
Schedule of Equity Method Investments [Line Items]
Percentage ownership						30.00%
Greysbridge Holdings Ltd | Warburg Pincus
Schedule of Equity Method Investments [Line Items]
Percentage ownership						30.00%
Coface
Schedule of Equity Method Investments [Line Items]
Percentage ownership	29.86%			29.86%	29.50%
Investment in affiliate, price per share | € / shares				€ 9.95
Equity method investment, aggregate cost	$ 546,000			€ 453
Operating affiliate gain on acquisition	74,500
Operating affiliates , deferred gain on acquisition	$ 36,000
Operating affiliates, deferred gain on acquisition, amortization period	5 years
Investment in operating affiliates	$ 630,500
Coface | Issued Shares Excluding Treasury Stock
Schedule of Equity Method Investments [Line Items]
Percentage ownership	30.10%			30.10%
Greysbridge Holdings Ltd
Schedule of Equity Method Investments [Line Items]
Percentage ownership						40.00%
Investment in affiliate, price per share | $ / shares						$ 35
Equity method investment, aggregate cost	$ 278,900
Operating affiliate gain on acquisition	95,700
Investment in operating affiliates	375,700
Gain (loss) on deconsolidation	$ (33,100)

Investment Information - Allowa

Investment Information - Allowance for expected credit losses (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2021		Dec. 31, 2020		Dec. 31, 2019
Debt Securities, Available-for-sale, Allowance for Credit Loss [Line Items]
Balance at beginning of period		$ 2,397
Additions for current-period provision for expected credit losses		2,100		$ 3,597		$ 0
Balance at end of period		2,883		2,397
Fixed maturities
Debt Securities, Available-for-sale, Allowance for Credit Loss [Line Items]
Balance at beginning of period		2,397		0
Cumulative effect of accounting change	[1]			634
Additions for current-period provision for expected credit losses		3,460		10,653
Additions (reductions) for previously recognized expected credit losses		(1,176)		(7,030)
Reductions due to disposals		(1,798)	[2]	(1,860)
Balance at end of period		2,883		2,397		0
Fixed maturities | Structured securities
Debt Securities, Available-for-sale, Allowance for Credit Loss [Line Items]
Balance at beginning of period	[3]	1,490		0
Cumulative effect of accounting change	[1],[3]			517
Additions for current-period provision for expected credit losses	[3]	602		2,942
Additions (reductions) for previously recognized expected credit losses	[3]	(847)		(1,398)
Reductions due to disposals	[3]	(443)	[2]	(571)
Balance at end of period	[3]	802		1,490		0
Fixed maturities | Municipal bonds
Debt Securities, Available-for-sale, Allowance for Credit Loss [Line Items]
Balance at beginning of period		11	[4],[5]	0
Cumulative effect of accounting change	[1]			0
Additions for current-period provision for expected credit losses		0		67
Additions (reductions) for previously recognized expected credit losses		(9)		6
Reductions due to disposals		0	[2]	(62)
Balance at end of period		2		11	[4],[5]	0
Fixed maturities | Corporate bonds
Debt Securities, Available-for-sale, Allowance for Credit Loss [Line Items]
Balance at beginning of period		896		0
Cumulative effect of accounting change	[1]			117
Additions for current-period provision for expected credit losses		2,858		7,644
Additions (reductions) for previously recognized expected credit losses		(320)		(5,638)
Reductions due to disposals		(1,355)	[2]	(1,227)
Balance at end of period		$ 2,079		$ 896		$ 0
[1]	Adoption of ASU 2016-13, “Financial Instruments - Credit Losses (Topic 326)”
[2]	Reduction for the 2021 periods primarily related to the Company’s deconsolidation of Somers.
[3]	Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.
[4]	Effective January 1, 2020, the Company adopted ASU 2016-13 and as a result any credit impairment losses on the Company’s available-for-sale investments are recorded as an allowance, subject to reversal.
[5]	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.” In 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions.

Investment Information - Restri

Investment Information - Restricted assets (Details) - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020
Restricted Assets [Line Items]
Restricted assets	$ 8,249,732	$ 8,733,309	[1]
Collateral or guarantees - affiliated transactions
Restricted Assets [Line Items]
Restricted assets	4,223,955	4,643,334
Collateral or guarantees - third party agreements
Restricted Assets [Line Items]
Restricted assets	2,721,160	3,083,324
Deposits with US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	798,100	827,552
Deposits with non-US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	$ 506,517	179,099
Somers Holdings Ltd.
Restricted Assets [Line Items]
Restricted assets		$ 1,036,000
[1]	2020 balances included $1.036 billion related to Somers.

Investment Information - Cash a

Investment Information - Cash and restricted cash (Details) - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Disclosure Investment Information [Abstract]
Cash	$ 858,668	$ 906,448	$ 726,230
Restricted cash (included in ‘other assets’)	456,103	384,096	177,468
Cash and restricted cash	$ 1,314,771	$ 1,290,544	$ 903,698	$ 724,643

Investment Information - Narrat

Investment Information - Narrative (Details) $ in Thousands	12 Months Ended
	Dec. 31, 2021USD ($)lots	Dec. 31, 2020USD ($)lots	Dec. 31, 2019USD ($)
Continuous unrealized loss, qualitative disclosures:
Number of positions in an unrealized loss position (lots) | lots	4,700	2,320
Total number of positions (lots) | lots	10,240	11,180
Largest single loss	$ 1,100	$ 900
Equity securities, at fair value	1,804,170	1,444,830
Equity Method Investment, Financial Statement, Reported Amounts [Abstract]
Equity in net income (loss) of investment funds accounted for using the equity method	$ 366,402	$ 146,693	$ 123,672
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

Fair Value - Fair Value Hierarc

Fair Value - Fair Value Hierarchy (Details) - Recurring - USD ($) $ in Thousands		Dec. 31, 2021	Dec. 31, 2020
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		$ 7,602,828	$ 9,280,391
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		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Residential Mortgage
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		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		4,744,517	5,463,356
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		0	0	[2]
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		0	0	[2]
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		0	0	[2]
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		0	0	[2]
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		4,744,517	5,463,356	[2]
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		0	0	[2]
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		0	0	[2]
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		1,052,822	1,920,565
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		1,762,864	1,401,653
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		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		42,625	494,817
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
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
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			164
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		528	420,131
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		21,745	23,373
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		20,352	51,149
Significant Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		14,923,923	15,724,091
Liabilities measured at fair value		(54,224)	(130,384)
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]	0	(21,679)
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		(54,224)	(108,705)
Significant Other Observable Inputs (Level 2) | Residential Mortgage
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		49,847
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		13,250,232	13,529,813
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		6,553,320	7,856,558	[2]
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		408,477	630,001	[2]
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		404,666	494,522	[2]
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		1,046,484	389,900	[2]
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		28,247	93,721	[2]
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		2,120,294	2,433,733	[2]
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		2,688,744	1,631,378	[2]
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		681,894	4,357
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		38,388	17,291
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		127,121	177,383
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		776,441	1,995,247
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		388,546	650,309
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			3,282
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			1,090
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
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		23,785	35,263
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		4,367	152,151
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		97,278	136,877
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		0	188
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		262,465	1,015,977
Significant Unobservable Inputs (Level 3)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		39,007	182,530
Liabilities measured at fair value		(16,960)	(461)
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		(16,960)	(461)
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		0	0
Significant Unobservable Inputs (Level 3) | Residential Mortgage
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		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		3,360	3,439
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		13	13	[2]
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		0	0	[2]
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		0	0	[2]
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		0	0	[2]
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		0	0	[2]
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		0	0	[2]
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		3,347	3,426	[2]
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) | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,918	42,015
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		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		32,729	137,076
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		0	985
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
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
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
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		4,748	68,988
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		27,981	67,103
Estimated Fair Value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		23,687,513	26,384,668
Liabilities measured at fair value		(71,184)	(130,845)
Estimated Fair Value | Contingent consideration liability
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(16,960)	(461)
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]	0	(21,679)
Estimated Fair Value | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(54,224)	(108,705)
Estimated Fair Value | Residential Mortgage
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		49,847
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		17,998,109	18,996,608
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		6,553,333	7,856,571	[2]
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		408,477	630,001	[2]
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		404,666	494,522	[2]
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		1,046,484	389,900	[2]
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		4,772,764	5,557,077	[2]
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		2,120,294	2,433,733	[2]
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		2,692,091	1,634,804	[2]
Estimated Fair Value | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,734,716	1,924,922
Estimated Fair Value | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,804,170	1,460,959
Estimated Fair Value | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		127,121	177,383
Estimated Fair Value | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,973,550	3,824,796
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		388,546	651,294
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			3,282
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			1,090
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			274
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		23,785	35,263
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		4,367	152,151
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		97,806	557,008
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		26,493	92,549
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		310,798	1,134,229
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	[3]	$ 1,121,755	$ 1,197,656
[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]	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.” In 2021, the Company terminated its securities lending program and no longer enters into securities lending agreements with financial institutions.
[3]	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, 2021		Dec. 31, 2020
Contingent consideration liability
Level 3 liabilities rollforward
Balance at beginning of year		$ (461)		$ (7,998)
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	0		(72)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0		0
Purchases, issuances, sales and settlements
Purchases		(16,494)		0
Issuances		0		0
Sales		0	[2]	0
Settlements		(5)		7,609
Transfers in and/or out of Level 3		0		0
Balance at end of year		(16,960)		(461)
Equity securities
Level 3 assets rollforward
Balance at beginning of year		42,015		55,889
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	1,958		8,214
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0		0
Purchases, issuances, sales and settlements
Purchases		5,718		4,030
Issuances		0		0
Sales		(46,773)	[2]	(26,118)
Settlements		0		0
Transfers in and/or out of Level 3		0		0
Balance at end of year		2,918		42,015
Available for sale | Structured securities
Level 3 assets rollforward
Balance at beginning of year	[3]	3,426		5,216
Total gains or (losses) (realized/unrealized) - included in earnings	[1],[3]	(135)		0
Total gains or (losses) (realized/unrealized) - included in other comprehensive income	[3]	133		(169)
Purchases, issuances, sales and settlements
Purchases	[3]	0		0
Issuances	[3]	0		0
Sales	[3]	0	[2]	0
Settlements	[3]	(77)		(1,413)
Transfers in and/or out of Level 3	[3]	0		(208)
Balance at end of year	[3]	3,347		3,426
Available for sale | Corporate bonds
Level 3 assets rollforward
Balance at beginning of year		13		8,851
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	0		(5,865)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0		397
Purchases, issuances, sales and settlements
Purchases		0		0
Issuances		0		0
Sales		0	[2]	0
Settlements		0		(1,462)
Transfers in and/or out of Level 3		0		(1,908)
Balance at end of year		13		13
Fair value option | Corporate bonds
Level 3 assets rollforward
Balance at beginning of year		985		932
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	13		(13)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0		0
Purchases, issuances, sales and settlements
Purchases		0		66
Issuances		0		0
Sales		(998)	[2]	0
Settlements		0		0
Transfers in and/or out of Level 3		0		0
Balance at end of year		0		985
Fair value option | Other investments
Level 3 assets rollforward
Balance at beginning of year		67,103		68,817
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	868		(314)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0		0
Purchases, issuances, sales and settlements
Purchases		13,213		52,449
Issuances		0		0
Sales		(53,203)	[2]	(56,833)
Settlements		0		0
Transfers in and/or out of Level 3		0		2,984
Balance at end of year		27,981		67,103
Fair value option | Equity securities
Level 3 assets rollforward
Balance at beginning of year		68,988		58,094
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	4,941		10,894
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		(69,181)	[2]	0
Settlements		0		0
Transfers in and/or out of Level 3		0		0
Balance at end of year		$ 4,748		$ 68,988
[1]	Gains or losses were included in net realized gains (losses).
[2]	Sales for the 2021 period primarily relates to the Company’s deconsolidation of Somers
[3]	Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities

Fair Value - Narrative (Details

Fair Value - Narrative (Details) - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Senior notes	$ 2,724,394	$ 2,861,113
Total assets and liabilities measured at fair value	23,800,000	26,500,000
Total assets and liabilities measured at fair value priced using non-binding broker quotes	$ 7,700	$ 150,100
Total assets and liabilities measured at fair value priced using non-binding broker quotes (percentage)	0.00%	0.60%
Unsecured debt | Senior Notes
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Senior notes	$ 2,700,000	$ 2,900,000
Estimated fair value of senior notes	$ 3,300,000	$ 3,700,000

Derivative Instruments (Details

Derivative Instruments (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Derivative offsetting [Abstract]
Derivative assets subject to master netting agreements		$ 122,300	$ 138,800
Derivative liabilities subject to master netting agreements		53,900	93,000
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(32,390)	179,675	$ 119,741
Not Designated as Hedging Instrument
Derivative [Line Items]
Asset derivatives - fair value		127,121	177,383
Liability derivatives - fair value		(54,224)	(108,705)
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(32,390)	179,675	119,741
Not Designated as Hedging Instrument | Futures contracts
Derivative [Line Items]
Net derivatives - notional value	[1],[2]	2,826,564	3,099,796
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(15,262)	114,987	114,123
Not Designated as Hedging Instrument | Futures contracts | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	34,999	11,046
Not Designated as Hedging Instrument | Futures contracts | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	(9,808)	(4,496)
Not Designated as Hedging Instrument | Foreign currency forward contracts
Derivative [Line Items]
Net derivatives - notional value	[1],[2]	915,962	1,656,729
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(39,755)	49,974	(9,499)
Not Designated as Hedging Instrument | Foreign currency forward contracts | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	7,734	52,716
Not Designated as Hedging Instrument | Foreign currency forward contracts | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	(11,390)	(6,202)
Not Designated as Hedging Instrument | TBAs
Derivative [Line Items]
Net derivatives - notional value	[1]	11,227	0
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(233)	1,129	463
Not Designated as Hedging Instrument | TBAs | Fixed maturities available for sale, at fair value
Derivative [Line Items]
Asset derivatives - fair value		11,227	0
Liability derivatives - fair value		0	0
Not Designated as Hedging Instrument | Other
Derivative [Line Items]
Net derivatives - notional value	[1],[2]	3,736,773	5,763,919
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		22,860	13,585	$ 14,654
Not Designated as Hedging Instrument | Other | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	73,161	113,621
Not Designated as Hedging Instrument | Other | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	$ (33,026)	$ (98,007)
[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.’

Variable Interest Entity and _3

Variable Interest Entity and Noncontrolling Interests - Variable interest entity (Details) - USD ($) $ in Thousands	1 Months Ended
	Mar. 31, 2014	Jul. 01, 2021	Mar. 31, 2015
Greysbridge Holdings Ltd
Variable Interest Entity [Line Items]
Percentage ownership		40.00%
Greysbridge Holdings Ltd | Kelso And Company
Variable Interest Entity [Line Items]
Percentage ownership		30.00%
Greysbridge Holdings Ltd | Warburg Pincus
Variable Interest Entity [Line Items]
Percentage ownership		30.00%
Variable Interest Entity, Primary Beneficiary | Somers Holdings Ltd.
Variable Interest Entity [Line Items]
Initial investment contribution amount	$ 100,000
Variable Interest Entity, Primary Beneficiary | Common shares | Somers Holdings Ltd.
Variable Interest Entity [Line Items]
Number of shares acquired			2,500,000

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, 2021	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Assets
Investments accounted for using the fair value option		$ 1,973,550	$ 3,824,796
Fixed maturities available for sale, at fair value		17,998,109	18,717,825
Equity securities, at fair value		1,804,170	1,444,830
Cash		858,668	906,448	$ 726,230
Accrued investment income		85,453	103,299
Premiums receivable		2,633,280	2,064,586	1,778,717
Ceded unearned premiums		1,729,455	1,234,075
Deferred acquisition costs		901,841	790,708
Receivable for securities sold		60,179	92,743
Goodwill and intangible assets		944,983	692,863	738,083
Other assets		2,453,849	1,724,288
Total assets of consolidated VIE		45,100,945	43,282,297	37,885,361
Liabilities
Reserve for losses and loss adjustment expenses		17,757,156	16,513,929	13,891,842	$ 11,853,297
Unearned premiums		6,011,942	4,838,965
Reinsurance balances payable		1,583,253	683,263
Revolving credit agreement borrowings		0	155,687
Senior notes		2,724,394	2,861,113
Payable for securities purchased		64,850	218,779
Other liabilities		1,329,742	1,510,888
Total liabilities of consolidated VIE		$ 31,545,816	29,294,856	$ 25,569,809
Somers Holdings Ltd. | Variable Interest Entity, Primary Beneficiary
Assets
Investments accounted for using the fair value option	[1]		1,790,385
Fixed maturities available for sale, at fair value			655,249
Equity securities, at fair value			52,410
Cash			211,451
Accrued investment income			14,679
Premiums receivable			224,377
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses			286,590
Ceded unearned premiums			122,339
Deferred acquisition costs			53,705
Receivable for securities sold			37,423
Goodwill and intangible assets			7,650
Other assets			75,801
Total assets of consolidated VIE			3,532,059
Liabilities
Reserve for losses and loss adjustment expenses			1,519,583
Unearned premiums			407,714
Reinsurance balances payable			63,269
Revolving credit agreement borrowings			155,687
Senior notes			172,689
Payable for securities purchased			25,881
Other liabilities			193,494
Total liabilities of consolidated VIE			2,538,317
Redeemable noncontrolling interests			$ 52,398
[1]	Included in “other investments” on the Company’s balance sheet

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, 2021	Dec. 31, 2020	Dec. 31, 2019
Variable Interest Entity [Line Items]
Net Cash Provided by (Used in) Operating Activities	$ 3,427,555	$ 2,886,505	$ 2,048,459
Net cash provided by (used for) investing activities	(2,139,732)	(3,043,226)	(1,806,483)
Net Cash Provided by (Used in) Financing Activities	(1,229,549)	521,278	(80,662)
Somers Holdings Ltd. | Variable Interest Entity, Primary Beneficiary
Variable Interest Entity [Line Items]
Net Cash Provided by (Used in) Operating Activities	46,991	181,736	239,284
Net cash provided by (used for) investing activities	96,325	258,589	(140,620)
Net Cash Provided by (Used in) Financing Activities	$ (2,042)	$ (335,776)	$ (61,433)

Variable Interest Entity and _6

Variable Interest Entity and Noncontrolling Interests - Non-redeemable noncontrolling interest (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interest, beginning of year	$ 823,007	$ 762,777
Amounts attributable to nonredeemable noncontrolling interests	(78,314)	(53,076)	$ (40,072)
Other comprehensive (income) loss attributable to noncontrolling interests	13,984	(9,062)	(9,130)
Non-redeemable noncontrolling interest, end of year	0	$ 823,007	762,777
Somers Holdings Ltd.
Noncontrolling Interest [Line Items]
Noncontrolling interest, ownership percentage by noncontrolling owners		87.00%
Somers Holdings Ltd. | Noncontrolling Interest
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interest, beginning of year	823,007	$ 762,777
Impact of deconsolidation of Somers	(918,874)	0
Additional paid in capital attributable to noncontrolling interests	22,113	1,334
Repurchases attributable to non-redeemable noncontrolling interests	0	(2,867)
Amounts attributable to nonredeemable noncontrolling interests	78,314	53,076
Other Amounts Attributable to Noncontrolling Interests	0	(375)
Other comprehensive (income) loss attributable to noncontrolling interests	(4,560)	9,062
Non-redeemable noncontrolling interest, end of year	$ 0	$ 823,007	$ 762,777

Variable Interest Entity and _7

Variable Interest Entity and Noncontrolling Interests - Redeemable noncontrolling interest (Details) - USD ($)	Aug. 01, 2019	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019	Jul. 31, 2019	Mar. 31, 2014
Redeemable Noncontrolling Interest [Line Items]
Balance, beginning of year		$ 58,548,000	$ 55,404,000	$ 206,292,000
Impact of deconsolidation of Somers		(48,919,000)	0	0
Redemption of noncontrolling interests		0	0	(157,709,000)
Accretion of preference share issuance costs		0	93,000	244,000
Other		(396,000)	3,051,000	6,577,000
Balance, end of year		$ 9,233,000	58,548,000	55,404,000
Preferred shares, par value per share		$ 0.01
Somers Holdings Ltd.
Redeemable Noncontrolling Interest [Line Items]
Preferred dividends including accretion of discount and issuance costs		$ 2,100,000	4,400,000	$ 17,800,000
Variable Interest Entity, Primary Beneficiary | Somers Holdings Ltd.
Redeemable Noncontrolling Interest [Line Items]
Preference shares, number of shares issued					9,065,200
Shares redeemed during the period, shares	6,919,998
Preferred shares, redemption price per share	$ 25.19748
Proceeds from Redemption Of Preferred Shares By Variable Interest Entity	$ 11,500,000
Noncontrolling Interest | Somers Holdings Ltd.
Redeemable Noncontrolling Interest [Line Items]
Impact of deconsolidation of Somers		$ (918,874,000)	$ 0
Redeemable Preferred Stock [Member] | Somers 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

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, 2021	Dec. 31, 2020	Dec. 31, 2019
Noncontrolling Interest [Line Items]
Amounts attributable to non-redeemable noncontrolling interests	$ (78,314)	$ (53,076)	$ (40,072)
Amounts attributable to redeemable noncontrolling interests	(4,299)	(7,114)	(16,909)
Net (income) loss attributable to noncontrolling interests	$ (82,613)	$ (60,190)	$ (56,981)

Variable Interest Entity and _9

Variable Interest Entity and Noncontrolling Interests - Other variable interest entity disclosures (Details) - USD ($) $ in Thousands		Dec. 31, 2021		Dec. 31, 2020	Dec. 31, 2019
Variable Interest Entity [Line Items]
Total VIE Assets		$ 45,100,945		$ 43,282,297	$ 37,885,361
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		3,248,206		2,232,609
Bellemeade 2020-2 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Remaining Coverage, Amount		1,000
Bellemeade 2020-3 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Remaining Coverage, Amount		16,000
Bellemeade 2020-4 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Remaining Coverage, Amount		9,000
Bellemeade 2021-1 Ltd Member | Directly provided capacity
Variable Interest Entity [Line Items]
Remaining Coverage, Amount		61,000
Bellemeade 2021-2 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Remaining Coverage, Amount		93,000
Bellemeade 2021-3 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Remaining Coverage, Amount		131,000
Variable Interest Entity, Not Primary Beneficiary
Variable Interest Entity [Line Items]
Total VIE Assets		4,336,596		3,859,058
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(4,434)		(7,969)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		42,202		56,320
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		37,768		48,351
Initial Coverage at Issuance		6,626,664
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2017-1 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		108,368		145,573
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(159)		(245)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		424		844
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		265		599
Initial Coverage at Issuance	[1]	368,114
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-1 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		181,136		250,095
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(528)		(903)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		1,268		2,245
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		740		1,342
Initial Coverage at Issuance	[2]	374,460
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-2 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		0		108,395
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		0		(138)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		0		280
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		0		142
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2018-3 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		302,563		302,563
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(1,018)		(1,320)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		2,496		3,262
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		1,478		1,942
Initial Coverage at Issuance	[3]	506,110
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-1 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		181,324		219,256
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(380)		(1,361)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		5,807		8,461
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		5,427		7,100
Initial Coverage at Issuance	[4]	341,790
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-2 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		398,316		398,316
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(515)		(730)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		3,998		5,201
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		3,483		4,471
Initial Coverage at Issuance	[5]	621,022
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-3 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		409,859		528,084
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(584)		(861)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		3,190		5,079
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		2,606		4,218
Initial Coverage at Issuance	[6]	700,920
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2019-4 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		411,954		468,737
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(462)		(890)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		4,759		6,676
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		4,297		5,786
Initial Coverage at Issuance	[7]	577,267
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-1 Ltd.
Variable Interest Entity [Line Items]
Total VIE Assets		0		275,068
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		0		(178)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		0		1,012
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		0		834
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-2 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets	[8]	217,766		423,420
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net	[8]	(177)		(556)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet	[8]	1,984		6,839
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount	[8]	1,807		6,283
Initial Coverage at Issuance	[9]	449,167
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-2 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance		26,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-3 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets	[10]	348,818		418,158
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net	[10]	(128)		(631)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet	[10]	5,793		9,605
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount	[10]	5,665		8,974
Initial Coverage at Issuance	[11]	451,816
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-3 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance		34,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-4 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets	[12]	176,826		321,393
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net	[12]	(50)		(156)
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet	[12]	1,630		6,816
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount	[12]	1,580		6,660
Initial Coverage at Issuance	[13]	337,013
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-4 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance		16,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-1 Ltd Member
Variable Interest Entity [Line Items]
Total VIE Assets		568,986	[14]	0
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(303)	[14]	0
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		3,283	[14]	0
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		2,980	[14]	0
Initial Coverage at Issuance	[15]	643,577
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-1 Ltd Member | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance		64,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-2 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		522,807	[16]	0
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		281	[16]	0
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		4,124	[16]	0
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		4,405	[16]	0
Initial Coverage at Issuance	[17]	616,017
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-2 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance		93,000
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-3 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		507,873	[18]	0
Variable Interest Entity, Maximum Exposure to Loss, On Balance Sheet, Asset (Liability) Net		(411)	[18]	0
Variable Interest Entity, Maximum Exposure to Loss, Off Balance Sheet		3,446	[18]	0
Variable Interest Entity, Reporting Entity Involvement, Maximum Loss Exposure, Amount		3,035	[18]	$ 0
Initial Coverage at Issuance	[19]	639,391
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-3 Ltd | Directly provided capacity
Variable Interest Entity [Line Items]
Initial Coverage at Issuance		$ 131,000
[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.
[8]	At December 31, 2021, $1 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table)
[9]	Issued in September 2020, covering in-force policies issued between January 1, 2020 and May 31, 2020. $423 million was directly funded by Bellemeade 2020-2 Ltd. with an additional $26 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers
[10]	At December 31, 2021, $16 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table).
[11]	Issued in November 2020, covering in-force policies issued between June 1, 2020 and August 31, 2020. $418 million was directly funded by Bellemeade 2020-3 Ltd. with an additional $34 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.
[12]	At December 31, 2021, $9 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table).
[13]	Issued in December 2020, covering in-force policies issued between July 1, 2019 and December 31, 2019. $321 million was directly funded by Bellemeade 2020-4 Ltd. with an additional $16 million of capacity provided directly to Arch MI U.S. by a separate panel of reinsurers
[14]	At December 31, 2021, $61 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table).
[15]	Issued in March 2021, covering in-force policies issued between September 1, 2020 and November 30, 2020. $580 million was directly funded by Bellemeade Re 2021-1 Ltd. with an additional $64 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers.
[16]	At December 31, 2021, $93 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table).
[17]	Issued in June 2021, covering in-force policies issued between December 1, 2020 and March 31, 2021. $523 million was directly funded by Bellemeade Re 2021-2 Ltd. via insurance-linked notes, with an additional $93 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers
[18]	At December 31, 2021, $131 million of coverage from a separate panel of reinsurers is remaining (not reflected in this table).
[19]	Issued in September 2021, covering in-force policies issued between April 1, 2021 and June 30, 2021. $508 million was directly funded by Bellemeade Re 2021-3 Ltd. via insurance-linked notes, with an additional $131 million capacity provided directly to Arch MI U.S. by a separate panel of reinsurers

Other Comprehensive Income - Co

Other Comprehensive Income - Components of accumulated other comprehensive income (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	$ 488,895	$ 212,091	$ (178,720)
Other comprehensive income (loss) before reclassifications	(437,427)	702,991	509,752
Amounts reclassified from accumulated other comprehensive income	(116,068)	(426,187)	(118,941)
Net current period other comprehensive income (loss)	(553,495)	276,804	390,811
Ending balance	(64,600)	488,895	212,091
Unrealized Appreciation on Available-For-Sale Investments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	501,295	258,486	(114,178)
Other comprehensive income (loss) before reclassifications	(371,741)	668,996	491,605
Amounts reclassified from accumulated other comprehensive income	(116,068)	(426,187)	(118,941)
Net current period other comprehensive income (loss)	(487,809)	242,809	372,664
Ending balance	13,486	501,295	258,486
Foreign Currency Translation Adjustments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Beginning balance	(12,400)	(46,395)	(64,542)
Other comprehensive income (loss) before reclassifications	(65,686)	33,995	18,147
Amounts reclassified from accumulated other comprehensive income	0	0	0
Net current period other comprehensive income (loss)	(65,686)	33,995	18,147
Ending balance	$ (78,086)	$ (12,400)	$ (46,395)

Other Comprehensive Income - Am

Other Comprehensive Income - Amounts reclassified from accumulated other comprehensive income (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Reclassification out of Accumulated Other Comprehensive Income [Line Items]
Provision for credit losses	$ (2,100)	$ (3,597)	$ 0
Other-than-temporary impairment losses	0	(533)
Other-than-temporary Impairment Loss, Debt Securities, Available-for-sale, Recognized in Earnings			(3,165)
Income (loss) before income taxes	2,368,042	1,577,549	1,849,110
Income tax (expense) benefit	(128,582)	(111,838)	(155,810)
Net of tax	2,156,849	1,405,521	1,636,319
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 (losses)	157,095	478,659	131,043
Provision for credit losses	(2,099)	(3,597)	0
Other-than-temporary impairment losses	0	(533)
Other-than-temporary Impairment Loss, Debt Securities, Available-for-sale, Recognized in Earnings			(3,165)
Income (loss) before income taxes	154,996	474,529	127,878
Income tax (expense) benefit	(38,928)	(48,342)	(8,937)
Net of tax	$ 116,068	$ 426,187	$ 118,941

Other Comprehensive Income - Ta

Other Comprehensive Income - Tax effects on components of other comprehensive income (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Before tax amount:
Unrealized holding gains (losses) arising during period, before tax	$ (406,774)	$ 754,572	$ 562,576
Less reclassification of net realized gains (losses) included in net income, before tax	154,996	474,529	127,878
Foreign currency translation adjustments, before tax	(64,423)	33,706	18,463
Other comprehensive income (loss), before tax	(626,193)	313,749	453,161
Tax expense (benefit):
Unrealized holding gains (losses) arising during period, tax	(19,845)	75,855	61,805
Less reclassification of net realized gains (losses) included in net income, tax	38,928	48,342	8,937
Foreign currency translation adjustments, tax	59	370	353
Other comprehensive income (loss), tax	(58,714)	27,883	53,221
Net of tax amount:
Unrealized holding gains (losses) arising during period, net of tax	(386,929)	678,717	500,771
Less reclassification of net realized gains (losses) included in net income, net of tax	116,068	426,187	118,941
Foreign currency translation adjustments, net of tax	(64,482)	33,336	18,110
Net current period other comprehensive income (loss)	$ (567,479)	$ 285,866	$ 399,940

Earnings Per Common Share (Deta

Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		12 Months Ended
		Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Numerator:
Net income		$ 2,239,462	$ 1,465,711	$ 1,693,300
Net (income) loss attributable to noncontrolling interests		(82,613)	(60,190)	(56,981)
Net income available to Arch		2,156,849	1,405,521	1,636,319
Preferred share dividends		(48,343)	(41,612)	(41,612)
Loss on redemption of preferred shares		(15,101)	0	0
Net income available to Arch common shareholders		$ 2,093,405	$ 1,363,909	$ 1,594,707
Denominator:
Weighted average common shares outstanding		391,748,715	403,062,179	401,802,815
Effect of dilutive common share equivalents:
Nonvested restricted shares		1,996,524	1,682,309	1,673,770
Stock options	[1]	6,600,697	5,514,967	8,132,893
Weighted average common shares and common share equivalents outstanding — diluted		400,345,936	410,259,455	411,609,478
Earnings per common share:
Basic (per share)		$ 5.34	$ 3.38	$ 3.97
Diluted (per share)		$ 5.23	$ 3.32	$ 3.87
Stock Options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)		2,398,608	2,249,821	1,302,017
[1]	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 2021, 2020 and 2019, the number of stock options excluded were 2,398,608, 2,249,821 and 1,302,017, respectively.

Income Taxes - Components of in

Income Taxes - Components of income tax (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Current expense (benefit):
United States	$ 284,274	$ 181,571	$ 139,407
Non-U.S.	11,259	16,091	4,954
Current Income Tax Expense (Benefit)	295,533	197,662	144,361
Deferred expense (benefit):
United States	(123,261)	(89,170)	11,849
Non-U.S.	(43,690)	3,346	(400)
Deferred Income Tax Expense (Benefit)	(166,951)	(85,824)	11,449
Income tax expense (benefit)	$ 128,582	$ 111,838	$ 155,810

Income Taxes - Income before ta

Income Taxes - Income before taxes by jurisdiction (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Income Tax Disclosure [Line Items]
Income (loss) before income taxes	$ 2,368,042	$ 1,577,549	$ 1,849,110
Bermuda
Income Tax Disclosure [Line Items]
Income (loss) before income taxes	1,518,616	1,114,117	1,122,952
United States
Income Tax Disclosure [Line Items]
Income (loss) before income taxes	643,239	409,893	701,480
Other
Income Tax Disclosure [Line Items]
Income (loss) before income taxes	$ 206,187	$ 53,539	$ 24,678

Income Taxes - Statutory tax ra

Income Taxes - Statutory tax rate by jurisdiction (Details)	12 Months Ended
	Dec. 31, 2021
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%
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)	12.50%
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)	25.00%

Income Taxes - Reconciliation o

Income Taxes - Reconciliation of effective tax rate (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Income Tax Disclosure [Abstract]
Expected income tax expense (benefit) computed on pre-tax income at weighted average income tax rate	$ 158,269	$ 111,947	$ 149,799
Addition (reduction) in income tax expense (benefit) resulting from:
Tax-exempt investment income	(23,572)	(1,824)	(3,091)
Meals and entertainment	379	547	1,134
State taxes, net of U.S. federal tax benefit	20,978	5,027	3,314
Foreign branch taxes	1,998	2,094	1,231
Prior year adjustment	(1,432)	3,983	632
Foreign exchange gains & losses	1,190	(1,736)	436
Changes in applicable tax rate	447	0	0
Dividend withholding taxes	12,211	7,105	6,510
Change in valuation allowance	(40,425)	13,190	1,628
Contingent consideration	0	9	190
Share based compensation	(5,339)	(2,533)	(6,592)
Effective Income Tax Reconciliation, Intercompany Loan Writeoff, Amount	0	(22,083)	0
Other	3,878	(3,888)	619
Income tax expense	$ 128,582	$ 111,838	$ 155,810

Income Taxes - Components of de

Income Taxes - Components of deferred tax assets and liabilities (Details) - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020
Deferred income tax assets:
Net operating loss	$ 87,960	$ 67,142
Uncrystallized losses	0	2,926
Discounting of net loss reserves	72,001	74,247
Net unearned premium reserve	75,483	66,368
Compensation liabilities	28,062	27,351
Foreign tax credit carryforward	20,058	19,160
Interest expense	755	622
Goodwill and intangible assets	0	14,450
Bad debt reserves	10,252	10,842
Depreciation and amortization	115,041	0
Lease liability	21,453	23,604
Net unrealized foreign exchange gains	166	165
Other, net	0	2,318
Deferred tax assets before valuation allowance	431,231	309,195
Valuation allowance	(43,953)	(88,255)
Deferred tax assets net of valuation allowance	387,278	220,940
Deferred income tax liabilities:
Depreciation and amortization	0	(495)
Deposit accounting liability	(1,578)	(1,751)
Goodwill and intangibles	(70,549)	0
Lloyds year of account deferral	(12,514)	0
Contingency reserve	(49,486)	(64,593)
Deferred policy acquisition costs	(25,612)	(42,045)
Investment related	(7,492)	(9,571)
Net unrealized appreciation of investments	(8,377)	(66,681)
Right-of-use asset	(17,406)	(19,239)
Other, net	(218)	(843)
Total deferred tax liabilities	(193,232)	(205,218)
Net deferred income tax assets	$ 194,046	$ 15,722

Income Taxes - Operating loss c

Income Taxes - Operating loss carryfowards and tax credits (Details) - USD ($) $ in Thousands		Dec. 31, 2021	Dec. 31, 2020
Operating Loss Carryforwards [Line Items]
U.K. foreign tax credits		$ 20,058	$ 19,160
United Kingdom
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		259,235
U.K. foreign tax credits		20,058
Ireland
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		9,032
Australia
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		39,981
Hong Kong
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards		23,203
United States
Operating Loss Carryforwards [Line Items]
Operating loss carryforwards	[1]	29,508
Operating loss carryforward, portion subject to utilization limits		7,600
Operating loss carryforward, annual utilization limit		$ 600
[1]	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 $7.6 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, 2021	Dec. 31, 2020
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, 2021
United States | Minimum
Income Tax Contingency [Line Items]
Open tax year	2015
United States | Maximum
Income Tax Contingency [Line Items]
Open tax year	2021
United Kingdom | Minimum
Income Tax Contingency [Line Items]
Open tax year	2020
United Kingdom | Maximum
Income Tax Contingency [Line Items]
Open tax year	2021
Ireland | Minimum
Income Tax Contingency [Line Items]
Open tax year	2017
Ireland | Maximum
Income Tax Contingency [Line Items]
Open tax year	2021
Canada | Minimum
Income Tax Contingency [Line Items]
Open tax year	2017
Canada | Maximum
Income Tax Contingency [Line Items]
Open tax year	2021
Switzerland | Minimum
Income Tax Contingency [Line Items]
Open tax year	2018
Switzerland | Maximum
Income Tax Contingency [Line Items]
Open tax year	2021
Denmark | Minimum
Income Tax Contingency [Line Items]
Open tax year	2017
Denmark | Maximum
Income Tax Contingency [Line Items]
Open tax year	2021
Australia | Minimum
Income Tax Contingency [Line Items]
Open tax year	2017
Australia | Maximum
Income Tax Contingency [Line Items]
Open tax year	2021

Income Taxes - Narrative (Detai

Income Taxes - Narrative (Details) - USD ($) $ in Millions	Dec. 31, 2021	Dec. 31, 2020
Operating Loss Carryforwards [Line Items]
Current income taxes payable	$ 14.8
Other assets | T&L Bonds
Operating Loss Carryforwards [Line Items]
US mortgage guaranty tax and loss bonds	$ 31.6	$ 88.1

Transactions with Related Par_2

Transactions with Related Parties (Details)	12 Months Ended
	Dec. 31, 2021USD ($)director	Dec. 31, 2020USD ($)	Dec. 31, 2019USD ($)	Jul. 01, 2021	Dec. 31, 2018USD ($)
Related Party Transaction [Line Items]
Purchases of other investments	$ 1,859,096,000	$ 1,808,727,000	$ 1,470,545,000
Net reserves	12,157,925,000	12,199,074,000	9,809,192,000		$ 9,039,006,000
Reinsurance recoverable for paid and unpaid claims and claims adjustments	5,880,735,000	4,500,802,000	4,346,816,000
Ceded premiums written	3,734,150,000	2,650,352,000	$ 2,099,893,000
Reinsurance balances payable	$ 1,583,253,000	683,263,000
Greysbridge Holdings Ltd
Related Party Transaction [Line Items]
Percentage ownership				40.00%
Premia Holdings Ltd
Related Party Transaction [Line Items]
Number of directors | director	7
Greysbridge Holdings Ltd | Kelso And Company
Related Party Transaction [Line Items]
Percentage ownership				30.00%
Greysbridge Holdings Ltd | Warburg Pincus
Related Party Transaction [Line Items]
Percentage ownership				30.00%
Arch Re Bermuda And Affiliates | Premia Holdings Ltd
Related Party Transaction [Line Items]
Number of directors | director	2
Equity Method Investee | Premia Holdings Ltd
Related Party Transaction [Line Items]
Percentage ownership			25.00%
Purchases of other investments			$ 100,000,000
Equity Method Investee | Barbican
Related Party Transaction [Line Items]
Net reserves	$ 380,000,000
Reinsurance recoverable for paid and unpaid claims and claims adjustments	0	199,800,000
Funds held liability	0	$ 149,600,000
Equity Method Investee | Somers Holdings Ltd.
Related Party Transaction [Line Items]
Reinsurance recoverable for paid and unpaid claims and claims adjustments	902,800,000
Ceded premiums written	453,900,000
Reinsurance balances payable	258,400,000
Senior notes	$ 35,000,000
Preferred shares, dividend rate (as a percent)	6.50%
Percentage ownership of affiliate preferred shares	6.60%

Leases - Additional information

Leases - Additional information regarding leases (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Lessee, Lease, Description [Line Items]
Operating lease costs		$ 31,691	$ 31,826	$ 30,500
Cash payments included in the measurement of lease liabilities reported in operating cash flows		32,094	30,365
Right-of-use assets obtained in exchange for new lease liabilities		22,686	$ 12,060
Operating lease liability		$ 126,711
Weighted average discount rate		3.90%	3.90%
Weighted average remaining lease term		5 years 10 months 24 days	5 years 9 months 18 days
Balance sheet location of right of use asset		Other assets
Balance sheet location of operating lease liability		Other liabilities
Other assets
Lessee, Lease, Description [Line Items]
Right-of-use assets	[1]	$ 106,836	$ 115,911
Other liabilities
Lessee, Lease, Description [Line Items]
Operating lease liability	[1]	$ 126,711	$ 136,015
Maximum
Lessee, Lease, Description [Line Items]
Operating lease term		11 years
[1]	The right-of-use assets are included in ‘ other assets

Leases - Contractual maturities

Leases - Contractual maturities (Details) $ in Thousands	Dec. 31, 2021USD ($)
Contractual maturities of operating lease liabilities
2022	$ 31,682
2023	25,288
2024	22,102
2025	16,253
2026	13,430
2027 and thereafter	34,173
Total undiscounted lease liability	142,928
Less: present value adjustment	(16,217)
Operating lease liability	$ 126,711

Commitments and Contingencies -

Commitments and Contingencies - Concentrations of credit risk (Details)	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Customer concentration risk | Gross written premiums
Concentration Risk [Line Items]
Concentration risk, threshold	10.00%
Customer concentration risk | Gross written premiums | Marsh & McLennan Companies and its subsidiaries
Concentration Risk [Line Items]
Concentration risk percentage	18.30%	13.30%	9.60%
Customer concentration risk | Gross written premiums | AON Corporation and its subsidiaries
Concentration Risk [Line Items]
Concentration risk percentage	12.20%	12.00%	12.20%
Credit concentration risk | Shareholders' equity
Concentration Risk [Line Items]
Concentration risk, threshold	10.00%

Commitments and Contingencies_2

Commitments and Contingencies - Other commitments (Details) - USD ($) $ in Millions	Dec. 31, 2021	Dec. 31, 2020
Commitments and Contingencies Disclosure [Abstract]
Investment commitments	$ 3,000	$ 2,100
Estimated purchase commitments, primarily related to software and computerized systems	$ 114.1	$ 73

Debt and Financing Arrangemen_3

Debt and Financing Arrangements - Schedule of senior notes outstanding (Details) - USD ($) $ in Thousands		Jul. 02, 2019	Dec. 31, 2021	Dec. 31, 2020
Debt Instrument [Line Items]
Carrying amount			$ 2,724,394	$ 2,861,113
Senior Notes
Debt Instrument [Line Items]
Principal amount			2,750,000
Carrying amount			$ 2,724,394	2,861,113
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			$ 297,488	297,367
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			$ 495,063	494,944
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			$ 497,633	497,211
Senior Notes | 5.031% senior notes due 2046
Debt Instrument [Line Items]
Stated interest rate (percentage)	[4]		5.031%
Principal amount			$ 450,000
Carrying amount			$ 445,490	445,402
Senior Notes | 3.635% senior notes due 2050
Debt Instrument [Line Items]
Stated interest rate (percentage)	[5]		3.635%
Principal amount			$ 1,000,000
Carrying amount			$ 988,720	988,500
Senior Notes | Somers Notes
Debt Instrument [Line Items]
Stated interest rate (percentage)	[6]
Principal amount
Carrying amount				137,689
Somers Holdings Ltd. | Variable Interest Entity, Primary Beneficiary
Debt Instrument [Line Items]
Carrying amount				$ 172,689
Somers Holdings Ltd. | Variable Interest Entity, Primary Beneficiary | Senior Notes
Debt Instrument [Line Items]
Purchase of senior notes		$ 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 Arch Capital issued on June 30, 2020 and due June 30, 2050 (“2050 notes”).
[6]	Senior notes of Somers issued on July 2, 2019 and due July 2, 2029 (“Somers Senior Notes”), reflecting the elimination of amounts owned by Arch-U.S. Effective July 1, 2021, the Company no longer consolidates Somers in its financials.

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, 2021	Dec. 31, 2020
Line of Credit Facility [Line Items]
Outstanding borrowings		$ 0	$ 155,687
Investments pledged as collateral		348,400
Advances from Federal Home Loan Banks		80,000	80,000
Investments pledged as security for FHLB advances		80,200	80,200
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		1,300,000
Remaining capacity		9,600
Outstanding borrowings		240,400
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		26,000
Other Arch Capital Subsidiaries | Unsecured revolving loan and letter of credit facility
Line of Credit Facility [Line Items]
Outstanding borrowings		$ 290,000
Somers Holdings Ltd. | Secured credit facility expiring November 2021
Line of Credit Facility [Line Items]
Outstanding borrowings			$ 155,687

Goodwill and Intangible Asset_2

Goodwill and Intangible Assets - Analysis of goodwill and intangible assets (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021		Dec. 31, 2020	Dec. 31, 2019
Goodwill
Goodwill, beginning of year	$ 314,629		$ 326,551
Goodwill, acquisitions	31,677	[1]	0
Goodwill, foreign currency translation adjustment	(1,441)		(11,922)
Goodwill, end of year	344,865		314,629	$ 326,551
Intangible assets (indefinite life)
Intangible assets with an indefinite life, beginning of year	79,219		85,911
Intangible assets with an indefinite life, acquisitions	0	[1]	0
Indefinite lived intangible assets, impact of deconsolidation of Somers	(7,650)
Intangible assets with an indefinite life, foreign currency translation adjustment	(212)		(6,692)
Intangible assets with an indefinite life, end of year	71,357		79,219	85,911
Intangible assets (finite life)
Intangible assets with a finite life, beginning of year	299,015		325,621
Intangible assets with a finite life, acquisitions	318,459	[1]	39,178
Intangible assets with a finite life, amortization	(82,955)		(69,031)	(82,104)
Intangible assets with a finite life, foreign currency translation adjustment	(5,758)		3,247
Intangible assets with a finite life, end of year	528,761		299,015	325,621
Total
Goodwill and intangible assets, beginning of year	692,863		738,083
Goodwill and intangible assets, acquisitions	350,136	[1]	39,178
Indefinite Lived and Finite Lived Intangible Assets Decrease Due To Deconsolidation	(7,650)
Goodwill and intangible assets, foreign currency movements and other adjustments	(7,411)		(15,367)
Goodwill and intangible assets, end of year	944,983		692,863	738,083
Goodwill and intangible assets, gross balance	1,515,386
Intangible assets with a finite life, accumulated amortization	(571,839)		(489,828)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	1,436		1,831
Goodwill and intangible assets	944,983		692,863	$ 738,083
Goodwill
Goodwill
Goodwill, end of year	344,865
Total
Goodwill, gross balance	342,842
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	2,023		$ (3,414)
Intangible assets with an indefinite life
Intangible assets (indefinite life)
Intangible assets with an indefinite life, end of year	71,357
Total
Indefinite-lived intangible assets, gross balance	70,246
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	1,111
Intangible assets with a finite life
Intangible assets (finite life)
Intangible assets with a finite life, end of year	528,761
Total
Intangible assets with a finite life, gross balance	1,102,298
Intangible assets with a finite life, accumulated amortization	(571,839)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	$ (1,698)
[1]	Certain amounts for the Company’s 2021 acquisitions are considered provisional.

Goodwill and Intangible Asset_3

Goodwill and Intangible Assets - Summary of intangible assets by major class (Details) - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	$ 1,515,386	$ 1,180,860
Intangible assets with a finite life, accumulated amortization	(571,839)	(489,828)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	1,436	1,831
Goodwill and intangible assets	944,983	692,863
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	9,435	9,147
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	0	0
Goodwill and intangible assets	(98)	(386)
Intangible assets with a finite life
Schedule of Goodwill And Intangible Assets [Line Items]
Intangible assets with a finite life, accumulated amortization	(571,839)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(1,698)
Intangible assets with a finite life | Acquired insurance contracts
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	451,505	451,505
Intangible assets with a finite life, accumulated amortization	(409,592)	(381,349)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	339	284
Goodwill and intangible assets	42,252	70,440
Intangible assets with a finite life | Operating platform
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	52,674	52,674
Intangible assets with a finite life, accumulated amortization	(48,838)	(44,347)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	56	60
Goodwill and intangible assets	3,892	8,387
Intangible assets with a finite life | Distribution relationships
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	602,518	285,141
Intangible assets with a finite life, accumulated amortization	(120,302)	(71,383)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	(2,207)	3,450
Goodwill and intangible assets	480,009	217,208
Intangible assets with a finite life | Other
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	5,134	5,134
Intangible assets with a finite life, accumulated amortization	(2,542)	(1,896)
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	114	127
Goodwill and intangible assets	2,706	3,365
Goodwill
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	342,842	318,043
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	2,023	(3,414)
Goodwill and intangible assets	344,865	314,629
Intangible assets with an indefinite life
Schedule of Goodwill And Intangible Assets [Line Items]
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	1,111
Intangible assets with an indefinite life | Insurance licenses
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	48,331	55,981
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	0	0
Goodwill and intangible assets	48,331	55,981
Intangible assets with an indefinite life | Syndicate capacity
Schedule of Goodwill And Intangible Assets [Line Items]
Gross balance	21,915	21,915
Goodwill and intangible assets, accumulated foreign currency translation and other adjustments	1,111	1,324
Goodwill and intangible assets	$ 23,026	$ 23,239

Goodwill and Intangible Asset_4

Goodwill and Intangible Assets - Future amortization expense (Details) - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Goodwill and Intangible Assets Disclosure [Abstract]
2022	$ 109,144
2023	99,620
2024	79,410
2025	44,523
2026	35,252
2027 and thereafter	160,812
Finite-Lived Intangible Assets, Net	$ 528,761	$ 299,015	$ 325,621

Goodwill and Intangible Asset_5

Goodwill and Intangible Assets - Narrative (Details)	12 Months Ended
	Dec. 31, 2021
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	15 years

Shareholders' Equity - Roll-for

Shareholders' Equity - Roll-forward of changes in issued and outstanding common shares (Details) - $ / shares		12 Months Ended
		Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Common Shares:
Shares issued, beginning of year		579,000,841	574,617,195	570,737,283
Shares issued	[1]	2,669,229	2,646,164	2,835,994
Restricted shares issued, net of cancellations		1,619,780	1,737,482	1,043,918
Shares issued, end of year		583,289,850	579,000,841	574,617,195
Common shares held in treasury, end of year		(204,365,956)	(172,280,199)	(168,997,994)
Common shares outstanding, end of year		378,923,894	406,720,642	405,619,201
Authorized and Issued:
Common shares authorized		1,800,000,000
Common shares, par value per share		$ 0.0011	$ 0.0011
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, the vesting of restricted share units and shares issued from the employee share purchase plan.

Shareholders' Equity - Share re

Shareholders' Equity - Share repurchase program (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Class of Stock [Line Items]
Aggregate cost of shares repurchased	$ 1,234,294	$ 83,472	$ 2,871
Number of shares repurchased (shares)	31,486,830	2,850,102	110,598
Average price per share repurchased	$ 39.20	$ 29.29	$ 25.96
Common shares held in treasury (shares)	204,365,956	172,280,199	168,997,994
Common shares held in treasury, at cost	$ 3,761,095	$ 2,503,909
Common shares
Class of Stock [Line Items]
Remaining share repurchase authorization	$ 1,200,000
Cumulative number of shares acquired since inception of share repurchase program	420,700,000
Aggregate purchase price of shares acquired since inception of share repurchase program	$ 5,300,000

Shareholders' Equity - Preferre

Shareholders' Equity - Preferred shares (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	Jan. 01, 2018	Jun. 30, 2021	Nov. 30, 2017	Aug. 31, 2017	Nov. 30, 2017	Dec. 31, 2021
Class of Stock [Line Items]
Preferred shares, par value per share						$ 0.01
Series C Preferred Shares
Class of Stock [Line Items]
Preferred shares, dividend rate (as a percent)	6.75%
Series E preferred shares
Class of Stock [Line Items]
Preferred shares, dividend rate (as a percent)	5.25%
Preferred shares, redemption price per share	$ 25
Series F Preferred Shares
Class of Stock [Line Items]
Preferred shares issued			$ 100	$ 230	$ 330
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
Series G Preferred Stock
Class of Stock [Line Items]
Preferred shares issued		$ 500
Preferred shares, dividend rate (as a percent)		4.55%
Preferred shares, par value per share		$ 0.01
Liquidation preference per share		25,000
Preferred shares, redemption price per share		$ 25,000
Series G depositary share equivalent
Class of Stock [Line Items]
Preference shares, number of shares issued		20
Proportionate interest of preference shares, per depositary share		0.10%
Liquidation preference per share		$ 25
Preferred shares, redemption price per share		$ 25

Share-Based Compensation - Long

Share-Based Compensation - Long Term Incentive Plan (Details) - shares	12 Months Ended
	Dec. 31, 2021	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	9,909,950
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	606,942
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	320,272
2007 Employee Share Purchase Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares available for issuance	1,608,354	4,689,777

Share-Based Compensation - Valu

Share-Based Compensation - Valuation assumptions (Details)	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Share-based Payment Arrangement [Abstract]
Dividend yield	0.00%	0.00%	0.00%
Expected volatility	24.20%	16.60%	18.10%
Risk free interest rate	1.00%	1.20%	2.50%
Expected option life	6 years	6 years	6 years

Share-Based Compensation - Stoc

Share-Based Compensation - Stock option activity (Details) - Stock Options $ / shares in Units, $ in Thousands	12 Months Ended
	Dec. 31, 2021USD ($)$ / sharesshares
Number of Options / SARs
Outstanding, beginning of year (in shares) | shares	17,839,333
Granted (in shares) | shares	1,243,984
Exercised (in shares) | shares	(1,931,320)
Forfeited or expired (in shares) | shares	(68,837)
Outstanding, end of year (in shares) | shares	17,083,160
Exercisable, end of year (in shares) | shares	14,730,147
Weighted Average Exercise Price
Outstanding, beginning of year, weighted average exercise price | $ / shares	$ 23.32
Granted, weighted average exercise price | $ / shares	35.90
Exercised, weighted average exercise price | $ / shares	15.57
Forfeited or expired, weighted average exercise price | $ / shares	35.39
Outstanding, end of year, weighted average exercise price | $ / shares	25.06
Exercisable, end of year, weighted average exercise price | $ / shares	$ 23.20
Weighted average contractual term, outstanding, end of year	4 years 4 months 28 days
Weighted average contractual term, exercisable, end of year	3 years 9 months 10 days
Aggregate intrinsic value, outstanding, end of year | $	$ 331,214
Aggregate intrinsic value, exercisable, end of year | $	$ 312,966

Share-Based Compensation - Opti

Share-Based Compensation - Options additional information (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
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	$ 10,100
Tax benefit from exercise of stock options and SARs	$ 5,400
Weighted average grant date fair value	$ 9.22	$ 8.14	$ 7.90
Aggregate intrinsic value of options exercised	$ 47,074	$ 59,723	$ 51,350

Share-Based Compensation - Rest

Share-Based Compensation - Restricted common shares and restricted stock units activity (Details)	12 Months Ended
	Dec. 31, 2021$ / sharesshares
Restricted Common Shares
Unvested Shares:
Unvested balance, beginning of year (in shares) | shares	1,635,845
Restricted shares and restricted unit awards granted | shares	1,085,811
Vested (in shares) | shares	(549,892)
Forfeited (in shares) | shares	(100,927)
Unvested balance, end of year (in shares) | shares	2,070,837
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year, weighted average grant date fair value | $ / shares	$ 36.34
Weighted average grant date fair value | $ / shares	36.14
Vested, weighted average grant date fair value | $ / shares	35.94
Forfeited, weighted average grant date fair value | $ / shares	36.28
Unvested balance, end of year, weighted average grant date fair value | $ / shares	$ 36.35
Restricted Unit Awards
Unvested Shares:
Unvested balance, beginning of year (in shares) | shares	1,121,719
Restricted shares and restricted unit awards granted | shares	175,962
Vested (in shares) | shares	(555,870)
Forfeited (in shares) | shares	(41,945)
Unvested balance, end of year (in shares) | shares	699,866
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year, weighted average grant date fair value | $ / shares	$ 31.43
Weighted average grant date fair value | $ / shares	35.94
Vested, weighted average grant date fair value | $ / shares	30.46
Forfeited, weighted average grant date fair value | $ / shares	32.23
Unvested balance, end of year, weighted average grant date fair value | $ / shares	$ 33.29

Share-Based Compensation - Re_2

Share-Based Compensation - Restricted stock additional information (Details) - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
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	1,261,773	1,535,330	1,195,741
Weighted average grant date fair value	$ 36.12	$ 37.55	$ 32.89
Aggregate fair value of vested restricted share and unit awards	$ 65,477	$ 39,703	$ 46,262
Aggregate intrinsic value of restricted units outstanding	$ 31,100

Share-Based Compensation - Perf

Share-Based Compensation - Performance shares and performance units activity (Details)	12 Months Ended
	Dec. 31, 2021$ / sharesshares
Performance Shares
Unvested Shares:
Unvested balance, beginning of year (in shares) | shares	1,851,382
Performance shares and units granted | shares	674,406
Share Based Compensation, Performance Adjustment | shares	(39,510)	[1],[2]
Vested (in shares) | shares	(624,518)
Unvested balance, end of year (in shares) | shares	1,861,760
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year, weighted average grant date fair value | $ / shares	$ 34.42
Weighted average grant date fair value | $ / shares	37.38
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Performance Adjustment, Weighted Average Grant Date Fair Value | $ / shares	24.78	[1],[2]
Vested, weighted average grant date fair value | $ / shares	24.78
Unvested balance, end of year, weighted average grant date fair value | $ / shares	$ 38.93
Performance Units
Unvested Shares:
Unvested balance, beginning of year (in shares) | shares	32,065
Performance shares and units granted | shares	10,698
Share Based Compensation, Performance Adjustment | shares	11,447	[1],[2]
Vested (in shares) | shares	(24,440)
Unvested balance, end of year (in shares) | shares	29,770
Weighted Average Grant Date Fair Value:
Unvested balance, beginning of year, weighted average grant date fair value | $ / shares	$ 33.48
Weighted average grant date fair value | $ / shares	37.38
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Performance Adjustment, Weighted Average Grant Date Fair Value | $ / shares	24.71	[1],[2]
Vested, weighted average grant date fair value | $ / shares	24.71
Unvested balance, end of year, weighted average grant date fair value | $ / shares	$ 38.71
[1]	The performance adjustment represents the change in PSUs, which vested following the end of the performance period. The performance units were granted at the target level of achievement
[2]	The performance adjustment represents the difference between the number of performance shares granted and earned, which vested following the end of the performance period. The performance shares were granted at the maximum level of achievement.

Share-Based Compensation - Pe_2

Share-Based Compensation - Performance shares and units additional information (Details) - $ / shares	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Expected volatility	24.20%	16.60%	18.10%
Risk free interest rate	1.00%	1.20%	2.50%
Performance Common Shares and Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Vesting period	3 years
Expected volatility	37.50%	18.10%	17.10%
Risk free interest rate	0.30%	1.10%	2.50%
Performance shares and units granted	685,104	557,204	696,360
Weighted average grant date fair value	$ 37.38	$ 44.17	$ 36.05
Performance Common Shares and Units | Minimum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Payout percentage	0.00%
Performance Common Shares and Units | Maximum
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Payout percentage	200.00%

Share-Based Compensation - Shar

Share-Based Compensation - Share-based compensation expense (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	$ 86,580	$ 69,892	$ 63,848
Share based compensation expense, net of tax	75,667	60,345	55,502
Options and SARs
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	12,316	11,744	12,866
Share based compensation expense, net of tax	10,927	10,388	11,450
Restricted Common Shares And Restricted Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	46,817	41,284	38,988
Share based compensation expense, net of tax	39,349	34,599	32,999
Performance Awards
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	23,696	14,729	8,949
Share based compensation expense, net of tax	21,920	13,380	8,295
Employee Share Purchase Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Share based compensation expense	3,751	2,135	3,045
Share based compensation expense, net of tax	$ 3,471	$ 1,978	$ 2,758

Share-Based Compensation - Unre

Share-Based Compensation - Unrecognized compensation cost and period for recognition (Details) $ in Millions	12 Months Ended
	Dec. 31, 2021USD ($)
Stock Options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation cost related to unvested awards	$ 8,233
Weighted average recognition period (years)	10 months 28 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	$ 45,936
Weighted average recognition period (years)	1 year 2 months 23 days
Performance Common Shares and Units
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Unrecognized compensation cost related to unvested awards	$ 7,635
Weighted average recognition period (years)	6 months 7 days

Retirement Plans (Details)

Retirement Plans (Details) - USD ($) $ in Millions	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Retirement Benefits [Abstract]
Defined contribution plan, expense	$ 60.4	$ 52	$ 44.8

Statutory Information - Summary

Statutory Information - Summary of statutory capital, surplus and net income (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Bermuda
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	$ 17,528,510	$ 17,390,943
Required statutory capital and surplus	[1]	5,661,301	5,234,121
Statutory net income (loss)		2,370,746	1,579,889	$ 1,801,486
Ireland
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	958,200	883,337
Required statutory capital and surplus	[1]	794,933	701,161
Statutory net income (loss)		25,191	18,397	26,367
United States
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	5,600,652	4,904,840
Required statutory capital and surplus	[1]	1,717,646	1,644,324
Statutory net income (loss)		345,790	143,271	481,188
United Kingdom
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	902,002	967,440
Required statutory capital and surplus	[1]	563,164	601,662
Statutory net income (loss)		35,286	4,078	(17,423)
Canada
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus	[1]	70,063	64,286
Required statutory capital and surplus	[1]	42,513	37,441
Statutory net income (loss)		6,985	(1,049)	(1,023)
Australia
Statutory Accounting Practices [Line Items]
Actual statutory capital and surplus		283,693	64,507
Required statutory capital and surplus		214,022	19,370
Statutory net income (loss)		$ 11,874	$ (8,601)	$ (6,199)
[1]	Such amounts include ownership interests in affiliated insurance and reinsurance subsidiaries.

Statutory Information - Narrati

Statutory Information - Narrative (Details) $ in Millions	12 Months Ended
	Dec. 31, 2021USD ($)subsidiary
Ireland
Statutory Accounting Practices [Line Items]
Number Of Subsidiaries | subsidiary	3
Mortgage | North Carolina or Wisconsin
Statutory Accounting Practices [Line Items]
Dividend required notice period	30 days
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 2022, total	$ 194.1
Arch Re US | United States
Statutory Accounting Practices [Line Items]
Dividends available for payment in 2022, total	$ 217.5
Arch Re Bermuda | Bermuda
Statutory Accounting Practices [Line Items]
Dividends, percentage permitted	25.00%
Dividend required notice period	7 days
Dividends available for payment in 2022 without prior regulatory approval	$ 3,800

Subsequent Event - (Details)

Subsequent Event - (Details) - USD ($) $ in Thousands	2 Months Ended	12 Months Ended
	Feb. 25, 2022	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019	Jan. 31, 2022
Subsequent Event [Line Items]
Number of shares repurchased (shares)		31,486,830	2,850,102	110,598
Aggregate cost of shares repurchased		$ 1,234,294	$ 83,472	$ 2,871
Common shares
Subsequent Event [Line Items]
Remaining share repurchase authorization		1,200,000
Variable Interest Entity, Not Primary Beneficiary
Subsequent Event [Line Items]
Initial Coverage at Issuance		$ 6,626,664
Subsequent Event | Common shares
Subsequent Event [Line Items]
Number of shares repurchased (shares)	890,180
Aggregate cost of shares repurchased	$ 41,500
Remaining share repurchase authorization	$ 1,140,000
Subsequent Event | Bellemeade Re 2022-1 Ltd
Subsequent Event [Line Items]
Pool Of Underlying Mortgages, Amount					$ 6,300,000
Subsequent Event | Variable Interest Entity, Not Primary Beneficiary | Bellemeade Re 2022-1 Ltd
Subsequent Event [Line Items]
Initial Coverage at Issuance					315,000
Subsequent Event | Variable Interest Entity, Not Primary Beneficiary | Bellemeade Re 2022-1 Ltd | Funded By VIE
Subsequent Event [Line Items]
Initial Coverage at Issuance					283,500
Subsequent Event | Variable Interest Entity, Not Primary Beneficiary | Bellemeade Re 2022-1 Ltd | Directly provided capacity
Subsequent Event [Line Items]
Initial Coverage at Issuance					$ 33,000

Schedule II - Condensed Finan_2

Schedule II - Condensed Financial Information of Registrant - Balance Sheet (Details) - USD ($) $ / shares in Units, $ in Thousands	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Assets
Total investments	$ 26,588,156	$ 28,761,358
Cash	858,668	906,448	$ 726,230
Investment in operating affiliates	1,135,655	129,291
Other assets	2,453,849	1,724,288
Total assets	45,100,945	43,282,297	37,885,361
Liabilities
Senior notes	2,724,394	2,861,113
Other liabilities	1,329,742	1,510,888
Total liabilities	31,545,816	29,294,856	25,569,809
Shareholders’ Equity
Non-cumulative preferred shares	830,000	780,000
Common shares ($0.0011 par, shares issued: 583,289,850 and 579,000,841)	648	643
Additional paid-in capital	2,085,075	1,977,794
Retained earnings	14,455,868	12,362,463
Accumulated other comprehensive income (loss), net of deferred income tax	(64,600)	488,895	212,091	$ (178,720)
Common shares held in treasury, at cost (shares: 204,365,956 and 172,280,199)	(3,761,095)	(2,503,909)
Total shareholders' equity	13,545,896	13,928,893	$ 12,260,148
Total liabilities, noncontrolling interests and shareholders' equity	$ 45,100,945	$ 43,282,297
Parenthetical information:
Common shares, par value per share	$ 0.0011	$ 0.0011
Common shares issued (shares)	583,289,850	579,000,841	574,617,195	570,737,283
Common shares held in treasury (shares)	204,365,956	172,280,199	168,997,994
Parent Company
Assets
Total investments	$ 2,038	$ 172
Cash	16,317	18,932
Investment in subsidiaries	14,822,024	14,377,529
Investment in operating affiliates	6,877	7,731
Due from Affiliates	11	0
Other assets	9,604	10,659
Total assets	14,856,871	14,415,023
Liabilities
Senior notes	1,286,208	1,285,867
Due to subsidiaries and affiliates	0	0
Other liabilities	24,767	23,270
Total liabilities	1,310,975	1,309,137
Shareholders’ Equity
Non-cumulative preferred shares	830,000	780,000
Common shares ($0.0011 par, shares issued: 583,289,850 and 579,000,841)	648	643
Additional paid-in capital	2,085,075	1,977,794
Retained earnings	14,455,868	12,362,463
Accumulated other comprehensive income (loss), net of deferred income tax	(64,600)	488,895
Common shares held in treasury, at cost (shares: 204,365,956 and 172,280,199)	(3,761,095)	(2,503,909)
Total shareholders' equity	13,545,896	13,105,886
Total liabilities, noncontrolling interests and shareholders' equity	$ 14,856,871	$ 14,415,023
Parenthetical information:
Common shares, par value per share	$ 0.0011	$ 0.0011
Common shares issued (shares)	583,289,850	579,000,841
Common shares held in treasury (shares)	204,365,956	172,280,199

Schedule II - Condensed Finan_3

Schedule II - Condensed Financial Information of Registrant - Statement of Income (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Revenues
Net investment income	$ 389,118	$ 519,608	$ 627,738
Net realized gains (losses)	379,845	823,460	363,198
Total revenues	9,249,980	8,508,509	6,925,967
Expenses
Corporate expenses	79,157	81,988	80,111
Interest expense	139,470	143,456	120,872
Net foreign exchange gains (losses)	41,529	(83,634)	(20,609)
Total expenses	7,146,629	6,947,726	5,079,090
Income (loss) from operating affiliates	264,693	16,766	2,233
Net income available to Arch	2,156,849	1,405,521	1,636,319
Preferred share dividends	(48,343)	(41,612)	(41,612)
Loss on redemption of preferred shares	(15,101)	0	0
Net income available to Arch common shareholders	2,093,405	1,363,909	1,594,707
Parent
Revenues
Net investment income	1,524	53	212
Net realized gains (losses)	0	(2,110)	0
Total revenues	1,524	(2,057)	212
Expenses
Corporate expenses	71,818	65,566	62,701
Interest expense	58,741	40,445	22,154
Net foreign exchange gains (losses)	7	3	1
Total expenses	130,566	106,014	84,856
Income (loss) before income taxes	(129,042)	(108,071)	(84,644)
Income (loss) from operating affiliates	(590)	(437)	(762)
Income (loss) before equity in net income of subsidiaries	(129,632)	(108,508)	(85,406)
Equity in net income of subsidiaries	2,286,481	1,514,029	1,721,725
Net income available to Arch	2,156,849	1,405,521	1,636,319
Preferred share dividends	(48,343)	(41,612)	(41,612)
Loss on redemption of preferred shares	(15,101)	0	0
Net income available to Arch common shareholders	$ 2,093,405	$ 1,363,909	$ 1,594,707

Schedule II - Condensed Finan_4

Schedule II - Condensed Financial Information of Registrant - Statement of Cash Flows (Details) - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Operating Activities:
Net Cash Provided by (Used in) Operating Activities	$ 3,427,555	$ 2,886,505	$ 2,048,459
Investing Activities:
Net (purchases) sales of short-term investments	165,272	(1,029,681)	39,833
Purchases of fixed assets	(41,394)	(39,872)	(37,837)
Net cash provided by (used for) investing activities	(2,139,732)	(3,043,226)	(1,806,483)
Financing Activities:
Purchases of common shares under share repurchase program	(1,234,294)	(83,472)	(2,871)
Proceeds from common shares issued, net	6,418	1,876	6,203
Proceeds from issuance of preferred shares, net	485,821	0	0
Redemption of preferred shares	(450,000)	0	0
Proceeds from borrowings	0	1,018,793	200,083
Preferred dividends paid	(48,280)	(41,612)	(41,612)
Net Cash Provided by (Used in) Financing Activities	(1,229,549)	521,278	(80,662)
Increase (decrease) in cash and restricted cash	24,227	386,846	179,055
Cash and restricted cash, beginning of year	1,290,544	903,698	724,643
Cash and restricted cash, end of year	1,314,771	1,290,544	903,698
Parent
Operating Activities:
Net Cash Provided by (Used in) Operating Activities	1,727,529	124,751	52,487
Investing Activities:
Net (purchases) sales of short-term investments	(1,866)	(130)	61
Capital contributed to subsidiaries	(487,161)	(988,975)	(2,121)
Purchases of fixed assets	(783)	(15)	(162)
Net cash provided by (used for) investing activities	(489,810)	(989,120)	(2,222)
Financing Activities:
Purchases of common shares under share repurchase program	(1,234,294)	(83,472)	(2,871)
Proceeds from common shares issued, net	6,418	1,876	6,203
Proceeds from issuance of preferred shares, net	485,821	0	0
Redemption of preferred shares	(450,000)	0	0
Proceeds from borrowings	0	988,393	0
Preferred dividends paid	(48,280)	(41,612)	(41,612)
Net Cash Provided by (Used in) Financing Activities	(1,240,335)	865,185	(38,280)
Increase (decrease) in cash and restricted cash	(2,616)	816	11,985
Cash and restricted cash, beginning of year	18,960	18,144	6,159
Cash and restricted cash, end of year	$ 16,344	$ 18,960	$ 18,144

Schedule III - Supplementary _2

Schedule III - Supplementary Insurance Information (Details) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs		$ 901,841	$ 790,708	$ 633,400
Reserves for Losses and Loss Adjustment Expenses		17,757,156	16,513,928	13,891,842
Unearned Premiums		6,011,942	4,838,965	4,339,549
Net Premiums Earned		8,082,298	6,991,935	5,786,498
Net Losses and Loss Adjustment Expenses Incurred		4,584,803	4,689,599	3,133,452
Amortization of Deferred Acquisition Costs		1,303,178	1,004,842	840,945
Other Operating Expenses	[1]	998,595	875,176	800,997
Net Premiums Written		9,018,337	7,437,716	6,039,067
Operating segments | Insurance
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs		378,265	254,833	188,684
Reserves for Losses and Loss Adjustment Expenses		9,810,622	8,989,930	7,900,328
Unearned Premiums		2,937,664	2,334,225	1,991,496
Net Premiums Earned		3,626,468	2,871,420	2,397,080
Net Losses and Loss Adjustment Expenses Incurred		2,344,365	2,092,453	1,615,475
Amortization of Deferred Acquisition Costs		606,265	418,483	361,614
Other Operating Expenses	[1]	558,906	489,153	454,770
Net Premiums Written		4,148,193	3,162,907	2,641,726
Operating segments | Reinsurance
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs		424,390	278,422	197,856
Reserves for Losses and Loss Adjustment Expenses		6,878,721	5,027,742	4,270,013
Unearned Premiums		2,263,264	1,356,983	971,776
Net Premiums Earned		2,840,443	2,162,229	1,466,389
Net Losses and Loss Adjustment Expenses Incurred		1,924,719	1,628,320	1,011,329
Amortization of Deferred Acquisition Costs		536,754	354,048	239,032
Other Operating Expenses	[1]	212,810	168,011	141,484
Net Premiums Written		3,254,374	2,457,370	1,602,723
Operating segments | Mortgage
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs		99,186	203,748	182,816
Reserves for Losses and Loss Adjustment Expenses		1,067,813	976,673	457,872
Unearned Premiums		811,014	740,043	937,370
Net Premiums Earned		1,283,419	1,397,935	1,366,340
Net Losses and Loss Adjustment Expenses Incurred		56,677	528,344	53,513
Amortization of Deferred Acquisition Costs		97,418	134,240	134,319
Other Operating Expenses	[1]	194,010	162,202	153,092
Net Premiums Written		1,261,068	1,279,850	1,261,756
Operating segments | Other
SEC Schedule, 12-16, Insurance Companies, Supplementary Insurance Information [Line Items]
Deferred Acquisition Costs			53,705	64,044
Reserves for Losses and Loss Adjustment Expenses			1,519,583	1,263,629
Unearned Premiums			407,714	438,907
Net Premiums Earned		331,968	560,351	556,689
Net Losses and Loss Adjustment Expenses Incurred		259,042	440,482	453,135
Amortization of Deferred Acquisition Costs		62,741	98,071	105,980
Other Operating Expenses	[1]	32,869	55,810	51,651
Net Premiums Written		$ 354,702	$ 537,589	$ 532,862
[1]	Certain other operating expenses relate to the Company’s corporate segment. 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		12 Months Ended
		Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount		$ 7,706,832	$ 6,553,910	$ 5,681,523
Ceded to other Companies		(3,734,150)	(2,650,352)	(2,099,893)
Assumed From Other Companies		5,045,655	3,534,158	2,457,437
Net Amount		$ 9,018,337	$ 7,437,716	$ 6,039,067
Percentage of Amount Assumed to Net		55.90%	47.50%	40.70%
Operating segments | Insurance
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount		$ 5,833,873	$ 4,659,416	$ 3,879,752
Ceded to other Companies	[1]	(1,719,541)	(1,525,655)	(1,266,267)
Assumed From Other Companies	[1]	33,861	29,146	28,241
Net Amount		$ 4,148,193	$ 3,162,907	$ 2,641,726
Percentage of Amount Assumed to Net		0.80%	0.90%	1.10%
Operating segments | Reinsurance
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount		$ 408,520	$ 305,435	$ 238,229
Ceded to other Companies	[1]	(1,839,556)	(1,014,716)	(720,500)
Assumed From Other Companies	[1]	4,685,410	3,166,651	2,084,994
Net Amount		$ 3,254,374	$ 2,457,370	$ 1,602,723
Percentage of Amount Assumed to Net		144.00%	128.90%	130.10%
Operating segments | Mortgage
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount		$ 1,213,333	$ 1,192,316	$ 1,224,373
Ceded to other Companies	[1]	(246,757)	(194,149)	(204,509)
Assumed From Other Companies	[1]	294,492	281,683	241,892
Net Amount		$ 1,261,068	$ 1,279,850	$ 1,261,756
Percentage of Amount Assumed to Net		23.40%	22.00%	19.20%
Operating segments | Other
SEC Schedule, 12-17, Insurance Companies, Reinsurance [Line Items]
Gross Amount		$ 251,106	$ 396,743	$ 339,169
Ceded to other Companies	[1]	(102,763)	(190,957)	(222,019)
Assumed From Other Companies	[1]	206,359	331,803	415,712
Net Amount		$ 354,702	$ 537,589	$ 532,862
Percentage of Amount Assumed to Net		58.20%	61.70%	78.00%
[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, 2021	Dec. 31, 2020	Dec. 31, 2019
SEC Schedule, 12-18, Supplemental Information, Property-Casualty Insurance Underwriters [Line Items]
Net Losses and Loss Adjustment Expenses Incurred Related to Current Year	$ 4,940,987	$ 4,851,051	$ 3,297,037
Net Losses and Loss Adjustment Expenses Incurred Related to Prior Years	(356,184)	(161,452)	(163,585)
Consolidated Subsidiaries
SEC Schedule, 12-18, Supplemental Information, Property-Casualty Insurance Underwriters [Line Items]
Deferred Acquisition Costs	901,841	790,708	633,400
Reserves for Losses and Loss Adjustment Expenses	17,757,156	16,513,929	13,891,842
Discount, if any, deducted in Column C	55,575	23,326	22,012
Unearned Premiums	6,011,942	4,838,965	4,339,549
Net Premiums Earned	8,082,298	6,991,935	5,786,498
Net investment income	389,118	519,608	627,738
Net Losses and Loss Adjustment Expenses Incurred Related to Current Year	4,940,987	4,851,051	3,297,037
Net Losses and Loss Adjustment Expenses Incurred Related to Prior Years	(356,184)	(161,452)	(163,585)
Amortization of Deferred Acquisition Costs	1,303,178	1,004,842	840,945
Net Paid Losses and Loss Adjustment Expenses	2,826,551	2,661,117	2,383,255
Net Premiums Written	$ 9,018,337	$ 7,437,716	$ 6,039,067