Arch Capital (ACGL) 10-Q 3 Nov 22 2022 Q3 Quarterly report Financial data

Document and Entity Information

Document and Entity Information - shares	9 Months Ended
	Sep. 30, 2022	Oct. 31, 2022
Document and Entity Information [Abstract]
Document Type	10-Q
Document Quarterly Report	true
Document Period End Date	Sep. 30, 2022
Document Transition Report	false
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 Current Reporting Status	Yes
Entity Interactive Data Current	Yes
Entity Filer Category	Large Accelerated Filer
Entity Small Business	false
Entity Emerging Growth Company	false
Entity Shell Company	false
Entity Common Stock, Shares Outstanding		369,873,027
Document Fiscal Period Focus	Q3
Document Fiscal Year Focus	2022
Current Fiscal Year End Date	--12-31
Entity Central Index Key	0000947484
Amendment Flag	false
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 1/1000th 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 1/1000th interest in a 4.55% Series G preferred share
Trading Symbol	ACGLN
Security Exchange Name	NASDAQ

Unaudited Consolidated Balance

Unaudited Consolidated Balance Sheets - USD ($) $ in Thousands	Sep. 30, 2022	Dec. 31, 2021
Investments:
Debt securities available for sale, at fair value	$ 20,061,584	$ 19,732,825
Equity securities, at fair value	809,869	1,804,170
Other investments, at fair value	1,578,751	1,973,550
Investments accounted for using the equity method	3,565,946	3,077,611
Total investments	26,016,150	26,588,156
Cash	813,583	858,668
Accrued investment income	116,263	85,453
Investment in operating affiliates	891,212	1,135,655
Premiums receivable (net of allowance for credit losses: $38,229 and $39,958)	3,579,380	2,633,280
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $17,366 and $13,230)	6,356,456	5,880,735
Contractholder receivables (net of allowance for credit losses: $2,360 and $3,437)	1,735,730	1,828,691
Ceded unearned premiums	2,115,539	1,729,455
Deferred acquisition costs	1,122,711	901,841
Receivable for securities sold	27,042	60,179
Goodwill and intangible assets	806,655	944,983
Other assets	2,756,383	2,453,849
Total assets	46,337,104	45,100,945
Liabilities
Reserve for losses and loss adjustment expenses	19,288,291	17,757,156
Unearned premiums	7,271,279	6,011,942
Reinsurance balances payable	1,669,592	1,583,253
Contractholder payables	1,738,089	1,832,127
Collateral held for insured obligations	254,720	242,352
Senior notes	2,725,153	2,724,394
Payable for securities purchased	174,769	64,850
Other liabilities	1,411,193	1,329,742
Total liabilities	34,533,086	31,545,816
Commitments and Contingencies
Redeemable noncontrolling interests	8,908	9,233
Shareholders' Equity
Non-cumulative preferred shares	830,000	830,000
Common shares ($0.0011 par, shares issued: 587,134,047 and 583,289,850)	652	648
Additional paid-in capital	2,186,599	2,085,075
Retained earnings	15,042,561	14,455,868
Accumulated other comprehensive income (loss), net of deferred income tax	(1,891,827)	(64,600)
Common shares held in treasury, at cost (shares: 217,812,057 and 204,365,956)	(4,372,875)	(3,761,095)
Total shareholders' equity available to Arch	11,795,110	13,545,896
Total liabilities, noncontrolling interests and shareholders' equity	46,337,104	45,100,945
Fixed maturities available for sale, at fair value (amortized cost: $19,913,055 and $17,973,823; net of allowance for credit losses: $45,993 and $2,883)
Investments:
Debt securities available for sale, at fair value	18,120,727	17,998,109
Short-term investments available for sale, at fair value (amortized cost: $1,941,071 and $1,734,738; net of allowance for credit losses: $0 and $0)
Investments:
Debt securities available for sale, at fair value	$ 1,940,857	$ 1,734,716

Unaudited Consolidated Balanc_2

Unaudited Consolidated Balance Sheets (Parentheticals) - USD ($) $ in Thousands	Sep. 30, 2022	Dec. 31, 2021
Available for sale securities, amortized cost	$ 21,854,126	$ 19,708,561
Allowance for credit losses on investments	45,993	2,883
Allowance for credit losses on premiums receivable	38,229	39,958
Allowance for credit losses on reinsurance recoverable	17,366	13,230
Allowance for credit losses on contractholder receivable	$ 2,360	$ 3,437
Common shares, par value per share	$ 0.0011	$ 0.0011
Common shares issued (shares)	587,134,047	583,289,850
Common shares held in treasury (shares)	217,812,057	204,365,956
Fixed maturities
Available for sale securities, amortized cost	$ 19,913,055	$ 17,973,823
Allowance for credit losses on investments	45,993	2,883
Short-term investments
Available for sale securities, amortized cost	1,941,071	1,734,738
Allowance for credit losses on investments	$ 0	$ 0

Unaudited Consolidated Statemen

Unaudited Consolidated Statements of Income - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Revenues
Net premiums earned	$ 2,470,750	$ 1,929,337	$ 6,917,158	$ 5,998,668
Net investment income	128,640	88,195	315,468	298,664
Net realized gains (losses)	(183,673)	(25,040)	(742,666)	320,328
Other underwriting income	3,077	7,274	11,944	18,913
Equity in net income (loss) of investment funds accounted for using the equity method	(18,861)	105,398	75,505	299,270
Other income (loss)	(13,684)	(3,960)	(34,486)	1,151
Total revenues	2,386,249	2,101,204	6,542,923	6,936,994
Expenses
Losses and loss adjustment expenses	1,682,696	1,226,019	3,786,187	3,588,950
Acquisition expenses	447,587	306,015	1,239,065	945,639
Other operating expenses	274,747	230,832	842,082	736,808
Corporate expenses	17,710	19,672	77,662	61,007
Amortization of intangible assets	26,104	20,135	80,478	49,823
Interest expense	33,063	33,176	98,566	107,222
Net foreign exchange (gains) losses	(90,509)	(36,078)	(182,129)	(38,366)
Total expenses	2,391,398	1,799,771	5,941,911	5,451,083
Income (loss) before income taxes and income (loss) from operating affiliates	(5,149)	301,433	601,012	1,485,911
Income tax expense	14,900	(4,137)	(19,042)	(94,176)
Income (loss) from operating affiliates	8,507	124,119	37,665	224,052
Net income (loss)	18,258	421,415	619,635	1,615,787
Net (income) loss attributable to noncontrolling interests	(1,157)	(1,473)	(2,390)	(82,203)
Net income (loss) available to Arch	17,101	419,942	617,245	1,533,584
Preferred dividends	(10,184)	(16,090)	(30,552)	(38,159)
Loss on redemption of preferred shares	0	(15,101)	0	(15,101)
Net income (loss) available to Arch common shareholders	$ 6,917	$ 388,751	$ 586,693	$ 1,480,324
Net income per common share and common share equivalent
Basic (per share)	$ 0.02	$ 1	$ 1.59	$ 3.74
Diluted (per share)	$ 0.02	$ 0.98	$ 1.55	$ 3.66
Weighted average common shares and common share equivalents outstanding
Basic (shares)	365,190,527	389,274,220	369,525,348	395,899,591
Diluted (shares)	373,727,277	397,903,347	378,373,180	404,260,485

Unaudited Consolidated Statem_2

Unaudited Consolidated Statements of Comprehensive Income - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Comprehensive Income
Net income (loss)	$ 18,258	$ 421,415	$ 619,635	$ 1,615,787
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during period	(609,759)	(95,923)	(1,892,119)	(279,102)
Reclassification of net realized (gains) losses, included in net income (loss)	46,585	(62,654)	206,573	(120,504)
Foreign currency translation adjustments	(70,388)	(31,710)	(141,681)	(54,089)
Comprehensive income (loss)	(615,304)	231,128	(1,207,592)	1,162,092
Net (income) loss attributable to noncontrolling interests	(1,157)	(1,473)	(2,390)	(82,203)
Other comprehensive (income) loss attributable to noncontrolling interests	0	9,423	0	13,983
Comprehensive income (loss) available to Arch	$ (616,461)	$ 239,078	$ (1,209,982)	$ 1,093,872

Unaudited Consolidated Statem_3

Unaudited Consolidated Statements of Changes in Shareholders' Equity - USD ($) $ in Thousands	Total	Non-cumulative preferred shares	Common shares	Additional paid-in capital	Retained earnings	Accumulated other comprehensive income (loss), net of deferred income tax	Unrealized appreciation (decline) in value of available-for-sale securities, 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 period at Dec. 31, 2020		$ 780,000	$ 643	$ 1,977,794	$ 12,362,463	$ 488,895	$ 501,295	$ (12,400)	$ (2,503,909)
Preferred shares issued		500,000
Preferred shares redeemed		(450,000)
Common shares issued, net			5
Amortization of share-based compensation				71,279
Issue costs on preferred shares				(14,179)
Loss on redemption of preferred shares	$ (15,101)			15,101	(15,101)
Other changes				11,911
Net income (loss)	1,615,787				1,615,787
Net (income) loss attributable to noncontrolling interests	(82,203)				(82,203)
Preferred share dividends	(38,159)				(38,159)
Unrealized holding gains (losses) during period, net of reclassification adjustment							(399,606)
Unrealized holding gains (losses) during period attributable to noncontrolling interests							15,188
Foreign currency translation adjustments	(54,089)							(54,089)
Foreign currency translation adjustments attributable to noncontrolling interests								(1,204)
Shares repurchased for treasury									(893,090)
Balance at end of period at Sep. 30, 2021	13,387,526	830,000	648	2,061,906	13,842,787	49,184	116,877	(67,693)	(3,396,999)
Balance at beginning of period at Jun. 30, 2021		1,280,000	647	2,028,919	13,454,036	230,048	264,702	(34,654)	(3,007,578)
Preferred shares issued		0
Preferred shares redeemed		(450,000)
Common shares issued, net			1
Amortization of share-based compensation				14,216
Issue costs on preferred shares				0
Loss on redemption of preferred shares	(15,101)			15,101	(15,101)
Other changes				3,670
Net income (loss)	421,415				421,415
Net (income) loss attributable to noncontrolling interests	(1,473)				(1,473)
Preferred share dividends	(16,090)				(16,090)
Unrealized holding gains (losses) during period, net of reclassification adjustment							(158,577)
Unrealized holding gains (losses) during period attributable to noncontrolling interests							10,752
Foreign currency translation adjustments	(31,710)							(31,710)
Foreign currency translation adjustments attributable to noncontrolling interests								(1,329)
Shares repurchased for treasury									(389,421)
Balance at end of period at Sep. 30, 2021	13,387,526	830,000	648	2,061,906	13,842,787	49,184	116,877	(67,693)	(3,396,999)
Balance at beginning of period 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)
Preferred shares issued		0
Preferred shares redeemed		0
Common shares issued, net			4
Amortization of share-based compensation				80,023
Issue costs on preferred shares				0
Loss on redemption of preferred shares	0			0	0
Other changes				21,501
Net income (loss)	619,635				619,635
Net (income) loss attributable to noncontrolling interests	(2,390)				(2,390)
Preferred share dividends	(30,552)				(30,552)
Unrealized holding gains (losses) during period, net of reclassification adjustment							(1,685,546)
Unrealized holding gains (losses) during period attributable to noncontrolling interests							0
Foreign currency translation adjustments	(141,681)							(141,681)
Foreign currency translation adjustments attributable to noncontrolling interests								0
Shares repurchased for treasury									(611,780)
Balance at end of period at Sep. 30, 2022	11,795,110	830,000	652	2,186,599	15,042,561	(1,891,827)	(1,672,060)	(219,767)	(4,372,875)
Balance at beginning of period at Jun. 30, 2022		830,000	652	2,170,661	15,035,644	(1,258,265)	(1,108,886)	(149,379)	(4,361,126)
Preferred shares issued		0
Preferred shares redeemed		0
Common shares issued, net			0
Amortization of share-based compensation				13,518
Issue costs on preferred shares				0
Loss on redemption of preferred shares	0			0	0
Other changes				2,420
Net income (loss)	18,258				18,258
Net (income) loss attributable to noncontrolling interests	(1,157)				(1,157)
Preferred share dividends	(10,184)				(10,184)
Unrealized holding gains (losses) during period, net of reclassification adjustment							(563,174)
Unrealized holding gains (losses) during period attributable to noncontrolling interests							0
Foreign currency translation adjustments	(70,388)							(70,388)
Foreign currency translation adjustments attributable to noncontrolling interests								0
Shares repurchased for treasury									(11,749)
Balance at end of period at Sep. 30, 2022	$ 11,795,110	$ 830,000	$ 652	$ 2,186,599	$ 15,042,561	$ (1,891,827)	$ (1,672,060)	$ (219,767)	$ (4,372,875)

Unaudited Consolidated Statem_4

Unaudited Consolidated Statements of Cash Flows - USD ($) $ in Thousands	9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021
Operating Activities
Net income (loss)	$ 619,635	$ 1,615,787
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses	742,680	(367,313)
Equity in net (income) or loss of investment funds accounted for using the equity method and other income or loss	106,405	(372,650)
Amortization of intangible assets	80,478	49,823
Share-based compensation	80,029	72,303
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	1,553,084	1,548,211
Unearned premiums, net of ceded unearned premiums	1,125,395	985,242
Premiums receivable	(1,095,741)	(847,098)
Deferred acquisition costs	(242,377)	(247,966)
Reinsurance balances payable	128,418	618,571
Other items, net	(264,289)	(427,359)
Net cash provided by operating activities	2,833,717	2,627,551
Investing Activities
Purchases of fixed maturity investments	(13,065,302)	(29,870,023)
Purchases of equity securities	(786,733)	(978,951)
Purchases of other investments	(1,270,099)	(1,350,056)
Proceeds from sales of fixed maturity investments	9,990,418	30,067,792
Proceeds from sales of equity securities	1,539,808	695,633
Proceeds from sales, redemptions and maturities of other investments	1,075,679	1,487,919
Proceeds from redemptions and maturities of fixed maturity investments	577,864	1,234,412
Net settlements of derivative instruments	(106,347)	(67,830)
Net (purchases) sales of short-term investments	(151,980)	(1,172,798)
Purchase of operating affiliate	0	(753,916)
Impact of the deconsolidation of the variable interest entity	0	(349,202)
Purchases of fixed assets	(38,383)	(34,407)
Other	128,354	(361,857)
Net cash used for investing activities	(2,106,721)	(1,453,284)
Financing Activities
Proceeds from issuance of preferred shares, net	0	485,821
Redemption of preferred shares	0	(450,000)
Purchases of common shares under share repurchase program	(585,823)	(872,197)
Proceeds from common shares issued, net	(2,863)	281
Third party investment in non-redeemable noncontrolling interests	0	15,971
Dividends paid to redeemable noncontrolling interests	0	(1,907)
Other	(84,639)	(21,752)
Preferred dividends paid	(30,552)	(38,096)
Net cash used for financing activities	(703,877)	(881,879)
Effects of exchange rate changes on foreign currency cash and restricted cash	(79,566)	(34,023)
Increase (decrease) in cash and restricted cash	(56,447)	258,365
Cash and restricted cash, beginning of year	1,314,771	1,290,544
Cash and restricted cash, end of period	$ 1,258,324	$ 1,548,909

Basis of Presentation and Recen

Basis of Presentation and Recent Accounting Pronouncements	9 Months Ended
	Sep. 30, 2022
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Basis of Presentation and Recent Accounting Pronouncements	General Arch Capital Group Ltd. (“Arch Capital”) is a public 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. The Company’s consolidated financial statements through June 30, 2021 included the results of Somers Group Holdings Ltd. (formerly Watford Holdings Ltd.) and its wholly owned subsidiaries (“Somers”). 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 11 . Basis of Presentation The interim consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”). 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. In the opinion of management, the accompanying unaudited interim consolidated financial statements reflect all adjustments (consisting of normally recurring accruals) necessary for a fair statement of results on an interim basis. The results of any interim period are not necessarily indicative of the results for a full year or any future periods. Certain information and footnote disclosures normally included in financial statements prepared in accordance with GAAP have been condensed or omitted; however, management believes that the disclosures are adequate to make the information presented not misleading. This report should be read in conjunction with the Company’s Annual Report on Form 10-K for the year ended December 31, 2021 (“2021 Form 10-K”), including the Company’s audited consolidated financial statements and related notes. The Company has reclassified the presentation of certain prior year information to conform to the current presentation. Such reclassifications had no effect on the Company’s net income, comprehensive income, shareholders’ equity or cash flows. Tabular amounts are in U.S. Dollars in thousands, except share amounts, unless otherwise noted. Recent Accounting Pronouncements Inflation Reduction Act of 2022 On August 16, 2022, the U.S. government enacted the Inflation Reduction Act of 2022, which among other things implements a 15% minimum tax on book income of certain large corporations, a 1% excise tax on net stock repurchases and several tax incentives to promote clean energy. The effective date of these provisions is January 1, 2023. Based on its current analysis of the provisions, the Company does not expect that this legislation will have a material effect on the Company’s consolidated financial statements. Recently Issued Accounting Standards Adopted For information regarding additional accounting standards that the Company has not yet adopted, see note 3(s), “Significant Accounting Policies—Recent Accounting Pronouncements,” of the notes to consolidated financial statements in the Company’s 2021 Form 10-K.

Share Transactions

Share Transactions	9 Months Ended
	Sep. 30, 2022
Stockholders' Equity Note [Abstract]
Share Transactions	Share Repurchases The board of directors of Arch Capital has authorized the investment in Arch Capital’s common shares through a share repurchase program. Since the inception of the share repurchase program, Arch Capital has repurchased 433.6 million common shares for an aggregate purchase price of $5.87 billion. For the nine months ended September 30, 2022, Arch Capital repurchased 12.9 million shares under the share repurchase program with an aggregate purchase price of $585.8 million. At September 30, 2022, $596.4 million of share repurchases were available under the program, which may be effected from time to time in open market or privately negotiated transactions. 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. The 2022 Long-Term Incentive and Share Award Plan (the“2022 Plan”) The 2022 Plan became effective as of May 4, 2022 following approval by shareholders of the Company. The 2022 Plan provides for the issuance of stock options, stock appreciation rights, restricted shares, restricted share units payable in common shares or cash, dividend equivalents, performance shares and performance units and other share-based awards to Arch Capital’s eligible employees and directors. The number of common shares reserved for grants under the 2022 Plan, subject to anti-dilution adjustments in the event of certain changes in Arch Capital’s capital structure, is 9,000,000; provided, that no more than 6,000,000 common shares may be issued as incentive stock options under Section 422 of the Code. The 2022 Plan will terminate as to future awards on February 25, 2032. At September 30, 2022, 9,000,000 shares are available for future issuance. 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 Shares offering of approximately $485.8 million were used to redeem the Company’s issued and outstanding 5.25% Series E Non-Cumulative Preferred Shares in September 2021. The preferred shares were redeemed at a redemption price equal to $25 per depositary 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.

Earnings Per Common Share

Earnings Per Common Share	9 Months Ended
	Sep. 30, 2022
Earnings Per Share [Abstract]
Earnings Per Common Share	The following table sets forth the computation of basic and diluted earnings per common share: Three Months Ended Nine Months Ended September 30, September 30, 2022 2021 2022 2021 Numerator: Net income (loss) $ 18,258 $ 421,415 $ 619,635 $ 1,615,787 Amounts attributable to noncontrolling interests (1,157) (1,473) (2,390) (82,203) Net income (loss) available to Arch 17,101 419,942 617,245 1,533,584 Preferred dividends (10,184) (16,090) (30,552) (38,159) Loss on redemption of preferred shares — (15,101) — (15,101) Net income (loss) available to Arch common shareholders $ 6,917 $ 388,751 $ 586,693 $ 1,480,324 Denominator: Weighted average common shares and common share equivalents outstanding — basic 365,190,527 389,274,220 369,525,348 395,899,591 Effect of dilutive common share equivalents: Nonvested restricted shares 2,351,039 2,131,915 2,171,158 1,877,930 Stock options (1) 6,185,711 6,497,212 6,676,674 6,482,964 Weighted average common shares and common share equivalents outstanding — diluted 373,727,277 397,903,347 378,373,180 404,260,485 Earnings per common share: Basic $ 0.02 $ 1.00 $ 1.59 $ 3.74 Diluted $ 0.02 $ 0.98 $ 1.55 $ 3.66 (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 the 2022 third quarter and 2021 third quarter, the number of stock options excluded were 774,481 and 1,948,006, respectively. For the nine months ended September 30, 2022 and 2021, the number of stock options excluded were 785,682 and 2,397,507, respectively.

Segment Information

Segment Information	9 Months Ended
	Sep. 30, 2022
Segment Reporting [Abstract]
Segment Information	The Company classifies its businesses into three underwriting segments — insurance, reinsurance and mortgage — and two other 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, the 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; excess and surplus casualty; lenders products; professional lines; programs; property, energy, marine and aviation; travel, accident and health; and other (consisting of alternative markets, excess workers' compensation and surety business). The reinsurance segment consists of the Company’s reinsurance underwriting units which offer specialty product lines on a worldwide basis. Product lines include: casualty; marine and aviation; other specialty; property catastrophe; property excluding property catastrophe (losses on a single risk, both excess of loss and pro rata); and other (consisting of life reinsurance, casualty clash and other). The mortgage segment includes the Company’s U.S. primary mortgage insurance business, investment and services related to U.S. credit-risk transfer (“CRT”) which are predominately with government sponsored enterprises (“GSE’s”) and international mortgage insurance and reinsurance operations. Arch Mortgage Insurance Company and United Guaranty Residential Insurance Company (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. Through June 30, 2021, the ‘other’ segment included the results of Somers. In July 2021, the Company announced the completion of the previously disclosed acquisition of Somers by Greysbridge. Based on the governing documents of Greysbridge, the Company has 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 . S ee note 11 . 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: Three Months Ended September 30, 2022 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 1,862,026 $ 1,639,061 $ 362,409 $ 3,860,683 $ — $ 3,860,683 Premiums ceded (493,267) (560,225) (86,230) (1,136,909) — (1,136,909) Net premiums written 1,368,759 1,078,836 276,179 2,723,774 — 2,723,774 Change in unearned premiums (181,851) (77,062) 5,889 (253,024) — (253,024) Net premiums earned 1,186,908 1,001,774 282,068 2,470,750 — 2,470,750 Other underwriting income (loss) — 452 2,625 3,077 — 3,077 Losses and loss adjustment expenses (822,663) (927,911) 67,878 (1,682,696) — (1,682,696) Acquisition expenses (232,469) (208,425) (6,693) (447,587) — (447,587) Other operating expenses (165,499) (62,777) (46,471) (274,747) — (274,747) Underwriting income (loss) $ (33,723) $ (196,887) $ 299,407 68,797 — 68,797 Net investment income 128,640 — 128,640 Net realized gains (losses) (183,673) — (183,673) Equity in net income (loss) of investment funds accounted for using the equity method (18,861) — (18,861) Other income (loss) (13,684) — (13,684) Corporate expenses (2) (17,634) — (17,634) Transaction costs and other (2) (76) — (76) Amortization of intangible assets (26,104) — (26,104) Interest expense (33,063) — (33,063) Net foreign exchange gains (losses) 90,509 — 90,509 Income (loss) before income taxes and income (loss) from operating affiliates (5,149) — (5,149) Income tax (expense) benefit 14,900 — 14,900 Income (loss) from operating affiliates 8,507 — 8,507 Net income (loss) 18,258 — 18,258 Amounts attributable to redeemable noncontrolling interests (1,157) — (1,157) Net income (loss) available to Arch 17,101 — 17,101 Preferred dividends (10,184) — (10,184) Net income (loss) available to Arch common shareholders $ 6,917 $ — $ 6,917 Underwriting Ratios Loss ratio 69.3 % 92.6 % (24.1) % 68.1 % — % 68.1 % Acquisition expense ratio 19.6 % 20.8 % 2.4 % 18.1 % — % 18.1 % Other operating expense ratio 13.9 % 6.3 % 16.5 % 11.1 % — % 11.1 % Combined ratio 102.8 % 119.7 % (5.2) % 97.3 % — % 97.3 % Goodwill and intangible assets $ 224,525 $ 140,800 $ 441,330 $ 806,655 $ — $ 806,655 (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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’ Three Months Ended September 30, 2021 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 1,596,619 $ 1,251,760 $ 360,934 $ 3,207,415 $ — $ 3,207,415 Premiums ceded (442,806) (630,371) (60,207) (1,131,486) — (1,131,486) Net premiums written 1,153,813 621,389 300,727 2,075,929 — 2,075,929 Change in unearned premiums (215,143) 57,313 11,238 (146,592) — (146,592) Net premiums earned 938,670 678,702 311,965 1,929,337 — 1,929,337 Other underwriting income (loss) — 3,293 3,981 7,274 — 7,274 Losses and loss adjustment expenses (668,630) (545,846) (11,543) (1,226,019) — (1,226,019) Acquisition expenses (152,467) (129,450) (24,098) (306,015) — (306,015) Other operating expenses (138,931) (45,647) (46,254) (230,832) — (230,832) Underwriting income (loss) $ (21,358) $ (38,948) $ 234,051 173,745 — 173,745 Net investment income 88,195 — 88,195 Net realized gains (losses) (25,040) — (25,040) Equity in net income (loss) of investment funds accounted for using the equity method 105,398 — 105,398 Other income (loss) (3,960) — (3,960) Corporate expenses (2) (18,636) — (18,636) Transaction costs and other (2) (1,036) — (1,036) Amortization of intangible assets (20,135) — (20,135) Interest expense (33,176) — (33,176) Net foreign exchange gains (losses) 36,078 — 36,078 Income (loss) before income taxes and income (loss) from operating affiliates 301,433 — 301,433 Income tax (expense) benefit (4,137) — (4,137) Income (loss) from operating affiliates 124,119 — 124,119 Net income (loss) 421,415 — 421,415 Amounts attributable to redeemable noncontrolling interests (1,473) — (1,473) Net income (loss) available to Arch 419,942 — 419,942 Preferred dividends (16,090) — (16,090) Loss on redemption of preferred shares (15,101) — (15,101) Net income (loss) available to Arch common shareholders $ 388,751 $ — $ 388,751 Underwriting Ratios Loss ratio 71.2 % 80.4 % 3.7 % 63.5 % — % 63.5 % Acquisition expense ratio 16.2 % 19.1 % 7.7 % 15.9 % — % 15.9 % Other operating expense ratio 14.8 % 6.7 % 14.8 % 12.0 % — % 12.0 % Combined ratio 102.2 % 106.2 % 26.2 % 91.4 % — % 91.4 % Goodwill and intangible assets $ 261,103 $ 176,128 $ 526,091 $ 963,322 $ — $ 963,322 (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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’ Nine Months Ended September 30, 2022 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 5,286,798 $ 5,151,401 $ 1,099,144 $ 11,531,185 $ — $ 11,531,185 Premiums ceded (1,482,886) (1,770,807) (241,097) (3,488,632) — (3,488,632) Net premiums written 3,803,912 3,380,594 858,047 8,042,553 — 8,042,553 Change in unearned premiums (488,164) (646,421) 9,190 (1,125,395) — (1,125,395) Net premiums earned 3,315,748 2,734,173 867,237 6,917,158 — 6,917,158 Other underwriting income (loss) — 5,814 6,130 11,944 — 11,944 Losses and loss adjustment expenses (2,053,161) (1,920,189) 187,163 (3,786,187) — (3,786,187) Acquisition expenses (641,807) (569,915) (27,343) (1,239,065) — (1,239,065) Other operating expenses (493,412) (198,606) (150,064) (842,082) — (842,082) Underwriting income (loss) $ 127,368 $ 51,277 $ 883,123 $ 1,061,768 $ — $ 1,061,768 Net investment income 315,468 — 315,468 Net realized gains (losses) (742,666) — (742,666) Equity in net income (loss) of investment funds accounted for using the equity method 75,505 — 75,505 Other income (loss) (34,486) — (34,486) Corporate expenses (2) (76,928) — (76,928) Transaction costs and other (2) (734) — (734) Amortization of intangible assets (80,478) — (80,478) Interest expense (98,566) — (98,566) Net foreign exchange gains (losses) 182,129 — 182,129 Income (loss) before income taxes and income (loss) from operating affiliates 601,012 — 601,012 Income tax (expense) benefit (19,042) — (19,042) Income (loss) from operating affiliates 37,665 — 37,665 Net income (loss) 619,635 — 619,635 Amounts attributable to redeemable noncontrolling interests (2,390) — (2,390) Net income (loss) available to Arch 617,245 — 617,245 Preferred dividends (30,552) — (30,552) Net income (loss) available to Arch common shareholders $ 586,693 $ — $ 586,693 Underwriting Ratios Loss ratio 61.9 % 70.2 % (21.6) % 54.7 % — % 54.7 % Acquisition expense ratio 19.4 % 20.8 % 3.2 % 17.9 % — % 17.9 % Other operating expense ratio 14.9 % 7.3 % 17.3 % 12.2 % — % 12.2 % Combined ratio 96.2 % 98.3 % (1.1) % 84.8 % — % 84.8 % (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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’ Nine Months Ended September 30, 2021 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 4,381,372 $ 4,080,840 $ 1,143,691 $ 9,602,213 $ 457,465 $ 9,890,912 Premiums ceded (1,269,165) (1,535,607) (171,923) (2,973,005) (102,763) (2,907,002) Net premiums written 3,112,207 2,545,233 971,768 6,629,208 354,702 6,983,910 Change in unearned premiums (488,636) (484,607) 10,735 (962,508) (22,734) (985,242) Net premiums earned 2,623,571 2,060,626 982,503 5,666,700 331,968 5,998,668 Other underwriting income (loss) — 3,148 15,026 18,174 739 18,913 Losses and loss adjustment expenses (1,750,257) (1,494,539) (85,112) (3,329,908) (259,042) (3,588,950) Acquisition expenses (417,541) (381,060) (84,297) (882,898) (62,741) (945,639) Other operating expenses (409,386) (150,856) (143,697) (703,939) (32,869) (736,808) Underwriting income (loss) $ 46,387 $ 37,319 $ 684,423 $ 768,129 $ (21,945) $ 746,184 Net investment income 256,354 42,310 298,664 Net realized gains (losses) 239,690 80,638 320,328 Equity in net income (loss) of investment funds accounted for using the equity method 299,270 — 299,270 Other income (loss) 1,151 — 1,151 Corporate expenses (2) (59,279) — (59,279) Transaction costs and other (2) (793) (935) (1,728) Amortization of intangible assets (48,925) (898) (49,823) Interest expense (98,812) (8,410) (107,222) Net foreign exchange gains (losses) 39,691 (1,325) 38,366 Income (loss) before income taxes and income (loss) from operating affiliates 1,396,476 89,435 1,485,911 Income tax (expense) benefit (93,942) (234) (94,176) Income (loss) from operating affiliates 224,052 — 224,052 Net income (loss) 1,526,586 89,201 1,615,787 Amounts attributable to redeemable noncontrolling interests (1,936) (1,953) (3,889) Amounts attributable to nonredeemable noncontrolling interests — (78,314) (78,314) Net income (loss) available to Arch 1,524,650 8,934 1,533,584 Preferred dividends (38,159) — (38,159) Loss on redemption of preferred shares (15,101) — (15,101) Net income (loss) available to Arch common shareholders $ 1,471,390 $ 8,934 $ 1,480,324 Underwriting Ratios Loss ratio 66.7 % 72.5 % 8.7 % 58.8 % 78.0 % 59.8 % Acquisition expense ratio 15.9 % 18.5 % 8.6 % 15.6 % 18.9 % 15.8 % Other operating expense ratio 15.6 % 7.3 % 14.6 % 12.4 % 9.9 % 12.3 % Combined ratio 98.2 % 98.3 % 31.9 % 86.8 % 106.8 % 87.9 % (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.

Reserve for Losses and Loss Adj

Reserve for Losses and Loss Adjustment Expenses	9 Months Ended
	Sep. 30, 2022
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: Three Months Ended Nine Months Ended September 30, September 30, 2022 2021 2022 2021 Reserve for losses and loss adjustment expenses at beginning of period $ 18,194,324 $ 17,196,648 $ 17,757,156 $ 16,513,929 Unpaid losses and loss adjustment expenses recoverable 5,686,348 4,146,020 5,599,231 4,314,855 Net reserve for losses and loss adjustment expenses at beginning of period 12,507,976 13,050,628 12,157,925 12,199,074 Net incurred losses and loss adjustment expenses relating to losses occurring in: Current year 1,863,519 1,348,528 4,280,048 3,812,381 Prior years (180,823) (122,509) (493,861) (223,431) Total net incurred losses and loss adjustment expenses 1,682,696 1,226,019 3,786,187 3,588,950 Net losses and loss adjustment expense reserves of acquired business (1) — 104,307 — 104,307 Retroactive reinsurance transactions (2) — — — (183,893) Impact of deconsolidation of Somers (3) — (1,460,611) — (1,460,611) Net foreign exchange (gains) losses and other (243,387) (78,152) (524,682) 10,818 Net paid losses and loss adjustment expenses relating to losses occurring in: Current year (226,575) (208,923) (463,847) (432,348) Prior years (538,967) (417,368) (1,773,840) (1,610,397) Total net paid losses and loss adjustment expenses (765,542) (626,291) (2,237,687) (2,042,745) Net reserve for losses and loss adjustment expenses at end of period 13,181,743 12,215,900 13,181,743 12,215,900 Unpaid losses and loss adjustment expenses recoverable 6,106,548 5,115,147 6,106,548 5,115,147 Reserve for losses and loss adjustment expenses at end of period $ 19,288,291 $ 17,331,047 $ 19,288,291 $ 17,331,047 (1) Represents activity related to the Company’s acquisitions in the 2021 period of the Westpac Lenders Mortgage Insurance Limited and Somerset Bridge Group Limited, Southern Rock Holdings Limited and affiliates. (2) During the 2021 first quarter, the Company entered into a reinsurance to close and other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the acquisition of Barbican Group Holdings Limited (“Barbican”). (3) See note 1 1 . Development on Prior Year Loss Reserves 2022 Third Quarter During the 2022 third quarter, the Company recorded net favorable development on prior year loss reserves of $180.8 million, which consisted of $5.4 million from the insurance segment, $49.2 million from the reinsurance segment and $126.2 million from the mortgage segment. The insurance segment’s net favorable development of $5.4 million, or 0.5 loss ratio points, for the 2022 third quarter consisted of $15.9 million of net favorable development in short-tailed lines and $10.5 million of net adverse development in medium-tailed and long-tailed lines. Net favorable development in short-tailed lines reflected $8.9 million of favorable development in property (excluding marine), primarily from 2020 and 2021 accident years ( i.e. , the year in which a loss occurred) and $5.7 million of favorable development in lenders products, primarily from the 2021 accident year. Net adverse development in medium-tailed lines included $11.3 million of adverse development in professional liability business, primarily from the 2013 to 2016 and 2020 accident years, partially offset by favorable development in marine business of $5.9 million, across most accident years. Net adverse development in long-tailed lines reflected $12.3 million related to casualty business, primarily from the 2014 and 2020 accident years, partially offset by favorable development in construction, executive assurance and other lines of business. The reinsurance segment’s net favorable development of $49.2 million, or 4.9 loss ratio points, for the 2022 third quarter consisted of $58.1 million of net favorable development in short-tailed and medium-tailed lines and $8.9 million of net adverse development in long-tailed lines. Net favorable development in short-tailed lines reflected $35.8 million of favorable development related to property other than property catastrophe business, primarily from 2015 to 2021 underwriting years (i.e., all premiums and losses attributable to contracts having an inception or renewal date within the given twelve-month period) and $12.7 million of favorable development related to property catastrophe business, primarily from the 2014 to 2017 underwriting years. Net favorable development in medium-tailed lines included $7.9 million in marine and aviation lines, across most underwriting years. Net adverse development in long-tailed lines reflected $9.5 million related to casualty business, primarily from the 2014 to 2017 underwriting years. The mortgage segment’s net favorable development was $126.2 million, or 44.7 loss ratio points, for the 2022 third quarter, with the largest contributor being reserve releases associated with the U.S. first lien portfolio from the 2020 and 2021 accident years. The Company’s credit risk transfer, international, second lien and student loan businesses also contributed to the favorable development. 2021 Third Quarter During the 2021 third quarter, the Company recorded net favorable development on prior year loss reserves of $122.5 million, which consisted of $5.1 million from the insurance segment, $72.3 million from the reinsurance segment and $45.1 million from the mortgage segment. The insurance segment’s net favorable development of $5.1 million, or 0.5 loss ratio points, for the 2021 third quarter consisted of $49.0 million of net favorable development in short-tailed and long-tailed lines and $43.9 million of net adverse development in medium-tailed lines. Net favorable development in short-tailed lines reflected $5.4 million of favorable development in lenders products, primarily from the 2020 accident year, $5.4 million of favorable development from property (excluding marine), primarily from the 2020 accident year, and $5.1 million of favorable development in travel and accident, across most accident years. Net favorable development in long-tailed lines reflected $26.3 million of favorable development related to construction and national accounts, across most accident years, and $6.7 million of favorable development related to other business, including alternative markets, primarily from the 2015 to 2018 accident years. Net adverse development in medium-tailed lines included $37.0 million of adverse development in contract binding business, across most accident years, partially offset by favorable development in marine and programs, primarily from more recent accident years. The reinsurance segment’s net favorable development of $72.3 million, or 10.7 loss ratio points, for the 2021 third quarter consisted of $65.4 million of net favorable development in short-tailed lines and $6.9 million in medium-tailed and long-tailed lines. Net favorable development in short-tailed lines reflected $46.1 million of favorable development related to property catastrophe and property other than property catastrophe business, primarily from the 2017 to 2020 underwriting years and $18.9 million of favorable development related to other specialty, primarily from the 2012 to 2017 underwriting years. Net favorable development in medium-tailed and long-tailed lines included $4.7 million of favorable development in casualty, primarily from the 2013 and 2014 underwriting years. The mortgage segment’s net favorable development was $45.1 million, or 14.5 loss ratio points, for the 2021 third quarter, about half of which came from U.S. primary mortgage insurance, from better than expected cure activity in pre-pandemic delinquencies and recoveries on second lien and student loans, and the other half from our CRT portfolio and international mortgage insurance. Nine Months Ended September 30, 2022 During the nine months ended September 30, 2022, the Company recorded net favorable development on prior year loss reserves of $493.9 million, which consisted of $19.4 million from the insurance segment, $128.1 million from the reinsurance segment and $346.4 million from the mortgage segment. The insurance segment’s net favorable development of $19.4 million, or 0.6 loss ratio points, for the 2022 period consisted of $49.1 million of net favorable development in short-tailed and $29.7 million of net adverse development in medium and long-tailed lines. Net favorable development in short-tailed lines reflected $36.5 million of favorable development in lenders products, primarily from the 2021 accident year, and $14.3 million of favorable development related to travel and accident business, primarily from the 2019 to 2021 accident years. Net adverse development in medium-tailed lines included $24.9 million of adverse development in professional liability business, primarily from the 2013 to 2015 and 2018 to 2020 accident years, and $5.5 million of adverse development in contract binding business, across most accident years, partially offset by $11.4 million of favorable development in marine business, across most accident years. Net adverse development in long-tailed lines reflected $18.0 million of adverse development related to casualty business, primarily from the 2020 and 2021 accident years, partially offset by $17.4 million of favorable development in other business, including alternative markets and excess workers’ compensation, primarily from the 2019 and prior accident years. The reinsurance segment’s net favorable development of $128.1 million, or 4.7 loss ratio points, for the 2022 period consisted of $147.8 million of net favorable development from short and medium-tailed lines, partially offset by $19.7 million of net adverse development from long-tailed lines. Net favorable development in short-tailed lines reflected $83.2 million of favorable development from property other than property catastrophe business, primarily from the 2015 to 2021 underwriting years, $22.4 million of favorable development from property catastrophe, primarily from the 2018 to 2020 underwriting years, and $19.8 million from other specialty business, primarily from the 2021 underwriting year. Net favorable development in medium-tailed lines included $22.7 million in marine and aviation lines, across most underwriting years. Net adverse development in long-tailed lines primarily reflected $19.3 million in casualty reserves, primarily from the 2021 underwriting year. The mortgage segment’s net favorable development was $346.4 million, or 39.9 loss ratio points, for the 2022 period, with the largest contributor being reserve releases associated with the U.S. first lien portfolio from the 2020 and 2021 accident years. The Company’s credit risk transfer, international, second lien and student loan businesses also contributed to the favorable development. Nine Months Ended September 30, 2021 During the nine months ended September 30, 2021, the Company recorded net favorable development on prior year loss reserves of $223.4 million, which consisted of $13.1 million from the insurance segment, $119.6 million from the reinsurance segment, $99.1 million from the mortgage segment, partially offset by $8.4 million of adverse development from the ‘other’ segment (activity for the six months ended June 30, 2021 prior to deconsolidation of Somers). The insurance segment’s net favorable development of $13.1 million, or 0.5 loss ratio points, for the 2021 period consisted of $102.5 million of net favorable development in short-tailed and long-tailed lines, partially offset by $89.4 million of net adverse development in medium-tailed lines. Net favorable development of $65.3 million in short-tailed lines reflected $27.0 million of favorable development from property (excluding marine), primarily from the 2019 and 2020 accident years, $24.0 million of favorable development in lenders products, primarily from the 2020 accident year, and $14.4 million of favorable development in travel and accident, primarily from the 2017 to 2020 accident years. Net favorable development of $37.1 million in long-tailed lines included favorable development primarily related to construction, national accounts and alternative markets, primarily from the 2016 to 2019 accident years. Net adverse development in medium-tailed lines reflected $57.1 million of adverse development in contract binding business, primarily from the 2014 to 2019 accident years, $26.2 million of adverse development in professional liability business, primarily from the 2019 and 2020 accident years, and $6.9 million of adverse development in programs business, primarily from the 2019 accident year. The reinsurance segment’s net favorable development of $119.6 million, or 5.8 loss ratio points, for the 2021 period consisted of $139.7 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $20.1 million of net adverse development from long-tailed lines. Net favorable development of $132.6 million in short-tailed lines reflected $97.1 million of favorable development from other specialty lines, primarily from the 2016 to 2019 underwriting years, and $71.7 million of favorable development from property other than property catastrophe business, primarily from the 2017 to 2020 underwriting years. Such amounts were partially offset by adverse development of $36.3 million from property catastrophe, primarily from the 2020 underwriting year. Adverse development in long-tailed lines reflected an increase in reserves from casualty, primarily from the 2018 underwriting year. The mortgage segment’s net favorable development was $99.1 million, or 10.1 loss ratio points, for the 2021 period, which included reserve releases associated with various vintage credit risk transfer contracts that were called by the GSEs, favorable development on U.S. and international business and subrogation recoveries on second lien and student loan business.

Allowance for Expected Credit L

Allowance for Expected Credit Losses	9 Months Ended
	Sep. 30, 2022
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: Premium Receivables, Net of Allowance Allowance for Expected Credit Losses Three Months Ended September 30, 2022 Balance at beginning of period $ 3,634,182 $ 38,170 Change for provision of expected credit losses (1) 59 Balance at end of period $ 3,579,380 $ 38,229 Three Months Ended September 30, 2021 Balance at beginning of period $ 2,866,578 $ 35,979 Change for provision of expected credit losses (1) 2,736 Balance at end of period $ 2,807,720 $ 38,715 Nine Months Ended September 30, 2022 Balance at beginning of period $ 2,633,280 $ 39,958 Change for provision of expected credit losses (1) (1,729) Balance at end of period $ 3,579,380 $ 38,229 Nine Months Ended September 30, 2021 Balance at beginning of period $ 2,064,586 $ 37,781 Change for provision of expected credit losses (1) 934 Balance at end of period $ 2,807,720 $ 38,715 (1) Amounts deemed uncollectible are written-off in operating expenses. For the 2022 third quarter and 2021 third quarter, amounts written off were $1.9 million and $1.2 million, respectively. For the nine months ended September 30, 2022 and 2021 period, amounts written off were $6.6 million and $2.4 million, respectively. Reinsurance Recoverables The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables: Reinsurance Recoverables, Net of Allowance Allowance for Expected Credit Losses Three Months Ended September 30, 2022 Balance at beginning of period $ 5,938,511 $ 14,740 Change for provision of expected credit losses 2,626 Balance at end of period $ 6,356,456 $ 17,366 Three Months Ended September 30, 2021 Balance at beginning of period $ 4,314,515 $ 11,029 Change for provision of expected credit losses 1,802 Balance at end of period $ 5,358,852 $ 12,831 Nine Months Ended September 30, 2022 Balance at beginning of period $ 5,880,735 $ 13,230 Change for provision of expected credit losses 4,136 Balance at end of period $ 6,356,456 $ 17,366 Nine Months Ended September 30, 2021 Balance at beginning of period $ 4,500,802 $ 11,636 Change for provision of expected credit losses 1,195 Balance at end of period $ 5,358,852 $ 12,831 The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums): September 30, December 31 2022 2021 Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses $ 6,356,456 $ 5,880,735 % due from carriers with A.M. Best rating of “A-” or better 69.5 % 69.7 % % due from all other rated carriers 0.1 % 0.1 % % due from all other carriers with no A.M. Best rating (1) 30.4 % 30.2 % Largest balance due from any one carrier as % of total shareholders’ equity 9.1 % 6.7 % (1) At September 30, 2022 and December 31, 2021 over 95% and 91% of such amount were collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively. Contractholder Receivables The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables: Contract-holder Receivables, Net of Allowance Allowance for Expected Credit Losses Three Months Ended September 30, 2022 Balance at beginning of period $ 1,758,018 $ 3,005 Change for provision of expected credit losses (645) Balance at end of period $ 1,735,730 $ 2,360 Three Months Ended September 30, 2021 Balance at beginning of period $ 1,882,948 $ 4,471 Change for provision of expected credit losses (987) Balance at end of period 1,824,990 $ 3,484 Nine Months Ended September 30, 2022 Balance at beginning of period $ 1,828,691 $ 3,437 Change for provision of expected credit losses (1,077) Balance at end of period $ 1,735,730 $ 2,360 Nine Months Ended September 30, 2021 Balance at beginning of period $ 1,986,924 $ 8,638 Change for provision of expected credit losses (5,154) Balance at end of period 1,824,990 $ 3,484

Investment Information

Investment Information	9 Months Ended
	Sep. 30, 2022
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 Gross Allowance for Expected Credit Losses Cost or September 30, 2022 Fixed maturities: Corporate bonds $ 7,096,269 $ 51,777 $ (895,365) $ (35,657) $ 7,975,514 Residential mortgage backed securities 763,371 7,561 (84,183) 2 839,991 Municipal bonds 407,724 5,437 (37,692) (99) 440,078 Commercial mortgage backed securities 1,064,238 3,079 (50,010) (1,583) 1,112,752 U.S. government and government agencies 5,126,407 36,074 (400,784) — 5,491,117 Non-U.S. government securities 2,073,170 9,315 (287,583) (1,720) 2,353,158 Asset backed securities 1,589,548 1,076 (105,037) (6,936) 1,700,445 Total 18,120,727 114,319 (1,860,654) (45,993) 19,913,055 Short-term investments 1,940,857 1,419 (1,633) — 1,941,071 Total $ 20,061,584 $ 115,738 $ (1,862,287) $ (45,993) $ 21,854,126 December 31, 2021 Fixed maturities: Corporate bonds $ 6,553,333 $ 104,170 $ (69,194) $ (2,037) $ 6,520,394 Residential 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 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 Gross Estimated Gross Estimated Gross September 30, 2022 Fixed maturities: Corporate bonds $ 5,596,229 $ (625,774) $ 1,470,800 $ (269,591) $ 7,067,029 $ (895,365) Residential mortgage backed securities 620,572 (63,732) 93,902 (20,451) 714,474 (84,183) Municipal bonds 373,219 (36,039) 9,399 (1,653) 382,618 (37,692) Commercial mortgage backed securities 995,680 (49,215) 34,445 (795) 1,030,125 (50,010) U.S. government and government agencies 4,205,475 (303,805) 715,347 (96,979) 4,920,822 (400,784) Non-U.S. government securities 1,728,965 (221,540) 301,298 (66,043) 2,030,263 (287,583) Asset backed securities 1,193,405 (74,885) 310,838 (30,152) 1,504,243 (105,037) Total 14,713,545 (1,374,990) 2,936,029 (485,664) 17,649,574 (1,860,654) Short-term investments 227,201 (1,633) — — 227,201 (1,633) Total $ 14,940,746 $ (1,376,623) $ 2,936,029 $ (485,664) $ 17,876,775 $ (1,862,287) December 31, 2021 Fixed maturities: Corporate bonds $ 3,639,582 $ (63,938) $ 98,867 $ (5,256) $ 3,738,449 $ (69,194) Residential 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) At September 30, 2022, on a lot level basis, approximately 9,590 security lots out of a total of approximately 11,500 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 $7.2 million. 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 contractual maturities of the Company’s fixed maturities 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. September 30, 2022 December 31, 2021 Maturity Estimated Amortized Estimated Amortized Due in one year or less $ 579,231 $ 599,970 $ 300,889 $ 299,772 Due after one year through five years 10,029,151 10,808,495 8,355,255 8,339,387 Due after five years through 10 years 3,856,180 4,495,113 4,689,155 4,684,393 Due after 10 years 239,008 356,289 505,758 493,927 14,703,570 16,259,867 13,851,057 13,817,479 Residential mortgage backed securities 763,371 839,991 408,477 411,110 Commercial mortgage backed securities 1,064,238 1,112,752 1,046,484 1,047,867 Asset backed securities 1,589,548 1,700,445 2,692,091 2,697,367 Total $ 18,120,727 $ 19,913,055 $ 17,998,109 $ 17,973,823 Equity Securities, at Fair Value At September 30, 2022, the Company held $0.8 billion of equity securities, at fair value, compared to $1.8 billion at December 31, 2021. Such holdings include publicly traded common stocks primarily in the consumer cyclical and non-cyclical, technology, communication and financial sectors and exchange-traded funds in fixed income, equity and other sectors. Other Investments, at Fair Value The following table summarizes the Company’s other investments and other investable assets: September 30, December 31, Fixed maturities $ 530,303 $ 416,698 Other investments 1,005,929 1,432,553 Short-term investments 28,614 97,806 Equity securities 13,905 26,493 Total $ 1,578,751 $ 1,973,550 The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy: September 30, December 31, Lending $ 398,789 $ 536,345 Investment grade fixed income 229,262 147,810 Term loan investments 151,649 484,950 Private equity 117,856 91,126 Energy 55,250 81,692 Credit related funds 53,123 70,278 Infrastructure — 20,352 Total $ 1,005,929 $ 1,432,553 Investments Accounted For Using the Equity Method The following table summarizes the Company’s investments accounted for using the equity method, by strategy: September 30, December 31, Credit related funds $ 1,135,623 $ 1,022,334 Private equity 761,997 436,042 Real estate 474,666 396,395 Lending 454,196 376,649 Equities 261,650 395,090 Infrastructure 236,920 230,070 Energy 113,778 119,141 Fixed income 127,116 101,890 Total $ 3,565,946 $ 3,077,611 Certain of the Company’s other investments 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 has determined that it is not required to consolidate these investments because it is not the primary beneficiary of 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 line item: September 30, December 31, Investments accounted for using the equity method (1) $ 3,565,946 $ 3,077,611 Investments accounted for using the fair value option (2) 120,498 170,595 Total $ 3,686,444 $ 3,248,206 (1) Aggregate unfunded commitments were $2.8 billion at September 30, 2022, compared to $2.6 billion at December 31, 2021. (2) Aggregate unfunded commitments were $21.5 million at September 30, 2022, compared to $18.8 million at December 31, 2021. Net Investment Income The components of net investment income were derived from the following sources: September 30, 2022 2021 Three Months Ended Fixed maturities $ 123,568 $ 75,964 Term loans 88 1,736 Equity securities 4,261 9,867 Short-term investments 9,304 1,858 Other (1) 8,556 17,378 Gross investment income 145,777 106,803 Investment expenses (17,137) (18,608) Net investment income $ 128,640 $ 88,195 Nine Months Ended Fixed maturities $ 310,963 $ 255,215 Term loans 2,106 33,343 Equity securities 16,620 24,101 Short-term investments 15,999 3,603 Other (1) 26,598 51,683 Gross investment income 372,286 367,945 Investment expenses (56,818) (69,281) Net investment income $ 315,468 $ 298,664 (1) Includes income distributions from investment funds and other items. Net Realized Gains (Losses) Net realized gains (losses), which include changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings were as follows: September 30, 2022 2021 Three Months Ended Available for sale securities: Gross gains on investment sales $ 18,030 $ 86,819 Gross losses on investment sales (73,970) (18,446) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities (19,304) (7,492) Other investments (17,882) 3,811 Equity securities (584) 3,042 Short-term investments (975) 16 Equity securities, at fair value: Net realized gains (losses) on sales during the period (6,401) 14,736 Net unrealized gains (losses) on equity securities still held at reporting date (36,162) (40,155) Allowance for credit losses: Investments related 8,652 (456) Underwriting related (4,232) (3,985) Derivative instruments (1) (48,196) (21,435) Other (2,649) (41,495) Net realized gains (losses) $ (183,673) $ (25,040) Nine Months Ended Available for sale securities: Gross gains on investment sales $ 52,923 $ 267,362 Gross losses on investment sales (239,493) (132,071) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities (89,148) 19,973 Other investments (35,203) 111,550 Equity securities (6,021) 10,599 Short-term investments (3,132) 648 Equity securities, at fair value: Net realized gains (losses) on sales during the period 75,689 86,155 Net unrealized gains (losses) on equity securities still held at reporting date (318,732) 45,400 Allowance for credit losses: Investments related (48,096) (1,208) Underwriting related (7,676) 2,664 Derivative instruments (1) (117,591) (36,428) Other (6,186) (54,316) Net realized gains (losses) $ (742,666) $ 320,328 (1) See note 9 for information on the Company’s derivative instruments. Equity in Net Income (Loss) of Investment Funds Accounted for Using the Equity Method The Company recorded a loss of $18.9 million related to investment funds accounted for using the equity method in the 2022 third quarter, compared to income of $105.4 million for the 2021 third quarter and an income of $75.5 million for the nine months ended September 30, 2022, compared to income of $299.3 million for nine months ended September 30, 2021. 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). Such investments are generally recorded on a one three 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 of September 30, 2022, the Company owned approximately 29.86% of the issued shares of Coface, or 30.05% excluding treasury shares, with a carrying value of $506.7 million, compared to $630.5 million at December 31, 2021. 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 September 30, 2022 the Company’s carrying value in Greysbridge was $277.6 million, compared to $375.7 million at December 31, 2021, 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. Income from operating affiliates for the 2022 third quarter was income of $8.5 million, compared to an income of $124.1 million, for the 2021 third quarter and income of $37.7 million for the nine months ended September 30, 2022, compared to income of $224.1 million for nine months ended September 30, 2021. 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: Structured Securities (1) Municipal Corporate Total Three Months Ended September 30, 2022 Balance at beginning of period $ 18,283 $ 298 $ 39,829 $ 58,410 Additions for current-period provision for expected credit losses 1,782 12 1,986 3,780 Additions (reductions) for previously recognized expected credit losses (9,767) (211) (2,552) (12,530) Reductions due to disposals (1,780) — (1,887) (3,667) Balance at end of period $ 8,518 $ 99 $ 37,376 $ 45,993 Three Months Ended September 30, 2021 Balance at beginning of period $ 759 $ 6 $ 1,359 $ 2,124 Additions for current-period provision for expected credit losses 48 — — 48 Additions (reductions) for previously recognized expected credit losses 14 (4) 395 405 Reductions due to disposals (234) — (232) (466) Balance at end of period $ 587 $ 2 $ 1,522 $ 2,111 Nine Months Ended September 30, 2022 Balance at beginning of period $ 802 $ 2 $ 2,079 $ 2,883 Additions for current-period provision for expected credit losses 12,560 359 40,602 53,521 Additions (reductions) for previously recognized expected credit losses (2,575) (262) (2,772) (5,609) Reductions due to disposals (2,269) — (2,533) (4,802) Balance at end of period $ 8,518 $ 99 $ 37,376 $ 45,993 Nine Months Ended September 30, 2021 Balance at beginning of period $ 1,490 $ 11 $ 896 $ 2,397 Additions for current-period provision for expected credit losses 282 — 2,428 2,710 Additions (reductions) for previously recognized expected credit losses (751) (9) (557) (1,317) Reductions due to disposals (434) — (1,245) (1,679) Balance at end of period $ 587 $ 2 $ 1,522 $ 2,111 (1) Includes asset backed securities, residential mortgage backed securities and commercial mortgage backed securities. Restricted Assets The Company is required to maintain assets on deposit, which primarily consist of fixed maturities, with various regulatory authorities to support its underwriting operations. The Company’s subsidiaries maintain assets in trust accounts as collateral for transactions with affiliated companies and also have investments in segregated portfolios primarily to provide collateral or guarantees for letters of credit to third parties. See note 18, “Commitments and Contingencies,” of the notes to consolidated financial statements in the Company’s 2021 Form 10-K. The following table details the value of the Company’s restricted assets: September 30, December 31, Assets used for collateral or guarantees: Affiliated transactions $ 4,212,521 $ 4,223,955 Third party agreements 2,847,814 2,721,160 Deposits with U.S. regulatory authorities 756,368 798,100 Deposits with non-U.S. regulatory authorities 519,254 506,517 Total restricted assets $ 8,335,957 $ 8,249,732 Reconciliation of Cash and Restricted Cash The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets: September 30, December 31, Cash $ 813,583 $ 858,668 Restricted cash (included in ‘other assets’) 444,741 456,103 Cash and restricted cash $ 1,258,324 $ 1,314,771

Fair Value

Fair Value	9 Months Ended
	Sep. 30, 2022
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 average number of 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. The Company did not adjust any of the prices obtained from the independent pricing sources at September 30, 2022. 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. Where quotes are unavailable, fair value is determined by the Investment Manager using quantitative and qualitative assessments such as internally modeled values. Of the $22.8 billion of financial assets and liabilities measured at fair value at September 30, 2022, approximately $12.6 million, or 0.1%, were priced using non-binding broker-dealer quotes or modeled valuations. 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 or modeled valuations. 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. 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. 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. Residential 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. 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. 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. The pricing services also review prepayment speeds and other indicators, when applicable. 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. The pricing services also review prepayment speeds and other indicators, when applicable. 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. Certain equity securities are included in Level 2 of the valuation hierarchy as the significant inputs used in the pricing process for such securities are observable market inputs. Other equity 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’s other investments 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. The fair values for certain of the Company’s other investments are determined using net asset values as advised by external fund managers. The net asset value is based on the fund manager’s valuation of the underlying holdings in accordance with the fund’s governing documents. 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. 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. Other liabilities The Company’s other liabilities include contingent and deferred consideration liabilities related to the Company’s acquisitions. Contingent consideration liabilities 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 the future payments using an income approach based on modeled inputs which include a weighted average cost of capital. Deferred consideration liabilities are measured at fair value on the transaction date. The Company determined that contingent and deferred 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 September 30, 2022: Estimated Fair Value Measurements Using: Estimated Quoted Prices in Significant Significant Assets measured at fair value: Available for sale securities: Fixed maturities: Corporate bonds $ 7,096,269 $ — $ 7,096,256 $ 13 Residential mortgage backed securities 763,371 — 763,371 — Municipal bonds 407,724 — 407,724 — Commercial mortgage backed securities 1,064,238 — 1,064,238 — U.S. government and government agencies 5,126,407 5,100,908 25,499 — Non-U.S. government securities 2,073,170 — 2,073,170 — Asset backed securities 1,589,548 — 1,589,548 — Total 18,120,727 5,100,908 13,019,806 13 Short-term investments 1,940,857 1,873,480 67,377 — Equity securities, at fair value 809,869 775,264 31,566 3,039 Derivative instruments (2) 176,160 — 176,160 — Residential mortgage loans 2,255 — 2,255 — Fair value option: Corporate bonds 524,177 — 524,177 — Non-U.S. government bonds 4,032 — 4,032 — Asset backed securities 2,094 — 2,094 — Short-term investments 28,614 405 28,209 — Equity securities 13,905 9,312 1 4,592 Other investments 175,259 — 141,021 34,238 Other investments measured at net asset value (1) 830,670 Total 1,578,751 9,717 699,534 38,830 Total assets measured at fair value $ 22,628,619 $ 7,759,369 $ 13,996,698 $ 41,882 Liabilities measured at fair value: Other liabilities $ (13,421) $ — $ — $ (13,421) Derivative instruments (2) (112,577) — (112,577) — Total liabilities measured at fair value $ (125,998) $ — $ (112,577) $ (13,421) (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) See note 9 . The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2021: Estimated Fair Value Measurements Using: Estimated Quoted Prices in Significant Significant Assets measured at fair value: Available for sale securities: Fixed maturities: Corporate bonds $ 6,553,333 $ — $ 6,553,320 $ 13 Residential 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 (2) 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: Other liabilities $ (16,960) $ — $ — $ (16,960) Derivative instruments (2) (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) See note 9 . 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: Assets Liabilities s Available For Sale Fair Value Option Fair Value Structured Securities (1) Corporate Corporate Other Equity Equity Other Liabilities Three Months Ended September 30, 2022 Balance at beginning of period $ 2,867 $ 3,570 $ — $ 33,331 $ 4,392 $ 2,906 $ (16,205) Total gains or (losses) (realized/unrealized) Included in earnings (2) (601) 52 — 116 200 133 (89) Included in other comprehensive income 144 (59) — — — — 965 Purchases, issuances, sales and settlements Purchases — — — 1,458 — — — Issuances — — — — — — — Sales (2,051) (3,550) — (667) — — — Settlements (359) — — — — — 1,908 Transfers in and/or out of Level 3 — — — — — — — Balance at end of period $ — $ 13 $ — $ 34,238 $ 4,592 $ 3,039 $ (13,421) Three Months Ended September 30, 2021 Balance at beginning of period $ 3,424 $ 13 $ 998 $ 73,900 $ 73,678 $ 49,136 $ (466) Total gains or (losses) (realized/unrealized) Included in earnings (2) 10 — — — 38 11 — Included in other comprehensive income 10 — — — — — — Purchases, issuances, sales and settlements Purchases — — — — — 208 (17,345) Issuances — — — — — — — Sales (3) — — (998) (44,143) (69,181) (46,773) — Settlements — — — — — — — Transfers in and/or out of Level 3 — — — — — — — Balance at end of period $ 3,444 $ 13 $ — $ 29,757 $ 4,535 $ 2,582 $ (17,811) Nine Months Ended September 30, 2022 Balance at beginning of year $ 3,347 $ 13 $ — $ 27,981 $ 4,748 $ 2,918 $ (16,960) Total gains or (losses) (realized/unrealized) Included in earnings (2) (592) 52 — 150 (156) (103) (284) Included in other comprehensive income (1) (59) — — — — 1,915 Purchases, issuances, sales and settlements Purchases — — — 12,228 — 227 — Issuances — — — — — — — Sales (2,051) (3,550) — (3,138) — (3) — Settlements (703) — — (2,983) — — 1,908 Transfers in and/or out of Level 3 — 3,557 — — — — — Balance at end of period $ — $ 13 $ — $ 34,238 $ 4,592 $ 3,039 $ (13,421) Nine Months Ended September 30, 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) (46) — 13 881 4,728 1,837 — Included in other comprehensive income 67 — — — — — — Purchases, issuances, sales and settlements Purchases — — — 13,003 — 5,503 (17,345) Issuances — — — — — — — Sales (3) — — (998) (51,230) (69,181) (46,773) — Settlements (3) — — — — — (5) Transfers in and/or out of Level 3 — — — — — — — Balance at end of period $ 3,444 $ 13 $ — $ 29,757 $ 4,535 $ 2,582 $ (17,811) (1) Includes asset backed securities, residential mortgage backed securities and commercial mortgage backed securities. (2) Gains or losses were included in net realized gains (losses). (3) Sales for the 2021 periods primarily related 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 September 30, 2022, due to their respective short maturities. As these financial instruments are not actively traded, their respective fair values are classified within Level 2.

Derivative Instruments

Derivative Instruments	9 Months Ended
	Sep. 30, 2022
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 Derivatives (1) Liability Derivatives (1) Notional September 30, 2022 Futures contracts $ 72,730 $ (60,684) $ 2,189,945 Foreign currency forward contracts 25,281 (26,995) 835,941 TBAs — — — Other 78,149 (24,898) 3,766,549 Total $ 176,160 $ (112,577) December 31, 2021 Futures contracts $ 34,999 $ (9,808) $ 2,826,564 Foreign currency forward contracts 7,734 (11,390) 915,962 TBAs 11,227 — 11,227 Other 73,161 (33,026) 3,736,773 Total $ 127,121 $ (54,224) (1) The fair value of asset derivatives are included in ‘ other assets other liabilities (2) Represents the absolute notional value of all outstanding contracts, consisting of long and short positions. The Company did not hold any derivatives which were designated as hedging instruments at September 30, 2022 or December 31, 2021. 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. Contractual close-out netting reduces derivatives credit exposure from gross to net exposure. At September 30, 2022, asset derivatives and liability derivatives of $164.9 million and $112.6 million, respectively, were subject to a master netting agreement, compared to $122.3 million and $53.9 million, respectively, at December 31, 2021. The remaining derivatives included in the preceding table 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 September 30, hedging instruments: 2022 2021 Three Months Ended Net realized gains (losses): Futures contracts $ (26,347) $ (10,073) Foreign currency forward contracts (18,340) (16,146) TBAs — (46) Other (1) (3,509) 4,830 Total $ (48,196) $ (21,435) Nine Months Ended Net realized gains (losses): Futures contracts $ (112,326) $ (17,394) Foreign currency forward contracts (46,016) (36,922) TBAs (51) (46) Other (1) 40,802 17,934 Total $ (117,591) $ (36,428) (1) Includes realized gains and losses on swaps, options and other derivatives contracts.

Commitments and Contingencies

Commitments and Contingencies	9 Months Ended
	Sep. 30, 2022
Commitments and Contingencies Disclosure [Abstract]
Commitments and Contingencies	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 April 7, 2022, Arch Capital and certain of its subsidiaries amended the existing five $113.2 million. In addition, certain of Arch Capital’s subsidiaries had outstanding secured and unsecured letters of credit through other facilities of $22.7 million and $290.0 million respectively, which were issued in the normal course of business. 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 $3.1 billion at September 30, 2022, compared to $3.0 billion at December 31, 2021. Interest Paid

Variable Interest Entities and

Variable Interest Entities and Noncontrolling Interests	9 Months Ended
	Sep. 30, 2022
Noncontrolling Interest [Abstract]
Variable Interest Entity and Noncontrolling Interests	Somers In March 2014, the Company invested $100.0 million and acquired approximately 11% of Somers’ outstanding common equity. 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 contemplated by the Merger Agreement and the related Greysbridge equity financing closed on July 1, 2021. In connection therewith and effective July 1, 2021, Somers became wholly owned by Greysbridge, and Greysbridge is now 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. Through June 30, 2021, Somers generated $47.0 million of cash provided by operating activities, $96.3 million of cash provided by investing activities and $2.0 million of cash used for financing activities. Redeemable noncontrolling interests The following table sets forth activity in the redeemable non-controlling interests: September 30, 2022 2021 Three Months Ended Balance, beginning of period $ 8,459 $ 57,533 Impact of deconsolidation of Somers — (48,919) Other 449 1,623 Balance, end of period $ 8,908 $ 10,237 Nine Months Ended Balance, beginning of year $ 9,233 $ 58,548 Impact of deconsolidation of Somers — (48,919) Other (325) 608 Balance, end of period $ 8,908 $ 10,237 The portion of income or loss attributable to third party investors, recorded in the Company’s consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests,’ are summarized in the table below: September 30, 2022 2021 Three Months Ended Amounts attributable to non-redeemable noncontrolling interests $ — $ — Amounts attributable to redeemable noncontrolling interests (1,157) (1,473) Net (income) loss attributable to noncontrolling interests $ (1,157) $ (1,473) Nine Months Ended Amounts attributable to non-redeemable noncontrolling interests $ — $ (78,314) Amounts attributable to redeemable noncontrolling interests (2,390) (3,889) Net (income) loss attributable to noncontrolling interests $ (2,390) $ (82,203) 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 and later 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. September 30, 2022 December 31, 2021 Maximum Exposure to Loss Maximum Exposure to Loss Bellemeade Entities Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total Coverage Remaining from Reinsurers (1) Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total 2017-1 Ltd. (Oct-17) $ 46,772 $ (23) $ 88 $ 65 $ — $ 108,368 $ (159) $ 424 $ 265 2018-1 Ltd. (Apr-18) 103,131 (220) 644 424 — 181,136 (528) 1,268 740 2018-3 Ltd. (Oct-18) 217,701 (862) 2,107 1,245 — 302,563 (1,018) 2,496 1,478 2019-1 Ltd. (Mar-19) 119,193 (496) 2,704 2,208 — 181,324 (380) 5,807 5,427 2019-2 Ltd. (Apr-19) 347,050 (656) 4,308 3,652 — 398,316 (515) 3,998 3,483 2019-3 Ltd. (Jul-19) 257,663 (192) 1,492 1,300 — 409,859 (584) 3,190 2,606 2019-4 Ltd. (Oct-19) 283,684 (532) 3,663 3,131 — 411,954 (462) 4,759 4,297 2020-2 Ltd. (Sep-20) 122,897 (20) 595 575 153 217,766 (177) 1,984 1,807 2020-3 Ltd. (Nov-20) 268,385 (204) 2,845 2,641 8,569 348,818 (128) 5,793 5,665 2020-4 Ltd. (Dec-20) 107,396 10 707 717 4,795 176,826 (50) 1,630 1,580 2021-1 Ltd. (Mar-21) 497,069 (2,234) 936 (1,298) 43,198 568,986 (303) 3,283 2,980 2021-2 Ltd. (Jun-21) 471,039 (2,047) 984 (1,063) 80,268 522,807 281 4,124 4,405 2021-3 Ltd. (Sep-21) 498,309 (2,414) 991 (1,423) 129,127 507,873 (411) 3,446 3,035 2022-1 Ltd. (Jan-22) 283,500 (1,326) 627 (699) 33,260 2022-2 Ltd. (Sep-22) 201,005 — 744 744 126,160 Total $ 3,824,794 $ (11,216) $ 23,435 $ 12,219 $ 425,530 $ 4,336,596 $ (4,434) $ 42,202 $ 37,768 (1) Coverage from a separate panel of reinsurers remaining at September 30, 2022.

Other Comprehensive Income (Los

Other Comprehensive Income (Loss)	9 Months Ended
	Sep. 30, 2022
Comprehensive Income Note Disclosure [Abstract]
Other Comprehensive Income (Loss)	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): Amounts Reclassified from AOCI Consolidated Statement of Income Three Months Ended Nine Months Ended Details About Line Item That Includes September 30, September 30, AOCI Components Reclassification 2022 2021 2022 2021 Unrealized appreciation (decline) on available-for-sale investments Net realized gains (losses) $ (55,940) $ 68,373 $ (186,570) $ 135,291 Provision for credit losses 8,652 (457) (48,096) (1,208) Total before tax (47,288) 67,916 (234,666) 134,083 Income tax (expense) benefit 703 (5,262) 28,093 (13,579) Net of tax $ (46,585) $ 62,654 $ (206,573) $ 120,504 Before Tax Amount Tax Expense (Benefit) Net of Tax Amount Three Months Ended September 30, 2022 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (671,907) $ (62,148) $ (609,759) Less reclassification of net realized gains (losses) included in net income (47,288) (703) (46,585) Foreign currency translation adjustments (70,388) — (70,388) Other comprehensive income (loss) $ (695,007) $ (61,445) $ (633,562) Three Months Ended September 30, 2021 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (104,607) $ (8,684) $ (95,923) Less reclassification of net realized gains (losses) included in net income 67,916 5,262 62,654 Foreign currency translation adjustments (32,060) (350) (31,710) Other comprehensive income (loss) $ (204,583) $ (14,296) $ (190,287) Nine Months Ended September 30, 2022 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (2,132,845) $ (240,726) $ (1,892,119) Less reclassification of net realized gains (losses) included in net income (234,666) (28,093) (206,573) Foreign currency translation adjustments (141,515) 166 (141,681) Other comprehensive income (loss) $ (2,039,694) $ (212,467) $ (1,827,227) Nine Months Ended September 30, 2021 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (307,910) $ (28,808) $ (279,102) Less reclassification of net realized gains (losses) included in net income 134,083 13,579 120,504 Foreign currency translation adjustments (54,083) 6 (54,089) Other comprehensive income (loss) $ (496,076) $ (42,381) $ (453,695)

Income Taxes

Income Taxes	9 Months Ended
	Sep. 30, 2022
Income Tax Disclosure [Abstract]
Income Taxes	The Company’s income tax provision on income before income taxes, including income (loss) from operating affiliates, resulted in an effective tax rate of 3.0% for the nine months ended September 30, 2022, compared to 5.5% for the nine months ended September 30, 2021. The effective tax rate for the nine months ended September 30, 2022 and 2021 periods included discrete income tax benefits of $36.5 million and $28.7 million, respectively. The discrete income tax benefits had the effect of decreasing the effective tax rate on net income available to Arch common shareholders by 5.7% and 1.7%, respectively. The discrete tax items in both periods were primarily related to the release of a valuation allowance on certain U.K. deferred tax assets. The Company’s effective tax rate, which is based upon the expected annual effective tax rate, may fluctuate from period to period based on the relative mix of income or loss reported by jurisdiction and the varying tax rates in each jurisdiction. The Company had a net deferred tax asset of $572.1 million at September 30, 2022, compared to a net deferred tax asset of $194.0 million at December 31, 2021. The change is primarily a result of market value fluctuations in the investment portfolio. In addition, the Company paid $201.6 million and $202.4 million of income taxes for the nine months ended September 30, 2022 and 2021, respectively.

Legal Proceedings

Legal Proceedings	9 Months Ended
	Sep. 30, 2022
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 September 30, 2022, 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.

Transactions With Related Parti

Transactions With Related Parties	9 Months Ended
	Sep. 30, 2022
Related Party Transactions [Abstract]
Transactions with related parties	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 September 30, 2022 and December 31, 2021. In July 2021, following consummation of the Merger Agreement and the related Greysbridge equity financing, pursuant to which Somers became wholly owned by Greysbridge, and Greysbridge became 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 the three and nine months ended September 30, 2022, the Company ceded premiums written related to such transactions of $236.5 million and $661.1 million, respectively (which includes reinsurance transactions in force as well as those entered into in conjunction with the Merger Agreement). For the three and nine months ended September 30, 2021, the Company ceded premiums written related to such transactions of $316.2 million. In addition, Somers paid certain acquisition costs and administrative fees to the Company. At September 30, 2022, reinsurance recoverable on unpaid and paid losses from Somers was $1.1 billion, with a reinsurance balance payable to Somers of $408.0 million. At December 31, 2021, reinsurance recoverable on unpaid and paid losses from Somers was $902.8 million, with a reinsurance balance payable to Somers of $258.4 million. See note 11 for information about Somers. 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.

Basis of Presentation and Rec_2

Basis of Presentation and Recent Accounting Pronouncements (Policies)	9 Months Ended
	Sep. 30, 2022
Organization, Consolidation and Presentation of Financial Statements [Abstract]
Basis of accounting	The interim consolidated financial statements have been prepared in conformity with accounting principles generally accepted in the United States of America (“GAAP”). 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. In the opinion of management, the accompanying unaudited interim consolidated financial statements reflect all adjustments (consisting of normally recurring accruals) necessary for a fair statement of results on an interim basis. The results of any interim period are not necessarily indicative of the results for a full year or any future periods.
Reclassification of prior periods	The Company has reclassified the presentation of certain prior year information to conform to the current presentation. Such reclassifications had no effect on the Company’s net income, comprehensive income, shareholders’ equity or cash flows.
Recent accounting pronouncements	Inflation Reduction Act of 2022 On August 16, 2022, the U.S. government enacted the Inflation Reduction Act of 2022, which among other things implements a 15% minimum tax on book income of certain large corporations, a 1% excise tax on net stock repurchases and several tax incentives to promote clean energy. The effective date of these provisions is January 1, 2023. Based on its current analysis of the provisions, the Company does not expect that this legislation will have a material effect on the Company’s consolidated financial statements. Recently Issued Accounting Standards Adopted

Earnings Per Common Share (Tabl

Earnings Per Common Share (Tables)	9 Months Ended
	Sep. 30, 2022
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: Three Months Ended Nine Months Ended September 30, September 30, 2022 2021 2022 2021 Numerator: Net income (loss) $ 18,258 $ 421,415 $ 619,635 $ 1,615,787 Amounts attributable to noncontrolling interests (1,157) (1,473) (2,390) (82,203) Net income (loss) available to Arch 17,101 419,942 617,245 1,533,584 Preferred dividends (10,184) (16,090) (30,552) (38,159) Loss on redemption of preferred shares — (15,101) — (15,101) Net income (loss) available to Arch common shareholders $ 6,917 $ 388,751 $ 586,693 $ 1,480,324 Denominator: Weighted average common shares and common share equivalents outstanding — basic 365,190,527 389,274,220 369,525,348 395,899,591 Effect of dilutive common share equivalents: Nonvested restricted shares 2,351,039 2,131,915 2,171,158 1,877,930 Stock options (1) 6,185,711 6,497,212 6,676,674 6,482,964 Weighted average common shares and common share equivalents outstanding — diluted 373,727,277 397,903,347 378,373,180 404,260,485 Earnings per common share: Basic $ 0.02 $ 1.00 $ 1.59 $ 3.74 Diluted $ 0.02 $ 0.98 $ 1.55 $ 3.66 (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 the 2022 third quarter and 2021 third quarter, the number of stock options excluded were 774,481 and 1,948,006, respectively. For the nine months ended September 30, 2022 and 2021, the number of stock options excluded were 785,682 and 2,397,507, respectively.

Segment Information (Tables)

Segment Information (Tables)	9 Months Ended
	Sep. 30, 2022
Segment Reporting [Abstract]
Analysis of underwriting income or loss by segment and reconciliation to net income 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: Three Months Ended September 30, 2022 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 1,862,026 $ 1,639,061 $ 362,409 $ 3,860,683 $ — $ 3,860,683 Premiums ceded (493,267) (560,225) (86,230) (1,136,909) — (1,136,909) Net premiums written 1,368,759 1,078,836 276,179 2,723,774 — 2,723,774 Change in unearned premiums (181,851) (77,062) 5,889 (253,024) — (253,024) Net premiums earned 1,186,908 1,001,774 282,068 2,470,750 — 2,470,750 Other underwriting income (loss) — 452 2,625 3,077 — 3,077 Losses and loss adjustment expenses (822,663) (927,911) 67,878 (1,682,696) — (1,682,696) Acquisition expenses (232,469) (208,425) (6,693) (447,587) — (447,587) Other operating expenses (165,499) (62,777) (46,471) (274,747) — (274,747) Underwriting income (loss) $ (33,723) $ (196,887) $ 299,407 68,797 — 68,797 Net investment income 128,640 — 128,640 Net realized gains (losses) (183,673) — (183,673) Equity in net income (loss) of investment funds accounted for using the equity method (18,861) — (18,861) Other income (loss) (13,684) — (13,684) Corporate expenses (2) (17,634) — (17,634) Transaction costs and other (2) (76) — (76) Amortization of intangible assets (26,104) — (26,104) Interest expense (33,063) — (33,063) Net foreign exchange gains (losses) 90,509 — 90,509 Income (loss) before income taxes and income (loss) from operating affiliates (5,149) — (5,149) Income tax (expense) benefit 14,900 — 14,900 Income (loss) from operating affiliates 8,507 — 8,507 Net income (loss) 18,258 — 18,258 Amounts attributable to redeemable noncontrolling interests (1,157) — (1,157) Net income (loss) available to Arch 17,101 — 17,101 Preferred dividends (10,184) — (10,184) Net income (loss) available to Arch common shareholders $ 6,917 $ — $ 6,917 Underwriting Ratios Loss ratio 69.3 % 92.6 % (24.1) % 68.1 % — % 68.1 % Acquisition expense ratio 19.6 % 20.8 % 2.4 % 18.1 % — % 18.1 % Other operating expense ratio 13.9 % 6.3 % 16.5 % 11.1 % — % 11.1 % Combined ratio 102.8 % 119.7 % (5.2) % 97.3 % — % 97.3 % Goodwill and intangible assets $ 224,525 $ 140,800 $ 441,330 $ 806,655 $ — $ 806,655 (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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’ Three Months Ended September 30, 2021 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 1,596,619 $ 1,251,760 $ 360,934 $ 3,207,415 $ — $ 3,207,415 Premiums ceded (442,806) (630,371) (60,207) (1,131,486) — (1,131,486) Net premiums written 1,153,813 621,389 300,727 2,075,929 — 2,075,929 Change in unearned premiums (215,143) 57,313 11,238 (146,592) — (146,592) Net premiums earned 938,670 678,702 311,965 1,929,337 — 1,929,337 Other underwriting income (loss) — 3,293 3,981 7,274 — 7,274 Losses and loss adjustment expenses (668,630) (545,846) (11,543) (1,226,019) — (1,226,019) Acquisition expenses (152,467) (129,450) (24,098) (306,015) — (306,015) Other operating expenses (138,931) (45,647) (46,254) (230,832) — (230,832) Underwriting income (loss) $ (21,358) $ (38,948) $ 234,051 173,745 — 173,745 Net investment income 88,195 — 88,195 Net realized gains (losses) (25,040) — (25,040) Equity in net income (loss) of investment funds accounted for using the equity method 105,398 — 105,398 Other income (loss) (3,960) — (3,960) Corporate expenses (2) (18,636) — (18,636) Transaction costs and other (2) (1,036) — (1,036) Amortization of intangible assets (20,135) — (20,135) Interest expense (33,176) — (33,176) Net foreign exchange gains (losses) 36,078 — 36,078 Income (loss) before income taxes and income (loss) from operating affiliates 301,433 — 301,433 Income tax (expense) benefit (4,137) — (4,137) Income (loss) from operating affiliates 124,119 — 124,119 Net income (loss) 421,415 — 421,415 Amounts attributable to redeemable noncontrolling interests (1,473) — (1,473) Net income (loss) available to Arch 419,942 — 419,942 Preferred dividends (16,090) — (16,090) Loss on redemption of preferred shares (15,101) — (15,101) Net income (loss) available to Arch common shareholders $ 388,751 $ — $ 388,751 Underwriting Ratios Loss ratio 71.2 % 80.4 % 3.7 % 63.5 % — % 63.5 % Acquisition expense ratio 16.2 % 19.1 % 7.7 % 15.9 % — % 15.9 % Other operating expense ratio 14.8 % 6.7 % 14.8 % 12.0 % — % 12.0 % Combined ratio 102.2 % 106.2 % 26.2 % 91.4 % — % 91.4 % Goodwill and intangible assets $ 261,103 $ 176,128 $ 526,091 $ 963,322 $ — $ 963,322 (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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’ Nine Months Ended September 30, 2022 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 5,286,798 $ 5,151,401 $ 1,099,144 $ 11,531,185 $ — $ 11,531,185 Premiums ceded (1,482,886) (1,770,807) (241,097) (3,488,632) — (3,488,632) Net premiums written 3,803,912 3,380,594 858,047 8,042,553 — 8,042,553 Change in unearned premiums (488,164) (646,421) 9,190 (1,125,395) — (1,125,395) Net premiums earned 3,315,748 2,734,173 867,237 6,917,158 — 6,917,158 Other underwriting income (loss) — 5,814 6,130 11,944 — 11,944 Losses and loss adjustment expenses (2,053,161) (1,920,189) 187,163 (3,786,187) — (3,786,187) Acquisition expenses (641,807) (569,915) (27,343) (1,239,065) — (1,239,065) Other operating expenses (493,412) (198,606) (150,064) (842,082) — (842,082) Underwriting income (loss) $ 127,368 $ 51,277 $ 883,123 $ 1,061,768 $ — $ 1,061,768 Net investment income 315,468 — 315,468 Net realized gains (losses) (742,666) — (742,666) Equity in net income (loss) of investment funds accounted for using the equity method 75,505 — 75,505 Other income (loss) (34,486) — (34,486) Corporate expenses (2) (76,928) — (76,928) Transaction costs and other (2) (734) — (734) Amortization of intangible assets (80,478) — (80,478) Interest expense (98,566) — (98,566) Net foreign exchange gains (losses) 182,129 — 182,129 Income (loss) before income taxes and income (loss) from operating affiliates 601,012 — 601,012 Income tax (expense) benefit (19,042) — (19,042) Income (loss) from operating affiliates 37,665 — 37,665 Net income (loss) 619,635 — 619,635 Amounts attributable to redeemable noncontrolling interests (2,390) — (2,390) Net income (loss) available to Arch 617,245 — 617,245 Preferred dividends (30,552) — (30,552) Net income (loss) available to Arch common shareholders $ 586,693 $ — $ 586,693 Underwriting Ratios Loss ratio 61.9 % 70.2 % (21.6) % 54.7 % — % 54.7 % Acquisition expense ratio 19.4 % 20.8 % 3.2 % 17.9 % — % 17.9 % Other operating expense ratio 14.9 % 7.3 % 17.3 % 12.2 % — % 12.2 % Combined ratio 96.2 % 98.3 % (1.1) % 84.8 % — % 84.8 % (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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’ Nine Months Ended September 30, 2021 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 4,381,372 $ 4,080,840 $ 1,143,691 $ 9,602,213 $ 457,465 $ 9,890,912 Premiums ceded (1,269,165) (1,535,607) (171,923) (2,973,005) (102,763) (2,907,002) Net premiums written 3,112,207 2,545,233 971,768 6,629,208 354,702 6,983,910 Change in unearned premiums (488,636) (484,607) 10,735 (962,508) (22,734) (985,242) Net premiums earned 2,623,571 2,060,626 982,503 5,666,700 331,968 5,998,668 Other underwriting income (loss) — 3,148 15,026 18,174 739 18,913 Losses and loss adjustment expenses (1,750,257) (1,494,539) (85,112) (3,329,908) (259,042) (3,588,950) Acquisition expenses (417,541) (381,060) (84,297) (882,898) (62,741) (945,639) Other operating expenses (409,386) (150,856) (143,697) (703,939) (32,869) (736,808) Underwriting income (loss) $ 46,387 $ 37,319 $ 684,423 $ 768,129 $ (21,945) $ 746,184 Net investment income 256,354 42,310 298,664 Net realized gains (losses) 239,690 80,638 320,328 Equity in net income (loss) of investment funds accounted for using the equity method 299,270 — 299,270 Other income (loss) 1,151 — 1,151 Corporate expenses (2) (59,279) — (59,279) Transaction costs and other (2) (793) (935) (1,728) Amortization of intangible assets (48,925) (898) (49,823) Interest expense (98,812) (8,410) (107,222) Net foreign exchange gains (losses) 39,691 (1,325) 38,366 Income (loss) before income taxes and income (loss) from operating affiliates 1,396,476 89,435 1,485,911 Income tax (expense) benefit (93,942) (234) (94,176) Income (loss) from operating affiliates 224,052 — 224,052 Net income (loss) 1,526,586 89,201 1,615,787 Amounts attributable to redeemable noncontrolling interests (1,936) (1,953) (3,889) Amounts attributable to nonredeemable noncontrolling interests — (78,314) (78,314) Net income (loss) available to Arch 1,524,650 8,934 1,533,584 Preferred dividends (38,159) — (38,159) Loss on redemption of preferred shares (15,101) — (15,101) Net income (loss) available to Arch common shareholders $ 1,471,390 $ 8,934 $ 1,480,324 Underwriting Ratios Loss ratio 66.7 % 72.5 % 8.7 % 58.8 % 78.0 % 59.8 % Acquisition expense ratio 15.9 % 18.5 % 8.6 % 15.6 % 18.9 % 15.8 % Other operating expense ratio 15.6 % 7.3 % 14.6 % 12.4 % 9.9 % 12.3 % Combined ratio 98.2 % 98.3 % 31.9 % 86.8 % 106.8 % 87.9 % (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.

Reserve for Losses and Loss A_2

Reserve for Losses and Loss Adjustment Expenses (Tables)	9 Months Ended
	Sep. 30, 2022
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: Three Months Ended Nine Months Ended September 30, September 30, 2022 2021 2022 2021 Reserve for losses and loss adjustment expenses at beginning of period $ 18,194,324 $ 17,196,648 $ 17,757,156 $ 16,513,929 Unpaid losses and loss adjustment expenses recoverable 5,686,348 4,146,020 5,599,231 4,314,855 Net reserve for losses and loss adjustment expenses at beginning of period 12,507,976 13,050,628 12,157,925 12,199,074 Net incurred losses and loss adjustment expenses relating to losses occurring in: Current year 1,863,519 1,348,528 4,280,048 3,812,381 Prior years (180,823) (122,509) (493,861) (223,431) Total net incurred losses and loss adjustment expenses 1,682,696 1,226,019 3,786,187 3,588,950 Net losses and loss adjustment expense reserves of acquired business (1) — 104,307 — 104,307 Retroactive reinsurance transactions (2) — — — (183,893) Impact of deconsolidation of Somers (3) — (1,460,611) — (1,460,611) Net foreign exchange (gains) losses and other (243,387) (78,152) (524,682) 10,818 Net paid losses and loss adjustment expenses relating to losses occurring in: Current year (226,575) (208,923) (463,847) (432,348) Prior years (538,967) (417,368) (1,773,840) (1,610,397) Total net paid losses and loss adjustment expenses (765,542) (626,291) (2,237,687) (2,042,745) Net reserve for losses and loss adjustment expenses at end of period 13,181,743 12,215,900 13,181,743 12,215,900 Unpaid losses and loss adjustment expenses recoverable 6,106,548 5,115,147 6,106,548 5,115,147 Reserve for losses and loss adjustment expenses at end of period $ 19,288,291 $ 17,331,047 $ 19,288,291 $ 17,331,047 (1) Represents activity related to the Company’s acquisitions in the 2021 period of the Westpac Lenders Mortgage Insurance Limited and Somerset Bridge Group Limited, Southern Rock Holdings Limited and affiliates. (2) During the 2021 first quarter, the Company entered into a reinsurance to close and other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the acquisition of Barbican Group Holdings Limited (“Barbican”). (3) See note 1 1 .

Allowance for Expected Credit_2

Allowance for Expected Credit Losses (Tables)	9 Months Ended
	Sep. 30, 2022
Credit Loss [Abstract]
Premiums receivable	The following table provides a roll forward of the allowance for expected credit losses of the Company’s premium receivables: Premium Receivables, Net of Allowance Allowance for Expected Credit Losses Three Months Ended September 30, 2022 Balance at beginning of period $ 3,634,182 $ 38,170 Change for provision of expected credit losses (1) 59 Balance at end of period $ 3,579,380 $ 38,229 Three Months Ended September 30, 2021 Balance at beginning of period $ 2,866,578 $ 35,979 Change for provision of expected credit losses (1) 2,736 Balance at end of period $ 2,807,720 $ 38,715 Nine Months Ended September 30, 2022 Balance at beginning of period $ 2,633,280 $ 39,958 Change for provision of expected credit losses (1) (1,729) Balance at end of period $ 3,579,380 $ 38,229 Nine Months Ended September 30, 2021 Balance at beginning of period $ 2,064,586 $ 37,781 Change for provision of expected credit losses (1) 934 Balance at end of period $ 2,807,720 $ 38,715 (1) Amounts deemed uncollectible are written-off in operating expenses. For the 2022 third quarter and 2021 third quarter, amounts written off were $1.9 million and $1.2 million, respectively. For the nine months ended September 30, 2022 and 2021 period, amounts written off were $6.6 million and $2.4 million, respectively.
Reinsurance recoverables	The following table provides a roll forward of the allowance for expected credit losses of the Company’s reinsurance recoverables: Reinsurance Recoverables, Net of Allowance Allowance for Expected Credit Losses Three Months Ended September 30, 2022 Balance at beginning of period $ 5,938,511 $ 14,740 Change for provision of expected credit losses 2,626 Balance at end of period $ 6,356,456 $ 17,366 Three Months Ended September 30, 2021 Balance at beginning of period $ 4,314,515 $ 11,029 Change for provision of expected credit losses 1,802 Balance at end of period $ 5,358,852 $ 12,831 Nine Months Ended September 30, 2022 Balance at beginning of period $ 5,880,735 $ 13,230 Change for provision of expected credit losses 4,136 Balance at end of period $ 6,356,456 $ 17,366 Nine Months Ended September 30, 2021 Balance at beginning of period $ 4,500,802 $ 11,636 Change for provision of expected credit losses 1,195 Balance at end of period $ 5,358,852 $ 12,831
Ceded credit risk	The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums): September 30, December 31 2022 2021 Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses $ 6,356,456 $ 5,880,735 % due from carriers with A.M. Best rating of “A-” or better 69.5 % 69.7 % % due from all other rated carriers 0.1 % 0.1 % % due from all other carriers with no A.M. Best rating (1) 30.4 % 30.2 % Largest balance due from any one carrier as % of total shareholders’ equity 9.1 % 6.7 % (1) At September 30, 2022 and December 31, 2021 over 95% and 91% of such amount were collateralized through reinsurance trusts, funds withheld arrangements, letters of credit or other, respectively.
Contractholder receivables	The following table provides a roll forward of the allowance for expected credit losses of the Company’s contractholder receivables: Contract-holder Receivables, Net of Allowance Allowance for Expected Credit Losses Three Months Ended September 30, 2022 Balance at beginning of period $ 1,758,018 $ 3,005 Change for provision of expected credit losses (645) Balance at end of period $ 1,735,730 $ 2,360 Three Months Ended September 30, 2021 Balance at beginning of period $ 1,882,948 $ 4,471 Change for provision of expected credit losses (987) Balance at end of period 1,824,990 $ 3,484 Nine Months Ended September 30, 2022 Balance at beginning of period $ 1,828,691 $ 3,437 Change for provision of expected credit losses (1,077) Balance at end of period $ 1,735,730 $ 2,360 Nine Months Ended September 30, 2021 Balance at beginning of period $ 1,986,924 $ 8,638 Change for provision of expected credit losses (5,154) Balance at end of period 1,824,990 $ 3,484

Investment Information (Tables)

Investment Information (Tables)	9 Months Ended
	Sep. 30, 2022
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 Gross Allowance for Expected Credit Losses Cost or September 30, 2022 Fixed maturities: Corporate bonds $ 7,096,269 $ 51,777 $ (895,365) $ (35,657) $ 7,975,514 Residential mortgage backed securities 763,371 7,561 (84,183) 2 839,991 Municipal bonds 407,724 5,437 (37,692) (99) 440,078 Commercial mortgage backed securities 1,064,238 3,079 (50,010) (1,583) 1,112,752 U.S. government and government agencies 5,126,407 36,074 (400,784) — 5,491,117 Non-U.S. government securities 2,073,170 9,315 (287,583) (1,720) 2,353,158 Asset backed securities 1,589,548 1,076 (105,037) (6,936) 1,700,445 Total 18,120,727 114,319 (1,860,654) (45,993) 19,913,055 Short-term investments 1,940,857 1,419 (1,633) — 1,941,071 Total $ 20,061,584 $ 115,738 $ (1,862,287) $ (45,993) $ 21,854,126 December 31, 2021 Fixed maturities: Corporate bonds $ 6,553,333 $ 104,170 $ (69,194) $ (2,037) $ 6,520,394 Residential 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
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 Gross Estimated Gross Estimated Gross September 30, 2022 Fixed maturities: Corporate bonds $ 5,596,229 $ (625,774) $ 1,470,800 $ (269,591) $ 7,067,029 $ (895,365) Residential mortgage backed securities 620,572 (63,732) 93,902 (20,451) 714,474 (84,183) Municipal bonds 373,219 (36,039) 9,399 (1,653) 382,618 (37,692) Commercial mortgage backed securities 995,680 (49,215) 34,445 (795) 1,030,125 (50,010) U.S. government and government agencies 4,205,475 (303,805) 715,347 (96,979) 4,920,822 (400,784) Non-U.S. government securities 1,728,965 (221,540) 301,298 (66,043) 2,030,263 (287,583) Asset backed securities 1,193,405 (74,885) 310,838 (30,152) 1,504,243 (105,037) Total 14,713,545 (1,374,990) 2,936,029 (485,664) 17,649,574 (1,860,654) Short-term investments 227,201 (1,633) — — 227,201 (1,633) Total $ 14,940,746 $ (1,376,623) $ 2,936,029 $ (485,664) $ 17,876,775 $ (1,862,287) December 31, 2021 Fixed maturities: Corporate bonds $ 3,639,582 $ (63,938) $ 98,867 $ (5,256) $ 3,738,449 $ (69,194) Residential 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)
Contractual maturities of the Company's fixed maturities	The contractual maturities of the Company’s fixed maturities 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. September 30, 2022 December 31, 2021 Maturity Estimated Amortized Estimated Amortized Due in one year or less $ 579,231 $ 599,970 $ 300,889 $ 299,772 Due after one year through five years 10,029,151 10,808,495 8,355,255 8,339,387 Due after five years through 10 years 3,856,180 4,495,113 4,689,155 4,684,393 Due after 10 years 239,008 356,289 505,758 493,927 14,703,570 16,259,867 13,851,057 13,817,479 Residential mortgage backed securities 763,371 839,991 408,477 411,110 Commercial mortgage backed securities 1,064,238 1,112,752 1,046,484 1,047,867 Asset backed securities 1,589,548 1,700,445 2,692,091 2,697,367 Total $ 18,120,727 $ 19,913,055 $ 17,998,109 $ 17,973,823
Summary of other investments and other investable assets	The following table summarizes the Company’s other investments and other investable assets: September 30, December 31, Fixed maturities $ 530,303 $ 416,698 Other investments 1,005,929 1,432,553 Short-term investments 28,614 97,806 Equity securities 13,905 26,493 Total $ 1,578,751 $ 1,973,550 The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy: September 30, December 31, Lending $ 398,789 $ 536,345 Investment grade fixed income 229,262 147,810 Term loan investments 151,649 484,950 Private equity 117,856 91,126 Energy 55,250 81,692 Credit related funds 53,123 70,278 Infrastructure — 20,352 Total $ 1,005,929 $ 1,432,553
Summary of investments accounted for using equity method	The following table summarizes the Company’s investments accounted for using the equity method, by strategy: September 30, December 31, Credit related funds $ 1,135,623 $ 1,022,334 Private equity 761,997 436,042 Real estate 474,666 396,395 Lending 454,196 376,649 Equities 261,650 395,090 Infrastructure 236,920 230,070 Energy 113,778 119,141 Fixed income 127,116 101,890 Total $ 3,565,946 $ 3,077,611
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 line item: September 30, December 31, Investments accounted for using the equity method (1) $ 3,565,946 $ 3,077,611 Investments accounted for using the fair value option (2) 120,498 170,595 Total $ 3,686,444 $ 3,248,206 (1) Aggregate unfunded commitments were $2.8 billion at September 30, 2022, compared to $2.6 billion at December 31, 2021. (2) Aggregate unfunded commitments were $21.5 million at September 30, 2022, compared to $18.8 million at December 31, 2021.
Components of net investment income	The components of net investment income were derived from the following sources: September 30, 2022 2021 Three Months Ended Fixed maturities $ 123,568 $ 75,964 Term loans 88 1,736 Equity securities 4,261 9,867 Short-term investments 9,304 1,858 Other (1) 8,556 17,378 Gross investment income 145,777 106,803 Investment expenses (17,137) (18,608) Net investment income $ 128,640 $ 88,195 Nine Months Ended Fixed maturities $ 310,963 $ 255,215 Term loans 2,106 33,343 Equity securities 16,620 24,101 Short-term investments 15,999 3,603 Other (1) 26,598 51,683 Gross investment income 372,286 367,945 Investment expenses (56,818) (69,281) Net investment income $ 315,468 $ 298,664
Summary of net realized gains (losses), including change in allowance for credit losses on financial assets and net impairment losses recognized in earnings	Net realized gains (losses), which include changes in the allowance for credit losses on financial assets and net impairment losses recognized in earnings were as follows: September 30, 2022 2021 Three Months Ended Available for sale securities: Gross gains on investment sales $ 18,030 $ 86,819 Gross losses on investment sales (73,970) (18,446) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities (19,304) (7,492) Other investments (17,882) 3,811 Equity securities (584) 3,042 Short-term investments (975) 16 Equity securities, at fair value: Net realized gains (losses) on sales during the period (6,401) 14,736 Net unrealized gains (losses) on equity securities still held at reporting date (36,162) (40,155) Allowance for credit losses: Investments related 8,652 (456) Underwriting related (4,232) (3,985) Derivative instruments (1) (48,196) (21,435) Other (2,649) (41,495) Net realized gains (losses) $ (183,673) $ (25,040) Nine Months Ended Available for sale securities: Gross gains on investment sales $ 52,923 $ 267,362 Gross losses on investment sales (239,493) (132,071) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities (89,148) 19,973 Other investments (35,203) 111,550 Equity securities (6,021) 10,599 Short-term investments (3,132) 648 Equity securities, at fair value: Net realized gains (losses) on sales during the period 75,689 86,155 Net unrealized gains (losses) on equity securities still held at reporting date (318,732) 45,400 Allowance for credit losses: Investments related (48,096) (1,208) Underwriting related (7,676) 2,664 Derivative instruments (1) (117,591) (36,428) Other (6,186) (54,316) Net realized gains (losses) $ (742,666) $ 320,328 (1) See note 9 for information on the Company’s derivative instruments.
Rollforward 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: Structured Securities (1) Municipal Corporate Total Three Months Ended September 30, 2022 Balance at beginning of period $ 18,283 $ 298 $ 39,829 $ 58,410 Additions for current-period provision for expected credit losses 1,782 12 1,986 3,780 Additions (reductions) for previously recognized expected credit losses (9,767) (211) (2,552) (12,530) Reductions due to disposals (1,780) — (1,887) (3,667) Balance at end of period $ 8,518 $ 99 $ 37,376 $ 45,993 Three Months Ended September 30, 2021 Balance at beginning of period $ 759 $ 6 $ 1,359 $ 2,124 Additions for current-period provision for expected credit losses 48 — — 48 Additions (reductions) for previously recognized expected credit losses 14 (4) 395 405 Reductions due to disposals (234) — (232) (466) Balance at end of period $ 587 $ 2 $ 1,522 $ 2,111 Nine Months Ended September 30, 2022 Balance at beginning of period $ 802 $ 2 $ 2,079 $ 2,883 Additions for current-period provision for expected credit losses 12,560 359 40,602 53,521 Additions (reductions) for previously recognized expected credit losses (2,575) (262) (2,772) (5,609) Reductions due to disposals (2,269) — (2,533) (4,802) Balance at end of period $ 8,518 $ 99 $ 37,376 $ 45,993 Nine Months Ended September 30, 2021 Balance at beginning of period $ 1,490 $ 11 $ 896 $ 2,397 Additions for current-period provision for expected credit losses 282 — 2,428 2,710 Additions (reductions) for previously recognized expected credit losses (751) (9) (557) (1,317) Reductions due to disposals (434) — (1,245) (1,679) Balance at end of period $ 587 $ 2 $ 1,522 $ 2,111 (1) Includes asset backed securities, residential mortgage backed securities and commercial mortgage backed securities.
Summary of restricted assets	The following table details the value of the Company’s restricted assets: September 30, December 31, Assets used for collateral or guarantees: Affiliated transactions $ 4,212,521 $ 4,223,955 Third party agreements 2,847,814 2,721,160 Deposits with U.S. regulatory authorities 756,368 798,100 Deposits with non-U.S. regulatory authorities 519,254 506,517 Total restricted assets $ 8,335,957 $ 8,249,732
Reconciliation of cash and restricted cash	The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets: September 30, December 31, Cash $ 813,583 $ 858,668 Restricted cash (included in ‘other assets’) 444,741 456,103 Cash and restricted cash $ 1,258,324 $ 1,314,771

Fair Value (Tables)

Fair Value (Tables)	9 Months Ended
	Sep. 30, 2022
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 September 30, 2022: Estimated Fair Value Measurements Using: Estimated Quoted Prices in Significant Significant Assets measured at fair value: Available for sale securities: Fixed maturities: Corporate bonds $ 7,096,269 $ — $ 7,096,256 $ 13 Residential mortgage backed securities 763,371 — 763,371 — Municipal bonds 407,724 — 407,724 — Commercial mortgage backed securities 1,064,238 — 1,064,238 — U.S. government and government agencies 5,126,407 5,100,908 25,499 — Non-U.S. government securities 2,073,170 — 2,073,170 — Asset backed securities 1,589,548 — 1,589,548 — Total 18,120,727 5,100,908 13,019,806 13 Short-term investments 1,940,857 1,873,480 67,377 — Equity securities, at fair value 809,869 775,264 31,566 3,039 Derivative instruments (2) 176,160 — 176,160 — Residential mortgage loans 2,255 — 2,255 — Fair value option: Corporate bonds 524,177 — 524,177 — Non-U.S. government bonds 4,032 — 4,032 — Asset backed securities 2,094 — 2,094 — Short-term investments 28,614 405 28,209 — Equity securities 13,905 9,312 1 4,592 Other investments 175,259 — 141,021 34,238 Other investments measured at net asset value (1) 830,670 Total 1,578,751 9,717 699,534 38,830 Total assets measured at fair value $ 22,628,619 $ 7,759,369 $ 13,996,698 $ 41,882 Liabilities measured at fair value: Other liabilities $ (13,421) $ — $ — $ (13,421) Derivative instruments (2) (112,577) — (112,577) — Total liabilities measured at fair value $ (125,998) $ — $ (112,577) $ (13,421) (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) See note 9 . The following table presents the Company’s financial assets and liabilities measured at fair value by level at December 31, 2021: Estimated Fair Value Measurements Using: Estimated Quoted Prices in Significant Significant Assets measured at fair value: Available for sale securities: Fixed maturities: Corporate bonds $ 6,553,333 $ — $ 6,553,320 $ 13 Residential 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 (2) 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: Other liabilities $ (16,960) $ — $ — $ (16,960) Derivative instruments (2) (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) See note 9 .
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: Assets Liabilities s Available For Sale Fair Value Option Fair Value Structured Securities (1) Corporate Corporate Other Equity Equity Other Liabilities Three Months Ended September 30, 2022 Balance at beginning of period $ 2,867 $ 3,570 $ — $ 33,331 $ 4,392 $ 2,906 $ (16,205) Total gains or (losses) (realized/unrealized) Included in earnings (2) (601) 52 — 116 200 133 (89) Included in other comprehensive income 144 (59) — — — — 965 Purchases, issuances, sales and settlements Purchases — — — 1,458 — — — Issuances — — — — — — — Sales (2,051) (3,550) — (667) — — — Settlements (359) — — — — — 1,908 Transfers in and/or out of Level 3 — — — — — — — Balance at end of period $ — $ 13 $ — $ 34,238 $ 4,592 $ 3,039 $ (13,421) Three Months Ended September 30, 2021 Balance at beginning of period $ 3,424 $ 13 $ 998 $ 73,900 $ 73,678 $ 49,136 $ (466) Total gains or (losses) (realized/unrealized) Included in earnings (2) 10 — — — 38 11 — Included in other comprehensive income 10 — — — — — — Purchases, issuances, sales and settlements Purchases — — — — — 208 (17,345) Issuances — — — — — — — Sales (3) — — (998) (44,143) (69,181) (46,773) — Settlements — — — — — — — Transfers in and/or out of Level 3 — — — — — — — Balance at end of period $ 3,444 $ 13 $ — $ 29,757 $ 4,535 $ 2,582 $ (17,811) Nine Months Ended September 30, 2022 Balance at beginning of year $ 3,347 $ 13 $ — $ 27,981 $ 4,748 $ 2,918 $ (16,960) Total gains or (losses) (realized/unrealized) Included in earnings (2) (592) 52 — 150 (156) (103) (284) Included in other comprehensive income (1) (59) — — — — 1,915 Purchases, issuances, sales and settlements Purchases — — — 12,228 — 227 — Issuances — — — — — — — Sales (2,051) (3,550) — (3,138) — (3) — Settlements (703) — — (2,983) — — 1,908 Transfers in and/or out of Level 3 — 3,557 — — — — — Balance at end of period $ — $ 13 $ — $ 34,238 $ 4,592 $ 3,039 $ (13,421) Nine Months Ended September 30, 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) (46) — 13 881 4,728 1,837 — Included in other comprehensive income 67 — — — — — — Purchases, issuances, sales and settlements Purchases — — — 13,003 — 5,503 (17,345) Issuances — — — — — — — Sales (3) — — (998) (51,230) (69,181) (46,773) — Settlements (3) — — — — — (5) Transfers in and/or out of Level 3 — — — — — — — Balance at end of period $ 3,444 $ 13 $ — $ 29,757 $ 4,535 $ 2,582 $ (17,811) (1) Includes asset backed securities, residential mortgage backed securities and commercial mortgage backed securities. (2) Gains or losses were included in net realized gains (losses). (3) Sales for the 2021 periods primarily related to the Company’s deconsolidation of Somers..

Derivative Instruments (Tables)

Derivative Instruments (Tables)	9 Months Ended
	Sep. 30, 2022
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 Derivatives (1) Liability Derivatives (1) Notional September 30, 2022 Futures contracts $ 72,730 $ (60,684) $ 2,189,945 Foreign currency forward contracts 25,281 (26,995) 835,941 TBAs — — — Other 78,149 (24,898) 3,766,549 Total $ 176,160 $ (112,577) December 31, 2021 Futures contracts $ 34,999 $ (9,808) $ 2,826,564 Foreign currency forward contracts 7,734 (11,390) 915,962 TBAs 11,227 — 11,227 Other 73,161 (33,026) 3,736,773 Total $ 127,121 $ (54,224) (1) The fair value of asset derivatives are included in ‘ other assets other liabilities (2) Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.
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 September 30, hedging instruments: 2022 2021 Three Months Ended Net realized gains (losses): Futures contracts $ (26,347) $ (10,073) Foreign currency forward contracts (18,340) (16,146) TBAs — (46) Other (1) (3,509) 4,830 Total $ (48,196) $ (21,435) Nine Months Ended Net realized gains (losses): Futures contracts $ (112,326) $ (17,394) Foreign currency forward contracts (46,016) (36,922) TBAs (51) (46) Other (1) 40,802 17,934 Total $ (117,591) $ (36,428) (1) Includes realized gains and losses on swaps, options and other derivatives contracts.

Variable Interest Entities an_2

Variable Interest Entities and Noncontrolling Interests (Tables)	9 Months Ended
	Sep. 30, 2022
Noncontrolling Interest [Abstract]
Activity in redeemable noncontrolling interests	The following table sets forth activity in the redeemable non-controlling interests: September 30, 2022 2021 Three Months Ended Balance, beginning of period $ 8,459 $ 57,533 Impact of deconsolidation of Somers — (48,919) Other 449 1,623 Balance, end of period $ 8,908 $ 10,237 Nine Months Ended Balance, beginning of year $ 9,233 $ 58,548 Impact of deconsolidation of Somers — (48,919) Other (325) 608 Balance, end of period $ 8,908 $ 10,237
Portion of income or loss attributable to third party investors	The portion of income or loss attributable to third party investors, recorded in the Company’s consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests,’ are summarized in the table below: September 30, 2022 2021 Three Months Ended Amounts attributable to non-redeemable noncontrolling interests $ — $ — Amounts attributable to redeemable noncontrolling interests (1,157) (1,473) Net (income) loss attributable to noncontrolling interests $ (1,157) $ (1,473) Nine Months Ended Amounts attributable to non-redeemable noncontrolling interests $ — $ (78,314) Amounts attributable to redeemable noncontrolling interests (2,390) (3,889) Net (income) loss attributable to noncontrolling interests $ (2,390) $ (82,203)
Total assets and maximum exposure to loss associated with VIEs	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 and later 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. September 30, 2022 December 31, 2021 Maximum Exposure to Loss Maximum Exposure to Loss Bellemeade Entities Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total Coverage Remaining from Reinsurers (1) Total VIE Assets On-Balance Sheet (Asset) Liability Off-Balance Sheet Total 2017-1 Ltd. (Oct-17) $ 46,772 $ (23) $ 88 $ 65 $ — $ 108,368 $ (159) $ 424 $ 265 2018-1 Ltd. (Apr-18) 103,131 (220) 644 424 — 181,136 (528) 1,268 740 2018-3 Ltd. (Oct-18) 217,701 (862) 2,107 1,245 — 302,563 (1,018) 2,496 1,478 2019-1 Ltd. (Mar-19) 119,193 (496) 2,704 2,208 — 181,324 (380) 5,807 5,427 2019-2 Ltd. (Apr-19) 347,050 (656) 4,308 3,652 — 398,316 (515) 3,998 3,483 2019-3 Ltd. (Jul-19) 257,663 (192) 1,492 1,300 — 409,859 (584) 3,190 2,606 2019-4 Ltd. (Oct-19) 283,684 (532) 3,663 3,131 — 411,954 (462) 4,759 4,297 2020-2 Ltd. (Sep-20) 122,897 (20) 595 575 153 217,766 (177) 1,984 1,807 2020-3 Ltd. (Nov-20) 268,385 (204) 2,845 2,641 8,569 348,818 (128) 5,793 5,665 2020-4 Ltd. (Dec-20) 107,396 10 707 717 4,795 176,826 (50) 1,630 1,580 2021-1 Ltd. (Mar-21) 497,069 (2,234) 936 (1,298) 43,198 568,986 (303) 3,283 2,980 2021-2 Ltd. (Jun-21) 471,039 (2,047) 984 (1,063) 80,268 522,807 281 4,124 4,405 2021-3 Ltd. (Sep-21) 498,309 (2,414) 991 (1,423) 129,127 507,873 (411) 3,446 3,035 2022-1 Ltd. (Jan-22) 283,500 (1,326) 627 (699) 33,260 2022-2 Ltd. (Sep-22) 201,005 — 744 744 126,160 Total $ 3,824,794 $ (11,216) $ 23,435 $ 12,219 $ 425,530 $ 4,336,596 $ (4,434) $ 42,202 $ 37,768 (1) Coverage from a separate panel of reinsurers remaining at September 30, 2022.

Other Comprehensive Income (L_2

Other Comprehensive Income (Loss) (Tables)	9 Months Ended
	Sep. 30, 2022
Comprehensive Income Note Disclosure [Abstract]
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): Amounts Reclassified from AOCI Consolidated Statement of Income Three Months Ended Nine Months Ended Details About Line Item That Includes September 30, September 30, AOCI Components Reclassification 2022 2021 2022 2021 Unrealized appreciation (decline) on available-for-sale investments Net realized gains (losses) $ (55,940) $ 68,373 $ (186,570) $ 135,291 Provision for credit losses 8,652 (457) (48,096) (1,208) Total before tax (47,288) 67,916 (234,666) 134,083 Income tax (expense) benefit 703 (5,262) 28,093 (13,579) Net of tax $ (46,585) $ 62,654 $ (206,573) $ 120,504
Schedule of comprehensive income (loss)	Before Tax Amount Tax Expense (Benefit) Net of Tax Amount Three Months Ended September 30, 2022 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (671,907) $ (62,148) $ (609,759) Less reclassification of net realized gains (losses) included in net income (47,288) (703) (46,585) Foreign currency translation adjustments (70,388) — (70,388) Other comprehensive income (loss) $ (695,007) $ (61,445) $ (633,562) Three Months Ended September 30, 2021 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (104,607) $ (8,684) $ (95,923) Less reclassification of net realized gains (losses) included in net income 67,916 5,262 62,654 Foreign currency translation adjustments (32,060) (350) (31,710) Other comprehensive income (loss) $ (204,583) $ (14,296) $ (190,287) Nine Months Ended September 30, 2022 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (2,132,845) $ (240,726) $ (1,892,119) Less reclassification of net realized gains (losses) included in net income (234,666) (28,093) (206,573) Foreign currency translation adjustments (141,515) 166 (141,681) Other comprehensive income (loss) $ (2,039,694) $ (212,467) $ (1,827,227) Nine Months Ended September 30, 2021 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (307,910) $ (28,808) $ (279,102) Less reclassification of net realized gains (losses) included in net income 134,083 13,579 120,504 Foreign currency translation adjustments (54,083) 6 (54,089) Other comprehensive income (loss) $ (496,076) $ (42,381) $ (453,695)

Basis of Presentation and Rec_3

Basis of Presentation and Recent Accounting Pronouncements (Details) - Greysbridge Holdings Ltd	Jul. 01, 2021
Schedule of Equity Method Investments [Line Items]
Percentage ownership	40%
Warburg Pincus LLC
Schedule of Equity Method Investments [Line Items]
Percentage ownership	30%
Kelso And Company
Schedule of Equity Method Investments [Line Items]
Percentage ownership	30%

Share Transactions - Share repu

Share Transactions - Share repurchases (Details) - Common shares shares in Millions, $ in Millions	9 Months Ended
	Sep. 30, 2022 USD ($) shares
Class of Stock [Line Items]
Cumulative number of shares acquired since inception of share repurchase program | shares	433.6
Aggregate purchase price of shares acquired since inception of share repurchase program	$ 5,870
Treasury stock, shares acquired (shares) | shares	12.9
Shares repurchased for treasury	$ 585.8
Remaining authorized repurchase amount	$ 596.4

Share Transactions - Long-Term

Share Transactions - Long-Term Incentive and Share Award Plan (Details) - 2022 Long-term incentive and share award plan - shares	Sep. 30, 2022	May 04, 2022
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares authorized (in shares)		9,000,000
Number of shares available for future issuance (in shares)	9,000,000
Stock options
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Number of shares authorized (in shares)		6,000,000

Share Transactions - Issuance o

Share Transactions - Issuance of preferred shares (Details) - USD ($) $ / shares in Units, $ in Thousands, shares in Millions	1 Months Ended		9 Months Ended
	Sep. 30, 2021	Jun. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Class of Stock [Line Items]
Proceeds from issuance of preferred shares, net			$ 0	$ 485,821
Series G Preferred Shares
Class of Stock [Line Items]
Preferred shares issued		$ 500,000
Preferred shares, dividend rate (as a percent)		4.55%
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
Proceeds from issuance of preferred shares, net		$ 485,800
Series G Depositary Share Equivalent
Class of Stock [Line Items]
Preferred shares issued		$ 500,000
Preference shares, number of shares issued		20
Liquidation preference per share	25			25
Preferred shares, redemption price per share	$ 25			$ 25
Proportionate interest of preference shares (per depositary share)	0.10%			0.10%
Series E Preferred Shares
Class of Stock [Line Items]
Preferred shares, dividend rate (as a percent)	5.25%
Series E Depositary Share Equivalent
Class of Stock [Line Items]
Preferred shares, redemption price per share	$ 25			$ 25

Earnings Per Common Share (Deta

Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended		9 Months Ended
		Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Numerator:
Net income (loss)		$ 18,258	$ 421,415	$ 619,635	$ 1,615,787
Amounts attributable to noncontrolling interests		(1,157)	(1,473)	(2,390)	(82,203)
Net income available to Arch		17,101	419,942	617,245	1,533,584
Preferred dividends		(10,184)	(16,090)	(30,552)	(38,159)
Loss on redemption of preferred shares		0	(15,101)	0	(15,101)
Net income (loss) available to Arch common shareholders		$ 6,917	$ 388,751	$ 586,693	$ 1,480,324
Denominator:
Weighted average common shares outstanding — basic		365,190,527	389,274,220	369,525,348	395,899,591
Effect of dilutive common share equivalents:
Nonvested restricted shares		2,351,039	2,131,915	2,171,158	1,877,930
Stock options	[1]	6,185,711	6,497,212	6,676,674	6,482,964
Weighted average common shares and common share equivalents outstanding — diluted		373,727,277	397,903,347	378,373,180	404,260,485
Earnings per common share:
Basic (per share)		$ 0.02	$ 1	$ 1.59	$ 3.74
Diluted (per share)		$ 0.02	$ 0.98	$ 1.55	$ 3.66
Stock options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)		774,481	1,948,006	785,682	2,397,507
[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 the 2022 third quarter and 2021 third quarter, the number of stock options excluded were 774,481 and 1,948,006, respectively. For the nine months ended September 30, 2022 and 2021, the number of stock options excluded were 785,682 and 2,397,507, respectively.

Segment Information - Summary o

Segment Information - Summary of underwriting income or loss by segment (Details) $ in Thousands		3 Months Ended		9 Months Ended
		Sep. 30, 2022 USD ($)	Sep. 30, 2021 USD ($)	Sep. 30, 2022 USD ($) segment	Sep. 30, 2021 USD ($)	Dec. 31, 2021 USD ($)
Segment Reporting Information [Line Items]
Gross premiums written		$ 3,860,683	$ 3,207,415	$ 11,531,185	$ 9,890,912
Premiums ceded		(1,136,909)	(1,131,486)	(3,488,632)	(2,907,002)
Net premiums written		2,723,774	2,075,929	8,042,553	6,983,910
Change in unearned premiums		(253,024)	(146,592)	(1,125,395)	(985,242)
Net premiums earned		2,470,750	1,929,337	6,917,158	5,998,668
Other underwriting income (loss)		3,077	7,274	11,944	18,913
Losses and loss adjustment expenses		(1,682,696)	(1,226,019)	(3,786,187)	(3,588,950)
Acquisition expenses		(447,587)	(306,015)	(1,239,065)	(945,639)
Other operating expenses		(274,747)	(230,832)	(842,082)	(736,808)
Underwriting income (loss)		68,797	173,745	1,061,768	746,184
Net investment income		128,640	88,195	315,468	298,664
Net realized gains (losses)		(183,673)	(25,040)	(742,666)	320,328
Equity in net income (loss) of investment funds accounted for using the equity method		(18,861)	105,398	75,505	299,270
Other income (loss)		(13,684)	(3,960)	(34,486)	1,151
Corporate expenses		(17,634)	(18,636)	(76,928)	(59,279)
Transaction costs and other		(76)	(1,036)	(734)	(1,728)
Amortization of intangible assets		(26,104)	(20,135)	(80,478)	(49,823)
Interest expense		(33,063)	(33,176)	(98,566)	(107,222)
Net foreign exchange gains (losses)		90,509	36,078	182,129	38,366
Income (loss) before income taxes and income (loss) from operating affiliates		(5,149)	301,433	601,012	1,485,911
Income tax expense (benefit)		14,900	(4,137)	(19,042)	(94,176)
Income (loss) from operating affiliates		8,507	124,119	37,665	224,052
Net income (loss)		18,258	421,415	619,635	1,615,787
Amounts attributable to redeemable noncontrolling interests		(1,157)	(1,473)	(2,390)	(3,889)
Amounts attributable to non-redeemable noncontrolling interests		0	0	0	(78,314)
Net income (loss) available to Arch		17,101	419,942	617,245	1,533,584
Preferred dividends		(10,184)	(16,090)	(30,552)	(38,159)
Loss on redemption of preferred shares		0	(15,101)	0	(15,101)
Net income (loss) available to Arch common shareholders		$ 6,917	$ 388,751	$ 586,693	$ 1,480,324
Underwriting Ratios
Loss ratio		68.10%	63.50%	54.70%	59.80%
Acquisition expense ratio		18.10%	15.90%	17.90%	15.80%
Other operating expense ratio		11.10%	12%	12.20%	12.30%
Combined ratio		97.30%	91.40%	84.80%	87.90%
Goodwill and intangible assets		$ 806,655	$ 963,322	$ 806,655	$ 963,322	$ 944,983
Operating segments | Underwriting Segments
Segment Reporting Information [Line Items]
Number of segments | segment				3
Gross premiums written	[1]	3,860,683	3,207,415	$ 11,531,185	9,602,213
Premiums ceded		(1,136,909)	(1,131,486)	(3,488,632)	(2,973,005)
Net premiums written		2,723,774	2,075,929	8,042,553	6,629,208
Change in unearned premiums		(253,024)	(146,592)	(1,125,395)	(962,508)
Net premiums earned		2,470,750	1,929,337	6,917,158	5,666,700
Other underwriting income (loss)		3,077	7,274	11,944	18,174
Losses and loss adjustment expenses		(1,682,696)	(1,226,019)	(3,786,187)	(3,329,908)
Acquisition expenses		(447,587)	(306,015)	(1,239,065)	(882,898)
Other operating expenses		(274,747)	(230,832)	(842,082)	(703,939)
Underwriting income (loss)		68,797	173,745	1,061,768	768,129
Net investment income		128,640	88,195	315,468	256,354
Net realized gains (losses)		(183,673)	(25,040)	(742,666)	239,690
Equity in net income (loss) of investment funds accounted for using the equity method		(18,861)	105,398	75,505	299,270
Other income (loss)		(13,684)	(3,960)	(34,486)	1,151
Corporate expenses	[2]	(17,634)	(18,636)	(76,928)	(59,279)
Transaction costs and other	[2]	(76)	(1,036)	(734)	(793)
Amortization of intangible assets		(26,104)	(20,135)	(80,478)	(48,925)
Interest expense		(33,063)	(33,176)	(98,566)	(98,812)
Net foreign exchange gains (losses)		90,509	36,078	182,129	39,691
Income (loss) before income taxes and income (loss) from operating affiliates		(5,149)	301,433	601,012	1,396,476
Income tax expense (benefit)		14,900	(4,137)	(19,042)	(93,942)
Income (loss) from operating affiliates		8,507	124,119	37,665	224,052
Net income (loss)		18,258	421,415	619,635	1,526,586
Amounts attributable to redeemable noncontrolling interests		(1,157)	(1,473)	(2,390)	(1,936)
Amounts attributable to non-redeemable noncontrolling interests					0
Net income (loss) available to Arch		17,101	419,942	617,245	1,524,650
Preferred dividends		(10,184)	(16,090)	(30,552)	(38,159)
Loss on redemption of preferred shares			(15,101)		(15,101)
Net income (loss) available to Arch common shareholders		$ 6,917	$ 388,751	$ 586,693	$ 1,471,390
Underwriting Ratios
Loss ratio		68.10%	63.50%	54.70%	58.80%
Acquisition expense ratio		18.10%	15.90%	17.90%	15.60%
Other operating expense ratio		11.10%	12%	12.20%	12.40%
Combined ratio		97.30%	91.40%	84.80%	86.80%
Goodwill and intangible assets		$ 806,655	$ 963,322	$ 806,655	$ 963,322
Operating segments | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,862,026	1,596,619	5,286,798	4,381,372
Premiums ceded		(493,267)	(442,806)	(1,482,886)	(1,269,165)
Net premiums written		1,368,759	1,153,813	3,803,912	3,112,207
Change in unearned premiums		(181,851)	(215,143)	(488,164)	(488,636)
Net premiums earned		1,186,908	938,670	3,315,748	2,623,571
Other underwriting income (loss)		0	0	0	0
Losses and loss adjustment expenses		(822,663)	(668,630)	(2,053,161)	(1,750,257)
Acquisition expenses		(232,469)	(152,467)	(641,807)	(417,541)
Other operating expenses		(165,499)	(138,931)	(493,412)	(409,386)
Underwriting income (loss)		$ (33,723)	$ (21,358)	$ 127,368	$ 46,387
Underwriting Ratios
Loss ratio		69.30%	71.20%	61.90%	66.70%
Acquisition expense ratio		19.60%	16.20%	19.40%	15.90%
Other operating expense ratio		13.90%	14.80%	14.90%	15.60%
Combined ratio		102.80%	102.20%	96.20%	98.20%
Goodwill and intangible assets		$ 224,525	$ 261,103	$ 224,525	$ 261,103
Operating segments | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,639,061	1,251,760	5,151,401	4,080,840
Premiums ceded		(560,225)	(630,371)	(1,770,807)	(1,535,607)
Net premiums written		1,078,836	621,389	3,380,594	2,545,233
Change in unearned premiums		(77,062)	57,313	(646,421)	(484,607)
Net premiums earned		1,001,774	678,702	2,734,173	2,060,626
Other underwriting income (loss)		452	3,293	5,814	3,148
Losses and loss adjustment expenses		(927,911)	(545,846)	(1,920,189)	(1,494,539)
Acquisition expenses		(208,425)	(129,450)	(569,915)	(381,060)
Other operating expenses		(62,777)	(45,647)	(198,606)	(150,856)
Underwriting income (loss)		$ (196,887)	$ (38,948)	$ 51,277	$ 37,319
Underwriting Ratios
Loss ratio		92.60%	80.40%	70.20%	72.50%
Acquisition expense ratio		20.80%	19.10%	20.80%	18.50%
Other operating expense ratio		6.30%	6.70%	7.30%	7.30%
Combined ratio		119.70%	106.20%	98.30%	98.30%
Goodwill and intangible assets		$ 140,800	$ 176,128	$ 140,800	$ 176,128
Operating segments | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[1]	362,409	360,934	1,099,144	1,143,691
Premiums ceded		(86,230)	(60,207)	(241,097)	(171,923)
Net premiums written		276,179	300,727	858,047	971,768
Change in unearned premiums		5,889	11,238	9,190	10,735
Net premiums earned		282,068	311,965	867,237	982,503
Other underwriting income (loss)		2,625	3,981	6,130	15,026
Losses and loss adjustment expenses		67,878	(11,543)	187,163	(85,112)
Acquisition expenses		(6,693)	(24,098)	(27,343)	(84,297)
Other operating expenses		(46,471)	(46,254)	(150,064)	(143,697)
Underwriting income (loss)		$ 299,407	$ 234,051	$ 883,123	$ 684,423
Underwriting Ratios
Loss ratio		(24.10%)	3.70%	(21.60%)	8.70%
Acquisition expense ratio		2.40%	7.70%	3.20%	8.60%
Other operating expense ratio		16.50%	14.80%	17.30%	14.60%
Combined ratio		(5.20%)	26.20%	(1.10%)	31.90%
Goodwill and intangible assets		$ 441,330	$ 526,091	$ 441,330	$ 526,091
Operating segments | Corporate and Other Segments
Segment Reporting Information [Line Items]
Number of segments | segment				2
Gross premiums written	[1]	0	0	$ 0	457,465
Premiums ceded		0	0	0	(102,763)
Net premiums written		0	0	0	354,702
Change in unearned premiums		0	0	0	(22,734)
Net premiums earned		0	0	0	331,968
Other underwriting income (loss)		0	0	0	739
Losses and loss adjustment expenses		0	0	0	(259,042)
Acquisition expenses		0	0	0	(62,741)
Other operating expenses		0	0	0	(32,869)
Underwriting income (loss)		0	0	0	(21,945)
Net investment income		0	0	0	42,310
Net realized gains (losses)		0	0	0	80,638
Equity in net income (loss) of investment funds accounted for using the equity method		0	0	0	0
Other income (loss)		0	0	0	0
Corporate expenses	[2]	0	0	0	0
Transaction costs and other	[2]	0	0	0	(935)
Amortization of intangible assets		0	0	0	(898)
Interest expense		0	0	0	(8,410)
Net foreign exchange gains (losses)		0	0	0	(1,325)
Income (loss) before income taxes and income (loss) from operating affiliates		0	0	0	89,435
Income tax expense (benefit)		0	0	0	(234)
Income (loss) from operating affiliates		0	0	0	0
Net income (loss)		0	0	0	89,201
Amounts attributable to redeemable noncontrolling interests		0	0	0	(1,953)
Amounts attributable to non-redeemable noncontrolling interests					(78,314)
Net income (loss) available to Arch		0	0	0	8,934
Preferred dividends		0	0	0	0
Loss on redemption of preferred shares			0		0
Net income (loss) available to Arch common shareholders		$ 0	$ 0	$ 0	$ 8,934
Underwriting Ratios
Loss ratio		0%	0%	0%	78%
Acquisition expense ratio		0%	0%	0%	18.90%
Other operating expense ratio		0%	0%	0%	9.90%
Combined ratio		0%	0%	0%	106.80%
Goodwill and intangible assets		$ 0	$ 0	$ 0	$ 0
[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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs 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		3 Months Ended		9 Months Ended
		Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]
Reserve for losses and loss adjustment expenses at beginning of period		$ 18,194,324	$ 17,196,648	$ 17,757,156	$ 16,513,929
Unpaid losses and loss adjustment expenses recoverable		5,686,348	4,146,020	5,599,231	4,314,855
Net reserve for losses and loss adjustment expenses at beginning of period		12,507,976	13,050,628	12,157,925	12,199,074
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year		1,863,519	1,348,528	4,280,048	3,812,381
Prior years		(180,823)	(122,509)	(493,861)	(223,431)
Total net incurred losses and loss adjustment expenses		1,682,696	1,226,019	3,786,187	3,588,950
Net losses and loss adjustment expense reserves of acquired business	[1]	0	104,307	0	104,307
Retroactive reinsurance transaction	[2]	0	0	0	(183,893)
Impact of deconsolidation of Somers		0	(1,460,611)	0	(1,460,611)
Net foreign exchange (gains) losses and other		(243,387)	(78,152)	(524,682)	10,818
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year		(226,575)	(208,923)	(463,847)	(432,348)
Prior years		(538,967)	(417,368)	(1,773,840)	(1,610,397)
Total net paid losses and loss adjustment expenses		(765,542)	(626,291)	(2,237,687)	(2,042,745)
Net reserve for losses and loss adjustment expenses at end of period		13,181,743	12,215,900	13,181,743	12,215,900
Unpaid losses and loss adjustment expenses recoverable		6,106,548	5,115,147	6,106,548	5,115,147
Reserve for losses and loss adjustment expenses at end of period		$ 19,288,291	$ 17,331,047	$ 19,288,291	$ 17,331,047
[1]Represents activity related to the Company’s acquisitions in the 2021 period of the Westpac Lenders Mortgage Insurance Limited and Somerset Bridge Group Limited, Southern Rock Holdings Limited and affiliates.[2]During the 2021 first quarter, the Company entered into a reinsurance to close and other related agreements with Premia Managing Agency Limited (“Premia”), in connection with the 2018 and prior years of account related to the acquisition of Barbican Group Holdings Limited (“Barbican”).

Reserve for Losses and Loss A_4

Reserve for Losses and Loss Adjustment Expenses - Prior year development (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 180,823	$ 122,509	$ 493,861	$ 223,431
Operating segments | Insurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 5,400	$ 5,100	$ 19,400	$ 13,100
Percentage of prior year development	0.50%	0.50%	0.60%	0.50%
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)	$ 15,900		$ 49,100	$ 65,300
Operating segments | Insurance | Short tailed lines | Property excluding marine
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	8,900	$ 5,400		27,000
Operating segments | Insurance | Short tailed lines | Travel and accident
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		5,100	14,300	14,400
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)	5,700	5,400	36,500	24,000
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)		(43,900)		(89,400)
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)				(6,900)
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)	(11,300)		(24,900)	(26,200)
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)		(37,000)	(5,500)	(57,100)
Operating segments | Insurance | Medium tailed lines | Marine
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	5,900		11,400
Operating segments | Insurance | Long tailed lines | Casualty
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(12,300)		(18,000)
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)		26,300
Operating segments | Insurance | Long tailed lines | Other Lines Of Business
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		6,700	17,400
Operating segments | Insurance | Long tailed lines | Construction, National Accounts And Alternative Markets
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)				37,100
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)	(10,500)		(29,700)
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)		49,000		102,500
Operating segments | Reinsurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 49,200	$ 72,300	$ 128,100	$ 119,600
Percentage of prior year development	4.90%	10.70%	4.70%	5.80%
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)		$ 65,400		$ 132,600
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)		46,100
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)	$ 12,700		$ 22,400	(36,300)
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)	35,800		83,200	71,700
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)		18,900	19,800	97,100
Operating segments | Reinsurance | Medium tailed lines | Marine and aviation
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	7,900		22,700
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)	(8,900)		(19,700)	(20,100)
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)	(9,500)		(19,300)
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)	58,100		147,800	139,700
Operating segments | Reinsurance | Medium tailed and long tailed lines
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		6,900
Operating segments | Reinsurance | Medium tailed and long tailed lines | Casualty
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		4,700
Operating segments | Mortgage
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 126,200	$ 45,100	$ 346,400	$ 99,100
Percentage of prior year development	44.70%	14.50%	39.90%	10.10%
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)

Allowance for Expected Credit_3

Allowance for Expected Credit Losses - Premiums receivable (Details) - USD ($) $ in Thousands		3 Months Ended		9 Months Ended
		Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Credit Loss [Abstract]
Balance at beginning of period		$ 3,634,182	$ 2,866,578	$ 2,633,280	$ 2,064,586
Balance at end of period		3,579,380	2,807,720	3,579,380	2,807,720
Allowance for Expected Credit Losses
Balance at beginning of period		38,170	35,979	39,958	37,781
Change for provision of expected credit losses	[1]	59	2,736	(1,729)	934
Balance at end of period		38,229	38,715	38,229	38,715
Premium receivable, write-offs during the period		$ 1,900	$ 1,200	$ 6,600	$ 2,400
[1]Amounts deemed uncollectible are written-off in operating expenses. For the 2022 third quarter and 2021 third quarter, amounts written off were $1.9 million and $1.2 million, respectively. For the nine months ended September 30, 2022 and 2021 period, amounts written off were $6.6 million and $2.4 million, respectively.

Allowance for Expected Credit_4

Allowance for Expected Credit Losses - Reinsurance recoverables (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Credit Loss [Abstract]
Balance at beginning of period	$ 5,938,511	$ 4,314,515	$ 5,880,735	$ 4,500,802
Balance at end of period	6,356,456	5,358,852	6,356,456	5,358,852
Allowance for Expected Credit Losses
Balance at beginning of period	14,740	11,029	13,230	11,636
Change for provision of expected credit losses	2,626	1,802	4,136	1,195
Balance at end of period	$ 17,366	$ 12,831	$ 17,366	$ 12,831

Allowance for Expected Credit_5

Allowance for Expected Credit Losses - Ceded credit risk (Details) - USD ($) $ in Thousands		9 Months Ended	12 Months Ended
		Sep. 30, 2022	Dec. 31, 2021	Jun. 30, 2022	Sep. 30, 2021	Jun. 30, 2021	Dec. 31, 2020
Ceded Credit Risk [Line Items]
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses		$ 6,356,456	$ 5,880,735	$ 5,938,511	$ 5,358,852	$ 4,314,515	$ 4,500,802
Reinsurance recoverable | Reinsurer concentration risk | AM Best A minus Or Better Rating
Ceded Credit Risk [Line Items]
Concentration risk percentage		69.50%	69.70%
Reinsurance recoverable | Reinsurer concentration risk | AM Best Rating Below A Minus | All Other Carriers
Ceded Credit Risk [Line Items]
Concentration risk percentage		0.10%	0.10%
Reinsurance recoverable | Reinsurer concentration risk | Not Rated | All Other Carriers
Ceded Credit Risk [Line Items]
Concentration risk percentage	[1]	30.40%	30.20%
Reinsurance recoverable | Reinsurer concentration risk | Not Rated | Reinsurance trusts or letters of credit
Ceded Credit Risk [Line Items]
Concentration risk percentage		95%	91%
Stockholders' equity | Reinsurer concentration risk | Largest Balance Due From Any One Carrier
Ceded Credit Risk [Line Items]
Concentration risk percentage		9.10%	6.70%
[1]At September 30, 2022 and December 31, 2021 over 95% and 91% of such amount were 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	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Credit Loss [Abstract]
Balance at beginning of period	$ 1,758,018	$ 1,882,948	$ 1,828,691	$ 1,986,924
Balance at end of period	1,735,730	1,824,990	1,735,730	1,824,990
Allowance for Expected Credit Losses
Balance at beginning of period	3,005	4,471	3,437	8,638
Change for provision of expected credit losses	(645)	(987)	(1,077)	(5,154)
Balance at end of period	$ 2,360	$ 3,484	$ 2,360	$ 3,484

Investment Information - Summar

Investment Information - Summary of available for sale securities (Details) - USD ($) $ in Thousands	Sep. 30, 2022	Jun. 30, 2022	Dec. 31, 2021	Sep. 30, 2021	Jun. 30, 2021	Dec. 31, 2020
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	$ 20,061,584		$ 19,732,825
Gross Unrealized Gains	115,738		198,691
Gross Unrealized Losses	(1,862,287)		(171,544)
Allowance for Expected Credit Losses	(45,993)	$ (58,410)	(2,883)	$ (2,111)	$ (2,124)	$ (2,397)
Cost or Amortized Cost	21,854,126		19,708,561
Fixed maturities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	18,120,727		17,998,109
Gross Unrealized Gains	114,319		198,123
Gross Unrealized Losses	(1,860,654)		(170,954)
Allowance for Expected Credit Losses	(45,993)		(2,883)
Cost or Amortized Cost	19,913,055		17,973,823
Corporate bonds
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	7,096,269		6,553,333
Gross Unrealized Gains	51,777		104,170
Gross Unrealized Losses	(895,365)		(69,194)
Allowance for Expected Credit Losses	(35,657)		(2,037)
Cost or Amortized Cost	7,975,514		6,520,394
Mortgage backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	763,371		408,477
Gross Unrealized Gains	7,561		2,825
Gross Unrealized Losses	(84,183)		(5,410)
Allowance for Expected Credit Losses	2		(48)
Cost or Amortized Cost	839,991		411,110
Municipal bonds
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	407,724		404,666
Gross Unrealized Gains	5,437		18,724
Gross Unrealized Losses	(37,692)		(1,409)
Allowance for Expected Credit Losses	(99)	$ (298)	(2)	$ (2)	$ (6)	$ (11)
Cost or Amortized Cost	440,078		387,353
Commercial mortgage backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	1,064,238		1,046,484
Gross Unrealized Gains	3,079		1,740
Gross Unrealized Losses	(50,010)		(3,117)
Allowance for Expected Credit Losses	(1,583)		(6)
Cost or Amortized Cost	1,112,752		1,047,867
US government and government agencies
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	5,126,407		4,772,764
Gross Unrealized Gains	36,074		10,076
Gross Unrealized Losses	(400,784)		(45,967)
Allowance for Expected Credit Losses	0		0
Cost or Amortized Cost	5,491,117		4,808,655
Non-US government securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	2,073,170		2,120,294
Gross Unrealized Gains	9,315		54,048
Gross Unrealized Losses	(287,583)		(34,749)
Allowance for Expected Credit Losses	(1,720)		(82)
Cost or Amortized Cost	2,353,158		2,101,077
Asset backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	1,589,548		2,692,091
Gross Unrealized Gains	1,076		6,540
Gross Unrealized Losses	(105,037)		(11,108)
Allowance for Expected Credit Losses	(6,936)		(708)
Cost or Amortized Cost	1,700,445		2,697,367
Short-term investments
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	1,940,857		1,734,716
Gross Unrealized Gains	1,419		568
Gross Unrealized Losses	(1,633)		(590)
Allowance for Expected Credit Losses	0		0
Cost or Amortized Cost	$ 1,941,071		$ 1,734,738

Investment Information - Aging

Investment Information - Aging of available for sale securities in an unrealized loss position (Details) - USD ($) $ in Thousands	Sep. 30, 2022	Dec. 31, 2021
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	$ 14,940,746	$ 12,238,683
Estimated Fair Value - 12 Months or More	2,936,029	297,357
Estimated Fair Value	17,876,775	12,536,040
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(1,376,623)	(157,279)
Gross Unrealized Losses - 12 Months or More	(485,664)	(14,265)
Gross Unrealized Losses	(1,862,287)	(171,544)
Fixed maturities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	14,713,545	11,953,950
Estimated Fair Value - 12 Months or More	2,936,029	297,357
Estimated Fair Value	17,649,574	12,251,307
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(1,374,990)	(156,689)
Gross Unrealized Losses - 12 Months or More	(485,664)	(14,265)
Gross Unrealized Losses	(1,860,654)	(170,954)
Corporate bonds
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	5,596,229	3,639,582
Estimated Fair Value - 12 Months or More	1,470,800	98,867
Estimated Fair Value	7,067,029	3,738,449
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(625,774)	(63,938)
Gross Unrealized Losses - 12 Months or More	(269,591)	(5,256)
Gross Unrealized Losses	(895,365)	(69,194)
Mortgage backed securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	620,572	222,176
Estimated Fair Value - 12 Months or More	93,902	46,809
Estimated Fair Value	714,474	268,985
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(63,732)	(3,545)
Gross Unrealized Losses - 12 Months or More	(20,451)	(1,865)
Gross Unrealized Losses	(84,183)	(5,410)
Municipal bonds
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	373,219	26,665
Estimated Fair Value - 12 Months or More	9,399	16,361
Estimated Fair Value	382,618	43,026
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(36,039)	(385)
Gross Unrealized Losses - 12 Months or More	(1,653)	(1,024)
Gross Unrealized Losses	(37,692)	(1,409)
Commercial mortgage backed securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	995,680	675,603
Estimated Fair Value - 12 Months or More	34,445	5,908
Estimated Fair Value	1,030,125	681,511
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(49,215)	(2,805)
Gross Unrealized Losses - 12 Months or More	(795)	(312)
Gross Unrealized Losses	(50,010)	(3,117)
US government and government agencies
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	4,205,475	4,211,621
Estimated Fair Value - 12 Months or More	715,347	33,373
Estimated Fair Value	4,920,822	4,244,994
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(303,805)	(44,180)
Gross Unrealized Losses - 12 Months or More	(96,979)	(1,787)
Gross Unrealized Losses	(400,784)	(45,967)
Non-US government securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	1,728,965	1,511,301
Estimated Fair Value - 12 Months or More	301,298	62,957
Estimated Fair Value	2,030,263	1,574,258
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(221,540)	(31,983)
Gross Unrealized Losses - 12 Months or More	(66,043)	(2,766)
Gross Unrealized Losses	(287,583)	(34,749)
Asset backed securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	1,193,405	1,667,002
Estimated Fair Value - 12 Months or More	310,838	33,082
Estimated Fair Value	1,504,243	1,700,084
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(74,885)	(9,853)
Gross Unrealized Losses - 12 Months or More	(30,152)	(1,255)
Gross Unrealized Losses	(105,037)	(11,108)
Short-term investments
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	227,201	284,733
Estimated Fair Value - 12 Months or More	0	0
Estimated Fair Value	227,201	284,733
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(1,633)	(590)
Gross Unrealized Losses - 12 Months or More	0	0
Gross Unrealized Losses	$ (1,633)	$ (590)

Investment Information - Maturi

Investment Information - Maturity profile of available for sale securities) (Details) - USD ($) $ in Thousands	Sep. 30, 2022	Dec. 31, 2021
Estimated Fair Value
Due in one year or less	$ 579,231	$ 300,889
Due after one year through five years	10,029,151	8,355,255
Due after five years through 10 years	3,856,180	4,689,155
Due after 10 years	239,008	505,758
Single maturity date	14,703,570	13,851,057
Estimated Fair Value	20,061,584	19,732,825
Amortized Cost
Due in one year or less	599,970	299,772
Due after one year through five years	10,808,495	8,339,387
Due after five years through 10 years	4,495,113	4,684,393
Due after 10 years	356,289	493,927
Single maturity date	16,259,867	13,817,479
Cost or Amortized Cost	21,854,126	19,708,561
Fixed maturities
Estimated Fair Value
Estimated Fair Value	18,120,727	17,998,109
Amortized Cost
Cost or Amortized Cost	19,913,055	17,973,823
Mortgage backed securities
Estimated Fair Value
Securities without single maturity date	763,371	408,477
Estimated Fair Value	763,371	408,477
Amortized Cost
Securities without single maturity date	839,991	411,110
Cost or Amortized Cost	839,991	411,110
Commercial mortgage backed securities
Estimated Fair Value
Securities without single maturity date	1,064,238	1,046,484
Estimated Fair Value	1,064,238	1,046,484
Amortized Cost
Securities without single maturity date	1,112,752	1,047,867
Cost or Amortized Cost	1,112,752	1,047,867
Asset backed securities
Estimated Fair Value
Securities without single maturity date	1,589,548	2,692,091
Estimated Fair Value	1,589,548	2,692,091
Amortized Cost
Securities without single maturity date	1,700,445	2,697,367
Cost or Amortized Cost	$ 1,700,445	$ 2,697,367

Investment Information - Other

Investment Information - Other investments (Details) - USD ($) $ in Thousands	Sep. 30, 2022	Dec. 31, 2021
Schedule Of Other Investments [Line Items]
Other investments, at fair value	$ 1,578,751	$ 1,973,550
Fixed maturities
Schedule Of Other Investments [Line Items]
Other investments, at fair value	530,303	416,698
Other investments
Schedule Of Other Investments [Line Items]
Other investments, at fair value	1,005,929	1,432,553
Other investments | Lending
Schedule Of Other Investments [Line Items]
Other investments, at fair value	398,789	536,345
Other investments | Investment grade fixed income
Schedule Of Other Investments [Line Items]
Other investments, at fair value	229,262	147,810
Other investments | Term loan investments
Schedule Of Other Investments [Line Items]
Other investments, at fair value	151,649	484,950
Other investments | Private equity
Schedule Of Other Investments [Line Items]
Other investments, at fair value	117,856	91,126
Other investments | Energy
Schedule Of Other Investments [Line Items]
Other investments, at fair value	55,250	81,692
Other investments | Credit related funds
Schedule Of Other Investments [Line Items]
Other investments, at fair value	53,123	70,278
Other investments | Infrastructure
Schedule Of Other Investments [Line Items]
Other investments, at fair value	0	20,352
Short-term investments
Schedule Of Other Investments [Line Items]
Other investments, at fair value	28,614	97,806
Equity securities
Schedule Of Other Investments [Line Items]
Other investments, at fair value	$ 13,905	$ 26,493

Investment Information - Equity

Investment Information - Equity method investments (Details) - USD ($) $ in Thousands	Sep. 30, 2022	Dec. 31, 2021
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 3,565,946	$ 3,077,611
Credit related funds
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	1,135,623	1,022,334
Private equity
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	761,997	436,042
Real estate
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	474,666	396,395
Lending
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	454,196	376,649
Equity securities
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	261,650	395,090
Infrastructure
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	236,920	230,070
Energy
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	113,778	119,141
Fixed income
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 127,116	$ 101,890

Investment Information - Limite

Investment Information - Limited partnership interests (Details) - USD ($) $ in Thousands		Sep. 30, 2022	Dec. 31, 2021
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss		$ 3,686,444	$ 3,248,206
Aggregate unfunded commitments		3,100,000	3,000,000
Equity method investments
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss	[1]	3,565,946	3,077,611
Aggregate unfunded commitments		2,800,000	2,600,000
Fair value option
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss	[2]	120,498	170,595
Aggregate unfunded commitments		$ 21,500	$ 18,800
[1]Aggregate unfunded commitments were $2.8 billion at September 30, 2022, compared to $2.6 billion at December 31, 2021.[2]Aggregate unfunded commitments were $21.5 million at September 30, 2022, compared to $18.8 million at December 31, 2021.

Investment Information - Net in

Investment Information - Net investment income (Details) - USD ($) $ in Thousands		3 Months Ended		9 Months Ended
		Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Net investment income:
Gross investment income		$ 145,777	$ 106,803	$ 372,286	$ 367,945
Investment expenses		(17,137)	(18,608)	(56,818)	(69,281)
Net investment income		128,640	88,195	315,468	298,664
Fixed maturities
Net investment income:
Gross investment income		123,568	75,964	310,963	255,215
Term loans
Net investment income:
Gross investment income		88	1,736	2,106	33,343
Equity securities
Net investment income:
Gross investment income		4,261	9,867	16,620	24,101
Short-term investments
Net investment income:
Gross investment income		9,304	1,858	15,999	3,603
Other
Net investment income:
Gross investment income	[1]	$ 8,556	$ 17,378	$ 26,598	$ 51,683
[1]Includes income distributions from investment funds and other items.

Investment Information - Net re

Investment Information - Net realized gains and losses (Details) - USD ($) $ in Thousands		3 Months Ended		9 Months Ended
		Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Available for sale securities:
Available for sale securities, gross gains on investment sales		$ 18,030	$ 86,819	$ 52,923	$ 267,362
Available for sale securities, gross losses on investment sales		(73,970)	(18,446)	(239,493)	(132,071)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period		(6,401)	14,736	75,689	86,155
Net unrealized gains (losses) on equity securities still held at reporting date		(36,162)	(40,155)	(318,732)	45,400
Allowance for credit losses:
Allowance for credit losses - investments related		8,652	(456)	(48,096)	(1,208)
Allowance for credit losses - underwriting related		(4,232)	(3,985)	(7,676)	2,664
Derivative instruments	[1]	(48,196)	(21,435)	(117,591)	(36,428)
Other		(2,649)	(41,495)	(6,186)	(54,316)
Net realized gains (losses)		(183,673)	(25,040)	(742,666)	320,328
Fixed maturities
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		(19,304)	(7,492)	(89,148)	19,973
Other investments
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		(17,882)	3,811	(35,203)	111,550
Equity securities
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		(584)	3,042	(6,021)	10,599
Short-term investments
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		$ (975)	$ 16	$ (3,132)	$ 648
[1]See note 9 for information on the Company’s derivative instruments.

Investment Information - Invest

Investment Information - Investment in operating affiliates (Details) € / shares in Units, $ / shares in Units, $ in Thousands, € in Millions	3 Months Ended		9 Months Ended		12 Months Ended
	Sep. 30, 2022 USD ($)	Sep. 30, 2021 USD ($)	Sep. 30, 2022 USD ($)	Sep. 30, 2021 USD ($)	Dec. 31, 2021 USD ($)	Dec. 31, 2021 EUR (€) € / shares	Jul. 01, 2021 $ / shares
Schedule of Equity Method Investments [Line Items]
Time lag for reporting			3 months
Investment in operating affiliates	$ 891,212		$ 891,212		$ 1,135,655
Income (loss) from operating affiliates	$ 8,507	$ 124,119	$ 37,665	$ 224,052
Coface
Schedule of Equity Method Investments [Line Items]
Percentage ownership	29.86%		29.86%		29.50%	29.50%
Investment in affiliate, price per share | € / shares						€ 9.95
Operating affiliate, aggregate cost					$ 546,000	€ 453
Investment in operating affiliates	$ 506,700		$ 506,700		630,500
Operating affiliate, gain on acquisition					74,500
Greysbridge Holdings Ltd
Schedule of Equity Method Investments [Line Items]
Percentage ownership							40%
Investment in affiliate, price per share | $ / shares							$ 35
Operating affiliate, aggregate cost					278,900
Investment in operating affiliates	$ 277,600		$ 277,600		375,700
Operating affiliate, gain on acquisition					$ 95,700
Issued Shares Excluding Treasury Stock | Coface
Schedule of Equity Method Investments [Line Items]
Percentage ownership	30.05%		30.05%
Kelso And Company | Greysbridge Holdings Ltd
Schedule of Equity Method Investments [Line Items]
Percentage ownership							30%
Warburg Pincus LLC | Greysbridge Holdings Ltd
Schedule of Equity Method Investments [Line Items]
Percentage ownership							30%

Investment Information - Allowa

Investment Information - Allowance for expected credit losses (Details) - USD ($) $ in Thousands		3 Months Ended		9 Months Ended
		Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Allowance for expected credit losses
Balance at beginning of period		$ 58,410	$ 2,124	$ 2,883	$ 2,397
Additions for current-period provision for expected credit losses		3,780	48	53,521	2,710
Additions (reductions) for previously recognized expected credit losses		(12,530)	405	(5,609)	(1,317)
Reductions due to disposals		(3,667)	(466)	(4,802)	(1,679)
Balance at end of period		45,993	2,111	45,993	2,111
Structured securities
Allowance for expected credit losses
Balance at beginning of period	[1]	18,283	759	802	1,490
Additions for current-period provision for expected credit losses	[1]	1,782	48	12,560	282
Additions (reductions) for previously recognized expected credit losses	[1]	(9,767)	14	(2,575)	(751)
Reductions due to disposals	[1]	(1,780)	(234)	(2,269)	(434)
Balance at end of period	[1]	8,518	587	8,518	587
Municipal bonds
Allowance for expected credit losses
Balance at beginning of period		298	6	2	11
Additions for current-period provision for expected credit losses		12	0	359	0
Additions (reductions) for previously recognized expected credit losses		(211)	(4)	(262)	(9)
Reductions due to disposals		0	0	0	0
Balance at end of period		99	2	99	2
Corporate bonds
Allowance for expected credit losses
Balance at beginning of period		39,829	1,359	2,079	896
Additions for current-period provision for expected credit losses		1,986	0	40,602	2,428
Additions (reductions) for previously recognized expected credit losses		(2,552)	395	(2,772)	(557)
Reductions due to disposals		(1,887)	(232)	(2,533)	(1,245)
Balance at end of period		$ 37,376	$ 1,522	$ 37,376	$ 1,522
[1]Includes asset backed securities, residential mortgage backed securities and commercial mortgage backed securities.

Investment Information - Restri

Investment Information - Restricted assets (Details) - USD ($) $ in Thousands	Sep. 30, 2022	Dec. 31, 2021
Restricted Assets [Line Items]
Restricted assets	$ 8,335,957	$ 8,249,732
Collateral or guarantees - affiliated transactions
Restricted Assets [Line Items]
Restricted assets	4,212,521	4,223,955
Collateral or guarantees - third party agreements
Restricted Assets [Line Items]
Restricted assets	2,847,814	2,721,160
Deposits with US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	756,368	798,100
Deposits with non-US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	$ 519,254	$ 506,517

Investment Information - Cash a

Investment Information - Cash and restricted cash (Details) - USD ($) $ in Thousands	Sep. 30, 2022	Dec. 31, 2021	Sep. 30, 2021	Dec. 31, 2020
Disclosure Investment Information [Abstract]
Cash	$ 813,583	$ 858,668
Restricted cash (included in ‘other assets’)	444,741	456,103
Cash and restricted cash	$ 1,258,324	$ 1,314,771	$ 1,548,909	$ 1,290,544

Investment Information - Narrat

Investment Information - Narrative (Details) $ in Thousands	3 Months Ended		9 Months Ended
	Sep. 30, 2022 USD ($) lots	Sep. 30, 2021 USD ($)	Sep. 30, 2022 USD ($) lots	Sep. 30, 2021 USD ($)	Dec. 31, 2021 USD ($) lots
Continuous unrealized loss, qualitative disclosures:
Number of positions in an unrealized loss position (lots) | lots	9,590		9,590		4,700
Total number of positions (lots) | lots	11,500		11,500		10,240
Largest single loss	$ 7,200		$ 7,200		$ 1,100
Narrative items:
Equity securities, at fair value	809,869		809,869		$ 1,804,170
Equity in net (loss) income of investment funds accounted for using the equity method	$ (18,861)	$ 105,398	$ 75,505	$ 299,270
Time lag for reporting			3 months
Minimum
Narrative items:
Time lag for reporting			1 month
Maximum
Narrative items:
Time lag for reporting			3 months

Fair Value - Fair Value Hierarc

Fair Value - Fair Value Hierarchy (Details) - Recurring - USD ($) $ in Thousands		Sep. 30, 2022	Dec. 31, 2021
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		$ 7,759,369	$ 7,602,828
Liabilities measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Other liabilities
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) | 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 loans
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) | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		5,100,908	4,744,517
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | 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) | Fixed maturities | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		5,100,908	4,744,517
Quoted Prices in Active Markets for Identical Assets (Level 1) | Fixed maturities | 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) | Fixed maturities | 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) | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,873,480	1,052,822
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		775,264	1,762,864
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		9,717	42,625
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 | 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		405	528
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		9,312	21,745
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		0	20,352
Significant Other Observable Inputs (Level 2)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		13,996,698	14,923,923
Liabilities measured at fair value		(112,577)	(54,224)
Significant Other Observable Inputs (Level 2) | Other liabilities
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) | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(112,577)	(54,224)
Significant Other Observable Inputs (Level 2) | Residential mortgage loans
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,255	49,847
Significant Other Observable Inputs (Level 2) | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		13,019,806	13,250,232
Significant Other Observable Inputs (Level 2) | Fixed maturities | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		7,096,256	6,553,320
Significant Other Observable Inputs (Level 2) | Fixed maturities | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		763,371	408,477
Significant Other Observable Inputs (Level 2) | Fixed maturities | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		407,724	404,666
Significant Other Observable Inputs (Level 2) | Fixed maturities | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,064,238	1,046,484
Significant Other Observable Inputs (Level 2) | Fixed maturities | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		25,499	28,247
Significant Other Observable Inputs (Level 2) | Fixed maturities | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,073,170	2,120,294
Significant Other Observable Inputs (Level 2) | Fixed maturities | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,589,548	2,688,744
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		67,377	681,894
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		31,566	38,388
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		176,160	127,121
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		699,534	776,441
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		524,177	388,546
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		4,032	23,785
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		2,094	4,367
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		28,209	97,278
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		1	0
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		141,021	262,465
Significant Unobservable Inputs (Level 3)
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		41,882	39,007
Liabilities measured at fair value		(13,421)	(16,960)
Significant Unobservable Inputs (Level 3) | Other liabilities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(13,421)	(16,960)
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 loans
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) | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		13	3,360
Significant Unobservable Inputs (Level 3) | Fixed maturities | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		13	13
Significant Unobservable Inputs (Level 3) | Fixed maturities | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	0
Significant Unobservable Inputs (Level 3) | Fixed maturities | 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) | Fixed maturities | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		0	3,347
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		3,039	2,918
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		38,830	32,729
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	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		4,592	4,748
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		34,238	27,981
Estimated Fair Value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		22,628,619	23,687,513
Liabilities measured at fair value		(125,998)	(71,184)
Estimated Fair Value | Other liabilities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(13,421)	(16,960)
Estimated Fair Value | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Liabilities measured at fair value		(112,577)	(54,224)
Estimated Fair Value | Residential mortgage loans
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,255	49,847
Estimated Fair Value | Fixed maturities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		18,120,727	17,998,109
Estimated Fair Value | Fixed maturities | Corporate bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		7,096,269	6,553,333
Estimated Fair Value | Fixed maturities | Mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		763,371	408,477
Estimated Fair Value | Fixed maturities | Municipal bonds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		407,724	404,666
Estimated Fair Value | Fixed maturities | Commercial mortgage backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,064,238	1,046,484
Estimated Fair Value | Fixed maturities | US government and government agencies
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		5,126,407	4,772,764
Estimated Fair Value | Fixed maturities | Non-US government securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		2,073,170	2,120,294
Estimated Fair Value | Fixed maturities | Asset backed securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,589,548	2,692,091
Estimated Fair Value | Short-term investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,940,857	1,734,716
Estimated Fair Value | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		809,869	1,804,170
Estimated Fair Value | Derivative instruments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		176,160	127,121
Estimated Fair Value | Fair value option
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		1,578,751	1,973,550
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		524,177	388,546
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		4,032	23,785
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		2,094	4,367
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		28,614	97,806
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		13,905	26,493
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		175,259	310,798
Estimated Fair Value | Fair value option | Other investments measured at net asset value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value	[1]	$ 830,670	$ 1,121,755
[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.

Fair Value - Rollforward of Lev

Fair Value - Rollforward of Level 3 assets and liabilities (Details) - Recurring - USD ($) $ in Thousands		3 Months Ended			9 Months Ended
		Sep. 30, 2022	Sep. 30, 2021		Sep. 30, 2022	Sep. 30, 2021
Other liabilities
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		$ (16,205)	$ (466)		$ (16,960)	$ (461)
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(89)	0		(284)	0
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		965	0		1,915	0
Purchases, issuances, sales and settlements
Purchases		0	(17,345)		0	(17,345)
Issuances		0	0		0	0
Sales		0	0	[2]	0	0	[2]
Settlements		1,908	0		1,908	(5)
Transfers in and/or out of Level 3		0	0		0	0
Balance at end of period		(13,421)	(17,811)		(13,421)	(17,811)
Available for sale | Structured securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period	[3]	2,867	3,424		3,347	3,426
Total gains or (losses) (realized/unrealized) - included in earnings	[1],[3]	(601)	10		(592)	(46)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income	[3]	144	10		(1)	67
Purchases, issuances, sales and settlements
Purchases	[3]	0	0		0	0
Issuances	[3]	0	0		0	0
Sales	[3]	(2,051)	0	[2]	(2,051)	0	[2]
Settlements	[3]	(359)	0		(703)	(3)
Transfers in and/or out of Level 3	[3]	0	0		0	0
Balance at end of period	[3]	0	3,444		0	3,444
Available for sale | Corporate bonds
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		3,570	13		13	13
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	52	0		52	0
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		(59)	0		(59)	0
Purchases, issuances, sales and settlements
Purchases		0	0		0	0
Issuances		0	0		0	0
Sales		(3,550)	0	[2]	(3,550)	0	[2]
Settlements		0	0		0	0
Transfers in and/or out of Level 3		0	0		3,557	0
Balance at end of period		13	13		13	13
Fair value option | Corporate bonds
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		0	998		0	985
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	0	0		0	13
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0		0	0
Purchases, issuances, sales and settlements
Purchases		0	0		0	0
Issuances		0	0		0	0
Sales		0	(998)	[2]	0	(998)	[2]
Settlements		0	0		0	0
Transfers in and/or out of Level 3		0	0		0	0
Balance at end of period		0	0		0	0
Fair value option | Other investments
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		33,331	73,900		27,981	67,103
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	116	0		150	881
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0		0	0
Purchases, issuances, sales and settlements
Purchases		1,458	0		12,228	13,003
Issuances		0	0		0	0
Sales		(667)	(44,143)	[2]	(3,138)	(51,230)	[2]
Settlements		0	0		(2,983)	0
Transfers in and/or out of Level 3		0	0		0	0
Balance at end of period		34,238	29,757		34,238	29,757
Fair value option | Equity securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		4,392	73,678		4,748	68,988
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	200	38		(156)	4,728
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0		0	0
Purchases, issuances, sales and settlements
Purchases		0	0		0	0
Issuances		0	0		0	0
Sales		0	(69,181)	[2]	0	(69,181)	[2]
Settlements		0	0		0	0
Transfers in and/or out of Level 3		0	0		0	0
Balance at end of period		4,592	4,535		4,592	4,535
Equity securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		2,906	49,136		2,918	42,015
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	133	11		(103)	1,837
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0		0	0
Purchases, issuances, sales and settlements
Purchases		0	208		227	5,503
Issuances		0	0		0	0
Sales		0	(46,773)	[2]	(3)	(46,773)	[2]
Settlements		0	0		0	0
Transfers in and/or out of Level 3		0	0		0	0
Balance at end of period		$ 3,039	$ 2,582		$ 3,039	$ 2,582
[1]Gains or losses were included in net realized gains (losses).[2]Sales for the 2021 periods primarily related to the Company’s deconsolidation of Somers..[3]Includes asset backed securities, residential mortgage backed securities and commercial mortgage backed securities.

Fair Value - Narrative (Details

Fair Value - Narrative (Details) - USD ($) $ in Thousands	Sep. 30, 2022	Dec. 31, 2021
Fair Value Disclosures [Abstract]
Total assets and liabilities measured at fair value	$ 22,800,000	$ 23,800,000
Total assets and liabilities measured at fair value priced using non-binding broker quotes	$ 12,600	$ 7,700
Total assets and liabilities measured at fair value priced using non-binding broker quotes (percentage)	0.10%	0%
Senior notes	$ 2,725,153	$ 2,724,394
Estimated fair value of senior notes	$ 2,300,000	$ 3,300,000

Derivative Instruments - Fair v

Derivative Instruments - Fair value and notional amount of derivatives (Details) - USD ($) $ in Thousands		Sep. 30, 2022	Dec. 31, 2021
Derivative offsetting
Derivative assets subject to master netting agreements		$ 164,900	$ 122,300
Derivative liabilities subject to master netting agreements		$ 112,600	$ 53,900
Derivative Asset, Statement of Financial Position [Extensible Enumeration]		Other assets	Other assets
Derivative Liability, Statement of Financial Position [Extensible Enumeration]		Other liabilities	Other liabilities
Not designated as hedging instrument
Derivative [Line Items]
Asset derivatives - fair value		$ 176,160	$ 127,121
Liability derivatives - fair value		(112,577)	(54,224)
Not designated as hedging instrument | Futures contracts
Derivative [Line Items]
Asset derivatives - fair value	[1]	72,730	34,999
Liability derivatives - fair value	[1]	(60,684)	(9,808)
Net derivatives - notional value	[2]	2,189,945	2,826,564
Not designated as hedging instrument | Foreign currency forward contracts
Derivative [Line Items]
Asset derivatives - fair value	[1]	25,281	7,734
Liability derivatives - fair value	[1]	(26,995)	(11,390)
Net derivatives - notional value	[2]	835,941	915,962
Not designated as hedging instrument | TBAs
Derivative [Line Items]
Asset derivatives - fair value	[1]	0	11,227
Liability derivatives - fair value	[1]	0	0
Net derivatives - notional value	[2]	0	11,227
Not designated as hedging instrument | Other
Derivative [Line Items]
Asset derivatives - fair value	[1]	78,149	73,161
Liability derivatives - fair value	[1]	(24,898)	(33,026)
Net derivatives - notional value	[2]	$ 3,766,549	$ 3,736,773
[1]The fair value of asset derivatives are included in ‘ other assets other liabilities

Derivative Instruments - Summar

Derivative Instruments - Summary of net realized gains (losses) recorded in the consolidated statements of income (Details) - USD ($) $ in Thousands		3 Months Ended		9 Months Ended
		Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments	[1]	$ (48,196)	$ (21,435)	$ (117,591)	$ (36,428)
Not designated as hedging instrument
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(48,196)	(21,435)	(117,591)	(36,428)
Not designated as hedging instrument | Futures contracts
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(26,347)	(10,073)	(112,326)	(17,394)
Not designated as hedging instrument | Foreign currency forward contracts
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(18,340)	(16,146)	(46,016)	(36,922)
Not designated as hedging instrument | TBAs
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		0	(46)	(51)	(46)
Not designated as hedging instrument | Other
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments	[2]	$ (3,509)	$ 4,830	$ 40,802	$ 17,934
[1]See note 9 for information on the Company’s derivative instruments.

Commitments and Contingencies (

Commitments and Contingencies (Details) - USD ($) $ in Millions		9 Months Ended
	Apr. 07, 2022	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2021
Commitments and Contingencies Disclosure [Abstract]
Investment commitments		$ 3,100		$ 3,000
Interest paid on senior notes and other borrowings		65	$ 75.8
Credit Agreement
Line of Credit Facility [Line Items]
Credit facility term	5 years
Maximum borrowing capacity	$ 925
Optional increased capacity	1,300
Secured Facility
Line of Credit Facility [Line Items]
Maximum borrowing capacity	425	425
Revolving credit agreement borrowings		311.8
Remaining capacity		113.2
Unsecured Facility
Line of Credit Facility [Line Items]
Maximum borrowing capacity	$ 500
Secured Letters of Credit | Subsidiaries
Line of Credit Facility [Line Items]
Revolving credit agreement borrowings		22.7
Unsecured Letters of Credit | Subsidiaries
Line of Credit Facility [Line Items]
Revolving credit agreement borrowings		$ 290

Variable Interest Entities an_3

Variable Interest Entities and Noncontrolling Interests - Variable interest entity (Details) - USD ($) $ in Thousands	1 Months Ended	6 Months Ended	9 Months Ended
	Mar. 31, 2014	Jun. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Jul. 01, 2021
Variable Interest Entity [Line Items]
Net cash provided by (used for) operating activities			$ 2,833,717	$ 2,627,551
Net cash provided by (used for) investing activities			(2,106,721)	(1,453,284)
Net cash (used for) provided by financing activities			$ (703,877)	$ (881,879)
Greysbridge Holdings Ltd
Variable Interest Entity [Line Items]
Percentage ownership					40%
Kelso And Company | Greysbridge Holdings Ltd
Variable Interest Entity [Line Items]
Percentage ownership					30%
Warburg Pincus LLC | Greysbridge Holdings Ltd
Variable Interest Entity [Line Items]
Percentage ownership					30%
Variable Interest Entity, Primary Beneficiary | Somers Holdings Ltd
Variable Interest Entity [Line Items]
Initial investment contribution amount	$ 100,000
Ownership percentage	11%
Net cash provided by (used for) operating activities		$ 47,000
Net cash provided by (used for) investing activities		96,300
Net cash (used for) provided by financing activities		$ (2,000)

Variable Interest Entities an_4

Variable Interest Entities and Noncontrolling Interests - Redeemable noncontrolling interests (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Redeemable Noncontrolling Interest [Line Items]
Redeemable noncontrolling interests, beginning of period			$ 9,233
Redeemable noncontrolling interests, end of period	$ 8,908		8,908
Somers Holdings Ltd
Redeemable Noncontrolling Interest [Line Items]
Redeemable noncontrolling interests, beginning of period	8,459	$ 57,533	9,233	$ 58,548
Impact of deconsolidation of Somers	0	(48,919)	0	(48,919)
Other	449	1,623	(325)	608
Redeemable noncontrolling interests, end of period	$ 8,908	$ 10,237	$ 8,908	$ 10,237

Variable Interest Entities an_5

Variable Interest Entities and Noncontrolling Interests - Income or loss attributable to third party investors (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Noncontrolling Interest [Abstract]
Amounts attributable to non-redeemable noncontrolling interests	$ 0	$ 0	$ 0	$ (78,314)
Amounts attributable to redeemable noncontrolling interests	(1,157)	(1,473)	(2,390)	(3,889)
Net (income) loss attributable to noncontrolling interests	$ (1,157)	$ (1,473)	$ (2,390)	$ (82,203)

Variable Interest Entities an_6

Variable Interest Entities and Noncontrolling Interests - Other variable interest entity disclosures (Details) - USD ($) $ in Thousands		Sep. 30, 2022	Dec. 31, 2021
Variable Interest Entity [Line Items]
Total VIE Assets		$ 46,337,104	$ 45,100,945
Maximum Exposure to Loss - Off-Balance Sheet		3,686,444	3,248,206
Variable Interest Entity, Not Primary Beneficiary
Variable Interest Entity [Line Items]
Total VIE Assets		3,824,794	4,336,596
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(11,216)	(4,434)
Maximum Exposure to Loss - Off-Balance Sheet		23,435	42,202
Maximum Exposure to Loss		12,219	37,768
Remaining Coverage, Amount		425,530
Variable Interest Entity, Not Primary Beneficiary | 2017-1 Ltd. (Oct-17)
Variable Interest Entity [Line Items]
Total VIE Assets		46,772	108,368
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(23)	(159)
Maximum Exposure to Loss - Off-Balance Sheet		88	424
Maximum Exposure to Loss		65	265
Variable Interest Entity, Not Primary Beneficiary | 2018-1 Ltd. (Apr-18)
Variable Interest Entity [Line Items]
Total VIE Assets		103,131	181,136
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(220)	(528)
Maximum Exposure to Loss - Off-Balance Sheet		644	1,268
Maximum Exposure to Loss		424	740
Variable Interest Entity, Not Primary Beneficiary | 2018-3 Ltd. (Oct-18)
Variable Interest Entity [Line Items]
Total VIE Assets		217,701	302,563
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(862)	(1,018)
Maximum Exposure to Loss - Off-Balance Sheet		2,107	2,496
Maximum Exposure to Loss		1,245	1,478
Variable Interest Entity, Not Primary Beneficiary | 2019-1 Ltd. (Mar-19)
Variable Interest Entity [Line Items]
Total VIE Assets		119,193	181,324
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(496)	(380)
Maximum Exposure to Loss - Off-Balance Sheet		2,704	5,807
Maximum Exposure to Loss		2,208	5,427
Variable Interest Entity, Not Primary Beneficiary | 2019-2 Ltd. (Apr-19)
Variable Interest Entity [Line Items]
Total VIE Assets		347,050	398,316
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(656)	(515)
Maximum Exposure to Loss - Off-Balance Sheet		4,308	3,998
Maximum Exposure to Loss		3,652	3,483
Variable Interest Entity, Not Primary Beneficiary | 2019-3 Ltd. (Jul-19)
Variable Interest Entity [Line Items]
Total VIE Assets		257,663	409,859
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(192)	(584)
Maximum Exposure to Loss - Off-Balance Sheet		1,492	3,190
Maximum Exposure to Loss		1,300	2,606
Variable Interest Entity, Not Primary Beneficiary | 2019-4 Ltd. (Oct-19)
Variable Interest Entity [Line Items]
Total VIE Assets		283,684	411,954
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(532)	(462)
Maximum Exposure to Loss - Off-Balance Sheet		3,663	4,759
Maximum Exposure to Loss		3,131	4,297
Variable Interest Entity, Not Primary Beneficiary | 2020-2 Ltd. (Sep-20)
Variable Interest Entity [Line Items]
Total VIE Assets		122,897	217,766
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(20)	(177)
Maximum Exposure to Loss - Off-Balance Sheet		595	1,984
Maximum Exposure to Loss		575	1,807
Remaining Coverage, Amount	[1]	153
Variable Interest Entity, Not Primary Beneficiary | 2020-3 Ltd. (Nov-20)
Variable Interest Entity [Line Items]
Total VIE Assets		268,385	348,818
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(204)	(128)
Maximum Exposure to Loss - Off-Balance Sheet		2,845	5,793
Maximum Exposure to Loss		2,641	5,665
Remaining Coverage, Amount	[1]	8,569
Variable Interest Entity, Not Primary Beneficiary | 2020-4 Ltd. (Dec-20)
Variable Interest Entity [Line Items]
Total VIE Assets		107,396	176,826
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		10	(50)
Maximum Exposure to Loss - Off-Balance Sheet		707	1,630
Maximum Exposure to Loss		717	1,580
Remaining Coverage, Amount	[1]	4,795
Variable Interest Entity, Not Primary Beneficiary | 2021-1 Ltd. (Mar-21)
Variable Interest Entity [Line Items]
Total VIE Assets		497,069	568,986
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(2,234)	(303)
Maximum Exposure to Loss - Off-Balance Sheet		936	3,283
Maximum Exposure to Loss		(1,298)	2,980
Remaining Coverage, Amount	[1]	43,198
Variable Interest Entity, Not Primary Beneficiary | 2021-2 Ltd. (Jun-21)
Variable Interest Entity [Line Items]
Total VIE Assets		471,039	522,807
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(2,047)	281
Maximum Exposure to Loss - Off-Balance Sheet		984	4,124
Maximum Exposure to Loss		(1,063)	4,405
Remaining Coverage, Amount	[1]	80,268
Variable Interest Entity, Not Primary Beneficiary | 2021-3 Ltd. (Sep-21)
Variable Interest Entity [Line Items]
Total VIE Assets		498,309	507,873
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(2,414)	(411)
Maximum Exposure to Loss - Off-Balance Sheet		991	3,446
Maximum Exposure to Loss		(1,423)	$ 3,035
Remaining Coverage, Amount	[1]	129,127
Variable Interest Entity, Not Primary Beneficiary | 2022-1 Ltd. (Jan-22)
Variable Interest Entity [Line Items]
Total VIE Assets		283,500
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(1,326)
Maximum Exposure to Loss - Off-Balance Sheet		627
Maximum Exposure to Loss		(699)
Remaining Coverage, Amount	[1]	33,260
Variable Interest Entity, Not Primary Beneficiary | 2022-2 Ltd. (Sep-22)
Variable Interest Entity [Line Items]
Total VIE Assets		201,005
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		0
Maximum Exposure to Loss - Off-Balance Sheet		744
Maximum Exposure to Loss		744
Remaining Coverage, Amount	[1]	$ 126,160
[1]Coverage from a separate panel of reinsurers remaining at September 30, 2022.

Other Comprehensive Income (L_3

Other Comprehensive Income (Loss) - Amounts reclassified from accumulated other comprehensive income (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Provision for credit losses	$ 8,652	$ (456)	$ (48,096)	$ (1,208)
Income tax expense	14,900	(4,137)	(19,042)	(94,176)
Net of tax	18,258	421,415	619,635	1,615,787
Reclassification out of accumulated other comprehensive income | Unrealized appreciation on available-for-sale investments
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Net realized gains (losses)	(55,940)	68,373	(186,570)	135,291
Provision for credit losses	8,652	(457)	(48,096)	(1,208)
Income (loss) before income taxes and income (loss) from operating affiliates	(47,288)	67,916	(234,666)	134,083
Income tax expense	703	(5,262)	28,093	(13,579)
Net of tax	$ (46,585)	$ 62,654	$ (206,573)	$ 120,504

Other Comprehensive Income (L_4

Other Comprehensive Income (Loss) - Components of other comprehensive income (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021
Before tax amount:
Unrealized holding gains (losses) arising during period, before tax	$ (671,907)	$ (104,607)	$ (2,132,845)	$ (307,910)
Less reclassification of net realized gains included in net income, before tax	(47,288)	67,916	(234,666)	134,083
Foreign currency translation adjustments, before tax	(70,388)	(32,060)	(141,515)	(54,083)
Other comprehensive income (loss), before tax	(695,007)	(204,583)	(2,039,694)	(496,076)
Tax expense (benefit):
Unrealized holding gains (losses) arising during period, tax	(62,148)	(8,684)	(240,726)	(28,808)
Less reclassification of net realized gains included in net income, tax	(703)	5,262	(28,093)	13,579
Foreign currency translation adjustments, tax	0	(350)	166	6
Other comprehensive income (loss), tax	(61,445)	(14,296)	(212,467)	(42,381)
Net of tax amount:
Unrealized holding gains (losses) arising during period, net of tax	(609,759)	(95,923)	(1,892,119)	(279,102)
Less reclassification of net realized gains included in net income, net of tax	(46,585)	62,654	(206,573)	120,504
Foreign currency translation adjustments, net of tax	(70,388)	(31,710)	(141,681)	(54,089)
Net current period other comprehensive income (loss)	$ (633,562)	$ (190,287)	$ (1,827,227)	$ (453,695)

Income Taxes (Details)

Income Taxes (Details) - USD ($) $ in Thousands	9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Dec. 31, 2021
Income Tax Disclosure [Abstract]
Effective tax rate on income before income taxes (percentage)	3%	5.50%
Tax benefit from change in valuation allowance on certain UK deferred tax assets	$ 36,500	$ 28,700
Decrease in effective tax rate due to change in valuation allowance on certain UK deferred tax assets	5.70%	1.70%
Net deferred tax asset	$ 572,100		$ 194,000
Income taxes paid	$ 201,600	$ 202,400

Transactions With Related Par_2

Transactions With Related Parties (Details) - USD ($) $ in Thousands	3 Months Ended		9 Months Ended
	Sep. 30, 2022	Sep. 30, 2021	Sep. 30, 2022	Sep. 30, 2021	Jan. 01, 2024	Jun. 30, 2022	Dec. 31, 2021	Jul. 01, 2021	Jun. 30, 2021	Jan. 01, 2021	Dec. 31, 2020
Related Party Transaction [Line Items]
Premiums ceded	$ 1,136,909	$ 1,131,486	$ 3,488,632	$ 2,907,002
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	6,356,456	5,358,852	6,356,456	5,358,852		$ 5,938,511	$ 5,880,735		$ 4,314,515		$ 4,500,802
Reinsurance balances payable	1,669,592		1,669,592				1,583,253
Forecast
Related Party Transaction [Line Items]
Put/call option, proportion of initial shares					33.30%
Greysbridge Holdings Ltd
Related Party Transaction [Line Items]
Percentage ownership								40%
Kelso And Company | Greysbridge Holdings Ltd
Related Party Transaction [Line Items]
Percentage ownership								30%
Warburg Pincus LLC | Greysbridge Holdings Ltd
Related Party Transaction [Line Items]
Percentage ownership								30%
Operating affiliates | Premia Holdings Ltd
Related Party Transaction [Line Items]
Legacy business, amount of liabilities transferred										$ 380,000
Operating affiliates | Somers Holdings Ltd
Related Party Transaction [Line Items]
Premiums ceded	236,500	$ 316,200	661,100	$ 316,200
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	1,100,000		1,100,000				902,800
Reinsurance balances payable	408,000		408,000				$ 258,400
Senior notes, face amount	$ 35,000		$ 35,000
Senior notes, stated percentage	6.50%		6.50%