Arch Capital (ACGL) 10-Q 3 Aug 22 2022 Q2 Quarterly report Financial data

Document and Entity Information

Document and Entity Information - shares	6 Months Ended
	Jun. 30, 2022	Jul. 29, 2022
Document and Entity Information [Abstract]
Document Type	10-Q
Document Quarterly Report	true
Document Period End Date	Jun. 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		369,137,188
Document Fiscal Period Focus	Q2
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	Jun. 30, 2022	Dec. 31, 2021
Investments:
Fixed maturities, available for sale, at fair value	$ 19,812,903	$ 19,732,825
Equity securities, at fair value	772,689	1,804,170
Other investments, at fair value	1,634,368	1,973,550
Investments accounted for using the equity method	3,496,341	3,077,611
Total investments	25,716,301	26,588,156
Cash	813,548	858,668
Accrued investment income	116,102	85,453
Investment in operating affiliates	967,603	1,135,655
Premiums receivable (net of allowance for credit losses: $38,170 and $39,958)	3,634,182	2,633,280
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses (net of allowance for credit losses: $14,740 and $13,230)	5,938,511	5,880,735
Contractholder receivables (net of allowance for credit losses: $3,005 and $3,437)	1,758,018	1,828,691
Ceded unearned premiums	2,123,915	1,729,455
Deferred acquisition costs	1,069,845	901,841
Receivable for securities sold	157,329	60,179
Goodwill and intangible assets	868,014	944,983
Other assets	2,555,826	2,453,849
Total assets	45,719,194	45,100,945
Liabilities
Reserve for losses and loss adjustment expenses	18,194,324	17,757,156
Unearned premiums	7,145,297	6,011,942
Reinsurance balances payable	1,634,700	1,583,253
Contractholder payables	1,761,023	1,832,127
Collateral held for insured obligations	251,063	242,352
Senior notes	2,724,896	2,724,394
Payable for securities purchased	292,106	64,850
Other liabilities	1,289,760	1,329,742
Total liabilities	33,293,169	31,545,816
Commitments and Contingencies
Redeemable noncontrolling interests	8,459	9,233
Shareholders' Equity
Non-cumulative preferred shares	830,000	830,000
Common shares ($0.0011 par, shares issued: 586,887,791 and 583,289,850)	652	648
Additional paid-in capital	2,170,661	2,085,075
Retained earnings	15,035,644	14,455,868
Accumulated other comprehensive income (loss), net of deferred income tax	(1,258,265)	(64,600)
Common shares held in treasury, at cost (shares: 217,540,976 and 204,365,956)	(4,361,126)	(3,761,095)
Total shareholders' equity available to Arch	12,417,566	13,545,896
Total liabilities, noncontrolling interests and shareholders' equity	45,719,194	45,100,945
Fixed maturities available for sale, at fair value (amortized cost: $18,816,372 and $17,973,823; net of allowance for credit losses: $58,410 and $2,883 )
Investments:
Fixed maturities, available for sale, at fair value	17,585,029	17,998,109
Short-term investments available for sale, at fair value (amortized cost: $2,226,673 and $1,734,738; net of allowance for credit losses: $0 and $0)
Investments:
Fixed maturities, available for sale, at fair value	$ 2,227,874	$ 1,734,716

Unaudited Consolidated Balanc_2

Unaudited Consolidated Balance Sheets (Parentheticals) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Available for sale securities, amortized cost	$ 21,043,045	$ 19,708,561
Allowance for credit losses on investments	58,410	2,883
Allowance for credit losses on premiums receivable	38,170	39,958
Allowance for credit losses on reinsurance recoverable	14,740	13,230
Allowance for credit losses on contractholder receivable	$ 3,005	$ 3,437
Common shares, par value per share	$ 0.0011	$ 0.0011
Common shares issued (shares)	586,887,791	583,289,850
Common shares held in treasury (shares)	217,540,976	204,365,956
Fixed maturities
Available for sale securities, amortized cost	$ 18,816,372	$ 17,973,823
Allowance for credit losses on investments	58,410	2,883
Short-term investments
Available for sale securities, amortized cost	2,226,673	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		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Revenues
Net premiums earned	$ 2,325,775	$ 2,120,909	$ 4,446,408	$ 4,069,331
Net investment income	106,392	111,613	186,828	210,469
Net realized gains (losses)	(266,579)	202,907	(558,993)	345,368
Other underwriting income	2,970	5,529	8,867	11,639
Equity in net income (loss) of investment funds accounted for using the equity method	58,061	122,186	94,366	193,872
Other income (loss)	(11,777)	6,852	(20,802)	5,111
Total revenues	2,214,842	2,569,996	4,156,674	4,835,790
Expenses
Losses and loss adjustment expenses	1,102,656	1,159,831	2,103,491	2,362,931
Acquisition expenses	413,319	335,143	791,478	639,624
Other operating expenses	277,392	244,943	567,335	505,976
Corporate expenses	27,620	15,951	59,952	41,335
Amortization of intangible assets	27,207	15,286	54,374	29,688
Interest expense	32,795	35,700	65,503	74,046
Net foreign exchange (gains) losses	(87,775)	17,775	(91,620)	(2,288)
Total expenses	1,793,214	1,824,629	3,550,513	3,651,312
Income (loss) before income taxes and income (loss) from operating affiliates	421,628	745,367	606,161	1,184,478
Income tax expense	(22,323)	(51,179)	(33,942)	(90,039)
Income (loss) from operating affiliates	4,640	24,476	29,158	99,933
Net income (loss)	403,945	718,664	601,377	1,194,372
Net (income) loss attributable to noncontrolling interests	399	(43,178)	(1,233)	(80,730)
Net income (loss) available to Arch	404,344	675,486	600,144	1,113,642
Preferred dividends	(10,184)	(11,666)	(20,368)	(22,069)
Net income (loss) available to Arch common shareholders	$ 394,160	$ 663,820	$ 579,776	$ 1,091,573
Net income per common share and common share equivalent
Basic (per share)	$ 1.07	$ 1.67	$ 1.56	$ 2.73
Diluted (per share)	$ 1.04	$ 1.63	$ 1.52	$ 2.68
Weighted average common shares and common share equivalents outstanding
Basic (shares)	369,241,193	397,743,402	371,728,683	399,267,183
Diluted (shares)	377,952,988	406,485,994	380,905,512	407,687,680

Unaudited Consolidated Statem_2

Unaudited Consolidated Statements of Comprehensive Income - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Comprehensive Income
Net income (loss)	$ 403,945	$ 718,664	$ 601,377	$ 1,194,372
Unrealized appreciation (decline) in value of available-for-sale investments:
Unrealized holding gains (losses) arising during period	(598,005)	78,571	(1,282,360)	(183,179)
Reclassification of net realized (gains) losses, included in net income (loss)	57,710	(60,547)	159,988	(57,850)
Foreign currency translation adjustments	(68,525)	6,205	(71,293)	(22,379)
Comprehensive income (loss)	(204,875)	742,893	(592,288)	930,964
Net (income) loss attributable to noncontrolling interests	399	(43,178)	(1,233)	(80,730)
Other comprehensive (income) loss attributable to noncontrolling interests	0	(10)	0	4,560
Comprehensive income (loss) available to Arch	$ (204,476)	$ 699,705	$ (593,521)	$ 854,794

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
Common shares issued, net			4
Amortization of share-based compensation				57,063
Issue costs on preferred shares				(14,179)
Other changes				8,241
Net income (loss)	$ 1,194,372				1,194,372
Net (income) loss attributable to noncontrolling interests	(80,730)				(80,730)
Preferred share dividends	(22,069)				(22,069)
Unrealized holding gains (losses) during period, net of reclassification adjustment							(241,029)
Unrealized holding gains (losses) during period attributable to noncontrolling interests							4,436
Foreign currency translation adjustments	(22,379)							(22,379)
Foreign currency translation adjustments attributable to noncontrolling interests								125
Shares repurchased for treasury									(503,669)
Balance at end of period at Jun. 30, 2021	13,986,072	1,280,000	647	2,028,919	13,454,036	230,048	264,702	(34,654)	(3,007,578)
Non-redeemable noncontrolling interests, end of period at Jun. 30, 2021	918,874
Total shareholders’ equity at Jun. 30, 2021	14,904,946
Balance at beginning of period at Mar. 31, 2021		780,000	645	2,014,741	12,790,216	205,827	246,711	(40,884)	(2,694,957)
Preferred shares issued		500,000
Common shares issued, net			2
Amortization of share-based compensation				16,490
Issue costs on preferred shares				(14,179)
Other changes				11,867
Net income (loss)	718,664				718,664
Net (income) loss attributable to noncontrolling interests	(43,178)				(43,178)
Preferred share dividends	(11,666)				(11,666)
Unrealized holding gains (losses) during period, net of reclassification adjustment							18,024
Unrealized holding gains (losses) during period attributable to noncontrolling interests							(33)
Foreign currency translation adjustments	6,205							6,205
Foreign currency translation adjustments attributable to noncontrolling interests								25
Shares repurchased for treasury									(312,621)
Balance at end of period at Jun. 30, 2021	13,986,072	1,280,000	647	2,028,919	13,454,036	230,048	264,702	(34,654)	(3,007,578)
Non-redeemable noncontrolling interests, end of period at Jun. 30, 2021	918,874
Total shareholders’ equity at Jun. 30, 2021	14,904,946
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
Common shares issued, net			4
Amortization of share-based compensation				66,505
Issue costs on preferred shares				0
Other changes				19,081
Net income (loss)	601,377				601,377
Net (income) loss attributable to noncontrolling interests	(1,233)				(1,233)
Preferred share dividends	(20,368)				(20,368)
Unrealized holding gains (losses) during period, net of reclassification adjustment							(1,122,372)
Unrealized holding gains (losses) during period attributable to noncontrolling interests							0
Foreign currency translation adjustments	(71,293)							(71,293)
Foreign currency translation adjustments attributable to noncontrolling interests								0
Shares repurchased for treasury									(600,031)
Balance at end of period at Jun. 30, 2022	12,417,566	830,000	652	2,170,661	15,035,644	(1,258,265)	(1,108,886)	(149,379)	(4,361,126)
Non-redeemable noncontrolling interests, end of period at Jun. 30, 2022	0
Total shareholders’ equity at Jun. 30, 2022	12,417,566
Balance at beginning of period at Mar. 31, 2022		830,000	651	2,134,241	14,641,484	(649,445)	(568,591)	(80,854)	(4,037,342)
Preferred shares issued		0
Common shares issued, net			1
Amortization of share-based compensation				21,137
Issue costs on preferred shares				0
Other changes				15,283
Net income (loss)	403,945				403,945
Net (income) loss attributable to noncontrolling interests	399				399
Preferred share dividends	(10,184)				(10,184)
Unrealized holding gains (losses) during period, net of reclassification adjustment							(540,295)
Unrealized holding gains (losses) during period attributable to noncontrolling interests							0
Foreign currency translation adjustments	(68,525)							(68,525)
Foreign currency translation adjustments attributable to noncontrolling interests								0
Shares repurchased for treasury									(323,784)
Balance at end of period at Jun. 30, 2022	12,417,566	$ 830,000	$ 652	$ 2,170,661	$ 15,035,644	$ (1,258,265)	$ (1,108,886)	$ (149,379)	$ (4,361,126)
Non-redeemable noncontrolling interests, end of period at Jun. 30, 2022	0
Total shareholders’ equity at Jun. 30, 2022	$ 12,417,566

Unaudited Consolidated Statem_4

Unaudited Consolidated Statements of Cash Flows - USD ($) $ in Thousands	6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021
Operating Activities
Net income (loss)	$ 601,377	$ 1,194,372
Adjustments to reconcile net income (loss) to net cash provided by operating activities:
Net realized (gains) losses	555,273	(379,049)
Equity in net (income) or loss of investment funds accounted for using the equity method and other income or loss	43,815	(181,028)
Amortization of intangible assets	54,374	29,688
Share-based compensation	66,518	57,564
Changes in:
Reserve for losses and loss adjustment expenses, net of unpaid losses and loss adjustment expenses recoverable	634,482	948,505
Unearned premiums, net of ceded unearned premiums	872,371	838,650
Premiums receivable	(1,085,790)	(781,391)
Deferred acquisition costs	(173,911)	(214,893)
Reinsurance balances payable	72,095	331,461
Other items, net	(186,636)	(231,307)
Net cash provided by (used for) operating activities	1,453,968	1,612,572
Investing Activities
Purchases of fixed maturity investments	(9,705,957)	(23,554,384)
Purchases of equity securities	(655,573)	(620,774)
Purchases of other investments	(920,384)	(1,033,134)
Proceeds from sales of fixed maturity investments	8,078,968	23,130,388
Proceeds from sales of equity securities	1,490,212	542,290
Proceeds from sales, redemptions and maturities of other investments	863,333	772,549
Proceeds from redemptions and maturities of fixed maturity investments	444,073	805,836
Net settlements of derivative instruments	(44,838)	17,286
Net (purchases) sales of short-term investments	(439,992)	(378,086)
Change in cash collateral related to securities lending	0	(826)
Purchase of operating affiliate	0	(546,349)
Purchases of fixed assets	(23,830)	(23,585)
Other	98,386	(204,889)
Net cash provided by (used for) investing activities	(815,602)	(1,093,678)
Financing Activities
Proceeds from issuance of preferred shares, net	0	485,821
Purchases of common shares under share repurchase program	(575,676)	(485,315)
Proceeds from common shares issued, net	(4,065)	185
Change in cash collateral related to securities lending	0	826
Third party investment in non-redeemable noncontrolling interests	0	15,971
Dividends paid to redeemable noncontrolling interests	0	(1,907)
Other	(82,007)	27,639
Preferred dividends paid	(20,368)	(20,805)
Net cash provided by (used for) financing activities	(682,116)	22,415
Effects of exchange rate changes on foreign currency cash and restricted cash	(42,790)	(13,390)
Increase (decrease) in cash and restricted cash	(86,540)	527,919
Cash and restricted cash, beginning of year	1,314,771	1,290,544
Cash and restricted cash, end of period	$ 1,228,231	$ 1,818,463

Basis of Presentation and Recen

Basis of Presentation and Recent Accounting Pronouncements	6 Months Ended
	Jun. 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 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	6 Months Ended
	Jun. 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 433.3 million common shares for an aggregate purchase price of $5.86 billion. For the six months ended June 30, 2022, Arch Capital repurchased 12.7 million shares under the share repurchase program with an aggregate purchase price of $575.7 million. At June 30, 2022, $606.6 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, will be 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 June 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.

Earnings Per Common Share

Earnings Per Common Share	6 Months Ended
	Jun. 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 Six Months Ended June 30, June 30, 2022 2021 2022 2021 Numerator: Net income (loss) $ 403,945 $ 718,664 $ 601,377 $ 1,194,372 Amounts attributable to noncontrolling interests 399 (43,178) (1,233) (80,730) Net income (loss) available to Arch 404,344 675,486 600,144 1,113,642 Preferred dividends (10,184) (11,666) (20,368) (22,069) Net income (loss) available to Arch common shareholders $ 394,160 $ 663,820 $ 579,776 $ 1,091,573 Denominator: Weighted average common shares and common share equivalents outstanding — basic 369,241,193 397,743,402 371,728,683 399,267,183 Effect of dilutive common share equivalents: Nonvested restricted shares 2,121,678 1,990,729 2,238,267 1,932,929 Stock options (1) 6,590,117 6,751,863 6,938,562 6,487,568 Weighted average common shares and common share equivalents outstanding — diluted 377,952,988 406,485,994 380,905,512 407,687,680 Earnings per common share: Basic $ 1.07 $ 1.67 $ 1.56 $ 2.73 Diluted $ 1.04 $ 1.63 $ 1.52 $ 2.68 (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 second quarter and 2021 second quarter, the number of stock options excluded were 773,163 and 1,974,849, respectively. For the six months ended June 30, 2022 and 2021, the number of stock options excluded were 778,724 and 2,395,749, respectively.

Segment Information

Segment Information	6 Months Ended
	Jun. 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 June 30, 2022 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 1,705,167 $ 1,793,398 $ 371,896 $ 3,869,727 $ — $ 3,869,727 Premiums ceded (476,910) (630,764) (78,148) (1,185,088) — (1,185,088) Net premiums written 1,228,257 1,162,634 293,748 2,684,639 — 2,684,639 Change in unearned premiums (126,113) (234,635) 1,884 (358,864) — (358,864) Net premiums earned 1,102,144 927,999 295,632 2,325,775 — 2,325,775 Other underwriting income (loss) — 4,526 (1,556) 2,970 — 2,970 Losses and loss adjustment expenses (629,759) (537,578) 64,681 (1,102,656) — (1,102,656) Acquisition expenses (213,688) (189,494) (10,137) (413,319) — (413,319) Other operating expenses (161,088) (66,053) (50,251) (277,392) — (277,392) Underwriting income (loss) $ 97,609 $ 139,400 $ 298,369 535,378 — 535,378 Net investment income 106,392 — 106,392 Net realized gains (losses) (266,579) — (266,579) Equity in net income (loss) of investment funds accounted for using the equity method 58,061 — 58,061 Other income (loss) (11,777) — (11,777) Corporate expenses (2) (27,359) — (27,359) Transaction costs and other (2) (261) — (261) Amortization of intangible assets (27,207) — (27,207) Interest expense (32,795) — (32,795) Net foreign exchange gains (losses) 87,775 — 87,775 Income (loss) before income taxes and income (loss) from operating affiliates 421,628 — 421,628 Income tax (expense) benefit (22,323) — (22,323) Income (loss) from operating affiliates 4,640 — 4,640 Net income (loss) 403,945 — 403,945 Amounts attributable to redeemable noncontrolling interests 399 — 399 Net income (loss) available to Arch 404,344 — 404,344 Preferred dividends (10,184) — (10,184) Net income (loss) available to Arch common shareholders $ 394,160 $ — $ 394,160 Underwriting Ratios Loss ratio 57.1 % 57.9 % (21.9) % 47.4 % — % 47.4 % Acquisition expense ratio 19.4 % 20.4 % 3.4 % 17.8 % — % 17.8 % Other operating expense ratio 14.6 % 7.1 % 17.0 % 11.9 % — % 11.9 % Combined ratio 91.1 % 85.4 % (1.5) % 77.1 % — % 77.1 % Goodwill and intangible assets $ 236,661 $ 166,437 $ 464,916 $ 868,014 $ — $ 868,014 (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 June 30, 2021 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 1,368,867 $ 1,358,020 $ 391,511 $ 3,117,505 $ 240,942 $ 3,286,291 Premiums ceded (405,312) (433,288) (55,665) (893,372) (65,551) (886,767) Net premiums written 963,555 924,732 335,846 2,224,133 175,391 2,399,524 Change in unearned premiums (98,128) (187,708) (1,625) (287,461) 8,846 (278,615) Net premiums earned 865,427 737,024 334,221 1,936,672 184,237 2,120,909 Other underwriting income (loss) — 1,053 4,148 5,201 328 5,529 Losses and loss adjustment expenses (545,880) (463,823) (9,880) (1,019,583) (140,248) (1,159,831) Acquisition expenses (136,852) (133,585) (30,117) (300,554) (34,589) (335,143) Other operating expenses (133,342) (44,695) (48,312) (226,349) (18,594) (244,943) Underwriting income (loss) $ 49,353 $ 95,974 $ 250,060 395,387 (8,866) 386,521 Net investment income 89,430 22,183 111,613 Net realized gains (losses) 163,394 39,513 202,907 Equity in net income (loss) of investment funds accounted for using the equity method 122,186 — 122,186 Other income (loss) 6,852 — 6,852 Corporate expenses (2) (17,175) — (17,175) Transaction costs and other (2) 1,444 (220) 1,224 Amortization of intangible assets (14,388) (898) (15,286) Interest expense (31,439) (4,261) (35,700) Net foreign exchange gains (losses) (17,892) 117 (17,775) Income (loss) before income taxes and income (loss) from operating affiliates 697,799 47,568 745,367 Income tax (expense) benefit (50,953) (226) (51,179) Income (loss) from operating affiliates 24,476 — 24,476 Net income (loss) 671,322 47,342 718,664 Amounts attributable to redeemable noncontrolling interests (580) (981) (1,561) Amounts attributable to nonredeemable noncontrolling interests — (41,617) (41,617) Net income (loss) available to Arch 670,742 4,744 675,486 Preferred dividends (11,666) — (11,666) Net income (loss) available to Arch common shareholders $ 659,076 $ 4,744 $ 663,820 Underwriting Ratios Loss ratio 63.1 % 62.9 % 3.0 % 52.6 % 76.1 % 54.7 % Acquisition expense ratio 15.8 % 18.1 % 9.0 % 15.5 % 18.8 % 15.8 % Other operating expense ratio 15.4 % 6.1 % 14.5 % 11.7 % 10.1 % 11.5 % Combined ratio 94.3 % 87.1 % 26.5 % 79.8 % 105.0 % 82.0 % Goodwill and intangible assets $ 270,262 $ 16,168 $ 370,405 $ 656,835 $ 10,318 $ 667,153 (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.’ Six Months Ended June 30, 2022 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 3,424,772 $ 3,512,340 $ 736,735 $ 7,670,502 $ — $ 7,670,502 Premiums ceded (989,619) (1,210,582) (154,867) (2,351,723) — (2,351,723) Net premiums written 2,435,153 2,301,758 581,868 5,318,779 — 5,318,779 Change in unearned premiums (306,313) (569,359) 3,301 (872,371) — (872,371) Net premiums earned 2,128,840 1,732,399 585,169 4,446,408 — 4,446,408 Other underwriting income (loss) — 5,362 3,505 8,867 — 8,867 Losses and loss adjustment expenses (1,230,498) (992,278) 119,285 (2,103,491) — (2,103,491) Acquisition expenses (409,338) (361,490) (20,650) (791,478) — (791,478) Other operating expenses (327,913) (135,829) (103,593) (567,335) — (567,335) Underwriting income (loss) $ 161,091 $ 248,164 $ 583,716 $ 992,971 $ — $ 992,971 Net investment income 186,828 — 186,828 Net realized gains (losses) (558,993) — (558,993) Equity in net income (loss) of investment funds accounted for using the equity method 94,366 — 94,366 Other income (loss) (20,802) — (20,802) Corporate expenses (2) (59,294) — (59,294) Transaction costs and other (2) (658) — (658) Amortization of intangible assets (54,374) — (54,374) Interest expense (65,503) — (65,503) Net foreign exchange gains (losses) 91,620 — 91,620 Income (loss) before income taxes and income (loss) from operating affiliates 606,161 — 606,161 Income tax (expense) benefit (33,942) — (33,942) Income (loss) from operating affiliates 29,158 — 29,158 Net income (loss) 601,377 — 601,377 Amounts attributable to redeemable noncontrolling interests (1,233) — (1,233) Net income (loss) available to Arch 600,144 — 600,144 Preferred dividends (20,368) — (20,368) Net income (loss) available to Arch common shareholders $ 579,776 $ — $ 579,776 Underwriting Ratios Loss ratio 57.8 % 57.3 % (20.4) % 47.3 % — % 47.3 % Acquisition expense ratio 19.2 % 20.9 % 3.5 % 17.8 % — % 17.8 % Other operating expense ratio 15.4 % 7.8 % 17.7 % 12.8 % — % 12.8 % Combined ratio 92.4 % 86.0 % 0.8 % 77.9 % — % 77.9 % (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. (2) Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’ Six Months Ended June 30, 2021 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 2,784,753 $ 2,829,080 $ 782,757 $ 6,394,798 $ 457,465 $ 6,683,497 Premiums ceded (826,359) (905,236) (111,716) (1,841,519) (102,763) (1,775,516) Net premiums written 1,958,394 1,923,844 671,041 4,553,279 354,702 4,907,981 Change in unearned premiums (273,493) (541,920) (503) (815,916) (22,734) (838,650) Net premiums earned 1,684,901 1,381,924 670,538 3,737,363 331,968 4,069,331 Other underwriting income (loss) — (145) 11,045 10,900 739 11,639 Losses and loss adjustment expenses (1,081,627) (948,693) (73,569) (2,103,889) (259,042) (2,362,931) Acquisition expenses (265,074) (251,610) (60,199) (576,883) (62,741) (639,624) Other operating expenses (270,455) (105,209) (97,443) (473,107) (32,869) (505,976) Underwriting income (loss) $ 67,745 $ 76,267 $ 450,372 $ 594,384 $ (21,945) $ 572,439 Net investment income 168,159 42,310 210,469 Net realized gains (losses) 264,730 80,638 345,368 Equity in net income (loss) of investment funds accounted for using the equity method 193,872 — 193,872 Other income (loss) 5,111 — 5,111 Corporate expenses (2) (40,643) — (40,643) Transaction costs and other (2) 243 (935) (692) Amortization of intangible assets (28,790) (898) (29,688) Interest expense (65,636) (8,410) (74,046) Net foreign exchange gains (losses) 3,613 (1,325) 2,288 Income (loss) before income taxes and income (loss) from operating affiliates 1,095,043 89,435 1,184,478 Income tax (expense) benefit (89,805) (234) (90,039) Income (loss) from operating affiliates 99,933 — 99,933 Net income (loss) 1,105,171 89,201 1,194,372 Amounts attributable to redeemable noncontrolling interests (463) (1,953) (2,416) Amounts attributable to nonredeemable noncontrolling interests — (78,314) (78,314) Net income (loss) available to Arch 1,104,708 8,934 1,113,642 Preferred dividends (22,069) — (22,069) Net income (loss) available to Arch common shareholders $ 1,082,639 $ 8,934 $ 1,091,573 Underwriting Ratios Loss ratio 64.2 % 68.7 % 11.0 % 56.3 % 78.0 % 58.1 % Acquisition expense ratio 15.7 % 18.2 % 9.0 % 15.4 % 18.9 % 15.7 % Other operating expense ratio 16.1 % 7.6 % 14.5 % 12.7 % 9.9 % 12.4 % Combined ratio 96.0 % 94.5 % 34.5 % 84.4 % 106.8 % 86.2 % (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	6 Months Ended
	Jun. 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 Six Months Ended June 30, June 30, 2022 2021 2022 2021 Reserve for losses and loss adjustment expenses at beginning of period $ 18,109,107 $ 16,443,952 $ 17,757,156 $ 16,513,929 Unpaid losses and loss adjustment expenses recoverable 5,709,998 3,916,650 5,599,231 4,314,855 Net reserve for losses and loss adjustment expenses at beginning of period 12,399,109 12,527,302 12,157,925 12,199,074 Net incurred losses and loss adjustment expenses relating to losses occurring in: Current year 1,273,882 1,219,081 2,416,529 2,463,853 Prior years (171,226) (59,250) (313,038) (100,922) Total net incurred losses and loss adjustment expenses 1,102,656 1,159,831 2,103,491 2,362,931 Retroactive reinsurance transactions (1) — — — (183,893) Net foreign exchange (gains) losses and other (248,655) 135,847 (281,295) 88,970 Net paid losses and loss adjustment expenses relating to losses occurring in: Current year (166,466) (164,441) (237,272) (223,425) Prior years (578,668) (607,911) (1,234,873) (1,193,029) Total net paid losses and loss adjustment expenses (745,134) (772,352) (1,472,145) (1,416,454) Net reserve for losses and loss adjustment expenses at end of period 12,507,976 13,050,628 12,507,976 13,050,628 Unpaid losses and loss adjustment expenses recoverable 5,686,348 4,146,020 5,686,348 4,146,020 Reserve for losses and loss adjustment expenses at end of period $ 18,194,324 $ 17,196,648 $ 18,194,324 $ 17,196,648 (1) 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”). Development on Prior Year Loss Reserves 2022 Second Quarter During the 2022 second quarter, the Company recorded net favorable development on prior year loss reserves of $171.2 million, which consisted of $6.7 million from the insurance segment, $46.4 million from the reinsurance segment and $118.1 million from the mortgage segment. The insurance segment’s net favorable development of $6.7 million, or 0.6 loss ratio points, for the 2022 second quarter consisted of $14.3 million of net favorable development in short-tailed lines and $7.5 million of net adverse development in medium-tailed and long-tailed lines. Net favorable development in short-tailed lines reflected $12.2 million of favorable development in lenders products, primarily from the 2021 accident year ( i.e. , the year in which a loss occurred). Net adverse development in medium-tailed lines included $6.3 million of adverse development in professional liability business, primarily from the 2018 and 2019 accident years, partially offset by favorable development in marine business of $2.6 million, primarily from the 2019 and prior accident years. Net adverse development in long-tailed lines reflected $5.7 million related to executive assurance business, primarily from the 2013 and 2020 accident years. The reinsurance segment’s net favorable development of $46.4 million, or 5.0 loss ratio points, for the 2022 second quarter consisted of $54.4 million of net favorable development in short-tailed and medium-tailed lines and $8.0 million of net adverse development in long-tailed lines. Net favorable development in short-tailed lines reflected $31.6 million of favorable development related to property other than property catastrophe business, primarily from 2016 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), $13.1 million of favorable development in other specialty business, primarily from the 2018 and 2021 underwriting year, and $6.3 million of favorable development related to property catastrophe business, primarily from the 2017 to 2021 underwriting years. Net favorable development in medium-tailed lines included $4.2 million in marine and aviation lines, across most underwriting years. Adverse development in long-tailed lines reflected an increase in casualty reserves, across several years, most notably the 2013 and 2021 underwriting years. The mortgage segment’s net favorable development was $118.1 million, or 39.9 loss ratio points, for the 2022 second quarter, primarily related to the U.S. first lien portfolio from the 2020 accident year. The Company’s credit risk transfer, international, second lien and student loan business also contributed to the favorable development. 2021 Second Quarter During the 2021 second quarter, the Company recorded net favorable development on prior year loss reserves of $59.3 million, which consisted of $4.0 million from the insurance segment, $20.5 million from the reinsurance segment and $43.1 million from the mortgage segment, partially offset by $8.3 million unfavorable from the ‘other’ segment. The insurance segment’s net favorable development of $4.0 million, or 0.5 loss ratio points, for the 2021 second quarter consisted of $28.5 million of net favorable development in short-tailed and long-tailed lines and $24.5 million of net adverse development in medium-tailed lines. Net favorable development in short-tailed lines reflected $10.7 million of favorable development in lenders products, primarily from the 2020 accident year, $7.1 million of favorable development from property (excluding marine), primarily from the 2017, 2019 and 2020 accident years and $6.7 million of favorable development in travel and accident, primarily from the 2020 accident year. Net favorable development in long-tailed lines reflected $5.6 million of favorable development related to construction and national accounts, primarily from the 2016 to 2020 accident years. Net adverse development in medium-tailed lines included $20.1 million of adverse development in contract binding business, primarily from the 2014 to 2019 accident years. The reinsurance segment’s net favorable development of $20.5 million, or 2.8 loss ratio points, for the 2021 second quarter consisted of $53.7 million of net favorable development in short-tailed and medium-tailed lines and $33.2 million of net adverse development in long-tailed lines. Net favorable development in short-tailed lines reflected $61.6 million of favorable development related to other specialty, primarily from the 2019 underwriting year, which was partially offset by $17.1 million of net adverse development related to property catastrophe, primarily from the 2020 underwriting year. Net favorable development of $4.0 million in medium-tailed lines reflected favorable development in marine and aviation, across most underwriting years. Net adverse development in long-tailed lines reflected $34.2 million of adverse development in casualty, primarily from the 2018 underwriting year. The mortgage segment’s net favorable development was $43.1 million, or 12.9 loss ratio points, for the 2021 second quarter, with the largest contributor being reserve releases associated with the various vintage credit risk transfer contracts that were called by the GSEs. The net favorable development also included reserve releases in our international portfolio and subrogation recoveries on second lien and student loan business. Six Months Ended June 30, 2022 During the six months ended June 30, 2022, the Company recorded net favorable development on prior year loss reserves of $313.0 million, which consisted of $14.0 million from the insurance segment, $78.9 million from the reinsurance segment and $220.2 million from the mortgage segment. The insurance segment’s net favorable development of $14.0 million, or 0.7 loss ratio points, for the 2022 period consisted of $33.2 million of net favorable development in short-tailed and $19.2 million of net adverse development in medium and long-tailed lines. Net favorable development in short-tailed lines reflected $30.8 million of favorable development in lenders products, primarily from the 2021 accident year. Net adverse development in medium-tailed lines included $13.6 million of adverse development in professional liability business, primarily from the 2018 and 2019 accident years, and $6.1 million of adverse development in contract binding business, across most accident years, partially offset by $5.5 million of favorable development in marine business, across most accident years, and $5.2 million of favorable development in program business, primarily from the 2020 accident year. Net adverse development in long-tailed lines primarily reflected $7.6 million of adverse development related to construction and national accounts, primarily from the 2020 and 2021 accident year. The reinsurance segment’s net favorable development of $78.9 million, or 4.6 loss ratio points, for the 2022 period consisted of $89.7 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $10.9 million of net adverse development from long-tailed lines. Net favorable development of $74.9 million in short-tailed lines reflected $47.4 million of favorable development from property other than property catastrophe business, primarily from the 2015 to 2021 underwriting years,$18.0 million of favorable development from other specialty business, primarily from the 2016 and 2021 underwriting years, and $9.7 million from property catastrophe, primarily from the 2018 and 2019 underwriting years. Net favorable development in medium-tailed lines included $14.9 million in marine and aviation lines, across most underwriting years. Adverse development in long-tailed lines reflected an increase in casualty reserves, primarily from the 2021 underwriting year. The mortgage segment’s net favorable development was $220.2 million, or 37.6 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 accident year. The Company’s credit risk transfer, international, second lien and student loan business also contributed to the favorable development. Six Months Ended June 30, 2021 During the six months ended June 30, 2021, the Company recorded net favorable development on prior year loss reserves of $100.9 million, which consisted of $8.1 million from the insurance segment, $47.3 million from the reinsurance segment, $54.0 million from the mortgage segment, partially offset by $8.4 million of adverse development from the ‘other’ segment. The insurance segment’s net favorable development of $8.1 million, or 0.5 loss ratio points, for the 2021 period consisted of $53.5 million of net favorable development in short-tailed and long-tailed lines, partially offset by $45.4 million of net adverse development in medium-tailed lines. Net favorable development of $49.4 million in short-tailed lines reflected $21.6 million of favorable development from property (excluding marine), primarily from the 2018 to 2020 accident years, $18.6 million of favorable development in lenders products, primarily from the 2020 accident year and $9.3 million of favorable development in travel and accident, primarily from the 2020 accident year. Net favorable development of in long-tailed lines included favorable development primarily related to construction and national accounts, primarily in the 2016 to 2019 accident years. Net adverse development in medium-tailed lines reflected $20.1 million of adverse development in contract binding business, primarily in the 2014 to 2019 accident years, $12.6 million of adverse development on programs business, primarily from the 2016 to 2020 accident years, and $11.2 million of adverse development in professional liability business, primarily from the 2019 and 2020 accident years. The reinsurance segment’s net favorable development of $47.3 million, or 3.4 loss ratio points, for the 2021 period consisted of $72.1 million of net favorable development from short-tailed and medium-tailed lines, partially offset by $24.8 million of net adverse development from long-tailed lines. Net favorable development of $67.2 million in short-tailed lines reflected $78.2 million of favorable development from other specialty lines, primarily from the 2019 underwriting year and $28.8 million of favorable development from property other than property catastrophe business, partially offset by adverse development of $39.6 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.

Allowance for Expected Credit L

Allowance for Expected Credit Losses	6 Months Ended
	Jun. 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 June 30, 2022 Balance at beginning of period $ 3,223,504 $ 39,073 Change for provision of expected credit losses (1) (903) Balance at end of period $ 3,634,182 $ 38,170 Three Months Ended June 30, 2021 Balance at beginning of period $ 2,618,175 $ 36,111 Change for provision of expected credit losses (1) (132) Balance at end of period $ 2,866,578 $ 35,979 Six Months Ended June 30, 2022 Balance at beginning of period $ 2,633,280 $ 39,958 Change for provision of expected credit losses (1) (1,788) Balance at end of period $ 3,634,182 $ 38,170 Six Months Ended June 30, 2021 Balance at beginning of period $ 2,064,586 $ 37,781 Change for provision of expected credit losses (1) (1,802) Balance at end of period $ 2,866,578 $ 35,979 (1) Amounts deemed uncollectible are written-off in operating expenses. For the 2022 second quarter and 2021 second quarter, amounts written off were $3.3 million and $1.1 million, respectively. For the six months ended June 30, 2022 and 2021 period, amounts written off were $4.8 million and $1.2 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 June 30, 2022 Balance at beginning of period $ 5,941,000 $ 18,483 Change for provision of expected credit losses (3,743) Balance at end of period $ 5,938,511 $ 14,740 Three Months Ended June 30, 2021 Balance at beginning of period $ 4,041,076 $ 10,872 Change for provision of expected credit losses 157 Balance at end of period $ 4,314,515 $ 11,029 Six Months Ended June 30, 2022 Balance at beginning of period $ 5,880,735 $ 13,230 Change for provision of expected credit losses 1,510 Balance at end of period $ 5,938,511 $ 14,740 Six Months Ended June 30, 2021 Balance at beginning of period $ 4,500,802 $ 11,636 Change for provision of expected credit losses (607) Balance at end of period $ 4,314,515 $ 11,029 The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums): June 30, December 31 2022 2021 Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses $ 5,938,511 $ 5,880,735 % due from carriers with A.M. Best rating of “A-” or better 69.3 % 69.7 % % due from all other rated carriers 0.1 % 0.1 % % due from all other carriers with no A.M. Best rating (1) 30.6 % 30.2 % Largest balance due from any one carrier as % of total shareholders’ equity 7.8 % 6.7 % (1) At June 30, 2022 and December 31, 2021 over 93% 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 June 30, 2022 Balance at beginning of period $ 1,810,199 $ 3,731 Change for provision of expected credit losses (726) Balance at end of period $ 1,758,018 $ 3,005 Three Months Ended June 30, 2021 Balance at beginning of period $ 1,919,655 $ 5,853 Change for provision of expected credit losses (1,382) Balance at end of period 1,882,948 $ 4,471 Six Months Ended June 30, 2022 Balance at beginning of period $ 1,828,691 $ 3,437 Change for provision of expected credit losses (432) Balance at end of period $ 1,758,018 $ 3,005 Six Months Ended June 30, 2021 Balance at beginning of period $ 1,986,924 $ 8,638 Change for provision of expected credit losses (4,167) Balance at end of period 1,882,948 $ 4,471

Investment Information

Investment Information	6 Months Ended
	Jun. 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 June 30, 2022 Fixed maturities: Corporate bonds $ 7,288,555 $ 32,021 $ (655,664) $ (38,494) $ 7,950,692 Mortgage backed securities 698,168 4,427 (55,898) — 749,639 Municipal bonds 417,380 4,129 (18,936) (298) 432,485 Commercial mortgage backed securities 1,023,088 1,533 (42,056) (3,594) 1,067,205 U.S. government and government agencies 4,368,150 25,112 (240,786) — 4,583,824 Non-U.S. government securities 2,181,943 16,175 (163,724) (1,335) 2,330,827 Asset backed securities 1,607,745 1,001 (80,267) (14,689) 1,701,700 Total 17,585,029 84,398 (1,257,331) (58,410) 18,816,372 Short-term investments 2,227,874 2,458 (1,257) — 2,226,673 Total $ 19,812,903 $ 86,856 $ (1,258,588) $ (58,410) $ 21,043,045 December 31, 2021 Fixed maturities: Corporate bonds $ 6,553,333 $ 104,170 $ (69,194) $ (2,037) $ 6,520,394 Mortgage backed securities 408,477 2,825 (5,410) (48) 411,110 Municipal bonds 404,666 18,724 (1,409) (2) 387,353 Commercial mortgage backed securities 1,046,484 1,740 (3,117) (6) 1,047,867 U.S. government and government agencies 4,772,764 10,076 (45,967) — 4,808,655 Non-U.S. government securities 2,120,294 54,048 (34,749) (82) 2,101,077 Asset backed securities 2,692,091 6,540 (11,108) (708) 2,697,367 Total 17,998,109 198,123 (170,954) (2,883) 17,973,823 Short-term investments 1,734,716 568 (590) — 1,734,738 Total $ 19,732,825 $ 198,691 $ (171,544) $ (2,883) $ 19,708,561 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 June 30, 2022 Fixed maturities: Corporate bonds $ 6,583,215 $ (580,235) $ 489,098 $ (75,429) $ 7,072,313 $ (655,664) Mortgage backed securities 595,485 (46,415) 61,751 (9,483) 657,236 (55,898) Municipal bonds 271,481 (17,908) 8,876 (1,028) 280,357 (18,936) Commercial mortgage backed securities 973,212 (42,056) — — 973,212 (42,056) U.S. government and government agencies 4,029,550 (235,510) 69,596 (5,276) 4,099,146 (240,786) Non-U.S. government securities 1,929,278 (148,781) 103,969 (14,943) 2,033,247 (163,724) Asset backed securities 1,292,087 (73,575) 136,119 (6,692) 1,428,206 (80,267) Total 15,674,308 (1,144,480) 869,409 (112,851) 16,543,717 (1,257,331) Short-term investments 505,798 (1,257) — — 505,798 (1,257) Total $ 16,180,106 $ (1,145,737) $ 869,409 $ (112,851) $ 17,049,515 $ (1,258,588) December 31, 2021 Fixed maturities: Corporate bonds $ 3,639,582 $ (63,938) $ 98,867 $ (5,256) $ 3,738,449 $ (69,194) Mortgage backed securities 222,176 (3,545) 46,809 (1,865) 268,985 (5,410) Municipal bonds 26,665 (385) 16,361 (1,024) 43,026 (1,409) Commercial mortgage backed securities 675,603 (2,805) 5,908 (312) 681,511 (3,117) U.S. government and government agencies 4,211,621 (44,180) 33,373 (1,787) 4,244,994 (45,967) Non-U.S. government securities 1,511,301 (31,983) 62,957 (2,766) 1,574,258 (34,749) Asset backed securities 1,667,002 (9,853) 33,082 (1,255) 1,700,084 (11,108) Total 11,953,950 (156,689) 297,357 (14,265) 12,251,307 (170,954) Short-term investments 284,733 (590) — — 284,733 (590) Total $ 12,238,683 $ (157,279) $ 297,357 $ (14,265) $ 12,536,040 $ (171,544) At June 30, 2022, on a lot level basis, approximately 8,360 security lots out of a total of approximately 10,440 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 $5.7 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. June 30, 2022 December 31, 2021 Maturity Estimated Amortized Estimated Amortized Due in one year or less $ 412,194 $ 414,752 $ 300,889 $ 299,772 Due after one year through five years 9,423,547 9,927,876 8,355,255 8,339,387 Due after five years through 10 years 4,070,099 4,512,685 4,689,155 4,684,393 Due after 10 years 350,188 442,515 505,758 493,927 14,256,028 15,297,828 13,851,057 13,817,479 Mortgage backed securities 698,168 749,639 408,477 411,110 Commercial mortgage backed securities 1,023,088 1,067,205 1,046,484 1,047,867 Asset backed securities 1,607,745 1,701,700 2,692,091 2,697,367 Total $ 17,585,029 $ 18,816,372 $ 17,998,109 $ 17,973,823 Equity Securities, at Fair Value At June 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: June 30, December 31, Fixed maturities $ 525,451 $ 416,698 Other investments 1,054,771 1,432,553 Short-term investments 39,657 97,806 Equity securities 14,489 26,493 Total $ 1,634,368 $ 1,973,550 The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy: June 30, December 31, Lending $ 427,812 $ 536,345 Investment grade fixed income 221,484 147,810 Term loan investments 152,277 484,950 Private equity 124,282 91,126 Energy 74,234 81,692 Credit related funds 54,682 70,278 Infrastructure — 20,352 Total $ 1,054,771 $ 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: June 30, December 31, Credit related funds $ 1,119,711 $ 1,022,334 Private equity 646,904 436,042 Real estate 455,044 396,395 Lending 447,028 376,649 Equities 350,587 395,090 Infrastructure 231,816 230,070 Energy 115,514 119,141 Fixed income 129,737 101,890 Total $ 3,496,341 $ 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: June 30, December 31, Investments accounted for using the equity method (1) 3,496,341 3,077,611 Investments accounted for using the fair value option (2) 128,826 170,595 Total $ 3,625,167 $ 3,248,206 (1) Aggregate unfunded commitments were $3.0 billion at June 30, 2022, compared to $2.6 billion at December 31, 2021. (2) Aggregate unfunded commitments were $21.7 million at June 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: June 30, 2022 2021 Three Months Ended Fixed maturities $ 105,342 $ 88,625 Term loans 401 16,879 Equity securities 6,121 8,584 Short-term investments 4,120 1,138 Other (1) 7,583 19,950 Gross investment income 123,567 135,176 Investment expenses (17,175) (23,563) Net investment income $ 106,392 $ 111,613 Six Months Ended Fixed maturities $ 187,395 $ 179,251 Term loans 2,018 31,607 Equity securities 12,359 14,234 Short-term investments 6,695 1,745 Other (1) 18,042 34,305 Gross investment income 226,509 261,142 Investment expenses (39,681) (50,673) Net investment income $ 186,828 $ 210,469 (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: June 30, 2022 2021 Three Months Ended Available for sale securities: Gross gains on investment sales $ 15,186 $ 115,541 Gross losses on investment sales (57,176) (50,627) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities (39,255) 10,912 Other investments (21,710) 60,884 Equity securities (2,124) 5,492 Short-term investments (2,008) (104) Equity securities, at fair value: Net realized gains (losses) on sales during the period 16,879 33,570 Net unrealized gains (losses) on equity securities still held at reporting date (106,375) 65,847 Allowance for credit losses: Investments related (25,026) 896 Underwriting related 842 1,381 Derivative instruments (1) (45,684) (51,109) Other (128) 10,224 Net realized gains (losses) $ (266,579) $ 202,907 Six Months Ended Available for sale securities: Gross gains on investment sales $ 34,893 $ 180,543 Gross losses on investment sales (165,523) (113,625) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities (69,844) 27,465 Other investments (17,321) 107,739 Equity securities (5,437) 7,557 Short-term investments (2,157) 632 Equity securities, at fair value: Net realized gains (losses) on sales during the period 82,090 71,419 Net unrealized gains (losses) on equity securities still held at reporting date (282,570) 85,555 Allowance for credit losses: Investments related (56,748) (752) Underwriting related (3,444) 6,649 Derivative instruments (1) (69,395) (14,993) Other (3,537) (12,821) Net realized gains (losses) $ (558,993) $ 345,368 (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 $58.1 million of equity in net income related to investment funds accounted for using the equity method in the 2022 second quarter, compared to income of $122.2 million for the 2021 second quarter and an income of $94.4 million for the six months ended June 30, 2022, compared to income of $193.9 million for six months ended June 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 June 30, 2022, the Company owned approximately 29.86% of the issued shares of Coface, or 30.09% excluding treasury shares, with a carrying value of $536.0 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 June 30, 2022 the Company’s carrying value in Greysbridge was $309.6 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 second quarter was income of $4.6 million, compared to an income of $24.5 million, for the 2021 second quarter and income of $29.2 million for the six months ended June 30, 2022, compared to income of $99.9 million for six months ended June 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 June 30, 2022 Balance at beginning of period $ 6,998 $ 106 $ 27,041 $ 34,145 Additions for current-period provision for expected credit losses 4,788 252 13,466 18,506 Additions (reductions) for previously recognized expected credit losses 6,705 (60) (205) 6,440 Reductions due to disposals (208) — (473) (681) Balance at end of period $ 18,283 $ 298 $ 39,829 $ 58,410 Three Months Ended June 30, 2021 Balance at beginning of period $ 1,207 $ 2 $ 2,621 $ 3,830 Additions for current-period provision for expected credit losses 52 — 7 59 Additions (reductions) for previously recognized expected credit losses (383) 4 (412) (791) Reductions due to disposals (117) — (857) (974) Balance at end of period $ 759 $ 6 $ 1,359 $ 2,124 Six Months Ended June 30, 2022 Balance at beginning of period $ 802 $ 2 $ 2,079 $ 2,883 Additions for current-period provision for expected credit losses 10,778 347 38,616 49,741 Additions (reductions) for previously recognized expected credit losses 7,192 (51) (220) 6,921 Reductions due to disposals (489) — (646) (1,135) Balance at end of period $ 18,283 $ 298 $ 39,829 $ 58,410 Six Months Ended June 30, 2021 Balance at beginning of period $ 1,490 $ 11 $ 896 $ 2,397 Additions for current-period provision for expected credit losses 234 — 2,428 2,662 Additions (reductions) for previously recognized expected credit losses (765) (5) (952) (1,722) Reductions due to disposals (200) — (1,013) (1,213) Balance at end of period $ 759 $ 6 $ 1,359 $ 2,124 (1) Includes asset backed securities, 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: June 30, December 31, Assets used for collateral or guarantees: Affiliated transactions $ 4,193,561 $ 4,223,955 Third party agreements 2,953,800 2,721,160 Deposits with U.S. regulatory authorities 781,024 798,100 Deposits with non-U.S. regulatory authorities 485,341 506,517 Total restricted assets $ 8,413,726 $ 8,249,732 Reconciliation of Cash and Restricted Cash The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets: June 30, December 31, Cash $ 813,548 $ 858,668 Restricted cash (included in ‘other assets’) $ 414,683 $ 456,103 Cash and restricted cash $ 1,228,231 $ 1,314,771

Fair Value

Fair Value	6 Months Ended
	Jun. 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 June 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 $22.4 billion of financial assets and liabilities measured at fair value at June 30, 2022, approximately $10.9 million, or 0.0%, 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. 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. Municipal bonds – valuations provided by independent pricing services, with all prices provided through index providers and pricing vendors. The fair values of these securities are generally determined using spreads obtained from broker-dealers who trade in the relevant security market, trade prices and the new issue market. As the significant inputs used in the pricing process for municipal bonds are observable market inputs, the fair value of these securities are classified within Level 2. Commercial mortgage-backed securities – valuations provided by independent pricing services, substantially all through index providers and pricing vendors with a small amount through broker-dealers. The fair values of these securities are generally determined through the use of pricing models which use spreads to determine the appropriate average life of the securities. These spreads are generally obtained from the new issue market, secondary trading and from broker-dealers who trade in the relevant security market. 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 June 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 $ 7,288,555 $ — $ 7,284,985 $ 3,570 Mortgage backed securities 698,168 — 698,168 — Municipal bonds 417,380 — 417,380 — Commercial mortgage backed securities 1,023,088 — 1,023,088 — U.S. government and government agencies 4,368,150 4,341,399 26,751 — Non-U.S. government securities 2,181,943 — 2,181,943 — Asset backed securities 1,607,745 — 1,604,878 2,867 Total 17,585,029 4,341,399 13,237,193 6,437 Short-term investments 2,227,874 2,049,235 178,639 — Equity securities, at fair value 772,689 736,343 33,440 2,906 Derivative instruments (2) 122,033 — 122,033 — Residential mortgage loans 3,929 — 3,929 — Fair value option: Corporate bonds 522,707 — 522,707 — Non-U.S. government bonds 611 — 611 — Asset backed securities 2,133 — 2,133 — Short-term investments 39,657 886 38,771 — Equity securities 14,489 10,097 — 4,392 Other investments 178,461 — 145,130 33,331 Other investments measured at net asset value (1) 876,310 Total 1,634,368 10,983 709,352 37,723 Total assets measured at fair value $ 22,345,922 $ 7,137,960 $ 14,284,586 $ 47,066 Liabilities measured at fair value: Other liabilities $ (16,205) $ — $ — $ (16,205) Derivative instruments (2) (75,147) — (75,147) — Total liabilities measured at fair value $ (91,352) $ — $ (75,147) $ (16,205) (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 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 June 30, 2022 Balance at beginning of period $ 3,152 $ 3,570 $ — $ 22,602 $ 4,511 $ 2,768 $ (17,591) Total gains or (losses) (realized/unrealized) Included in earnings (2) (1) — — 27 (119) (89) (97) Included in other comprehensive income (85) — — — — — 1,483 Purchases, issuances, sales and settlements Purchases — — — 10,702 — 227 — Issuances — — — — — — — Sales — — — — — — — Settlements (199) — — — — — — Transfers in and/or out of Level 3 — — — — — — — Balance at end of period $ 2,867 $ 3,570 $ — $ 33,331 $ 4,392 $ 2,906 $ (16,205) Three Months Ended June 30, 2021 Balance at beginning of period $ 3,472 $ 13 $ 989 $ 67,930 $ 71,176 $ 43,112 $ (465) Total gains or (losses) (realized/unrealized) Included in earnings (2) 12 — 9 633 2,502 922 (1) Included in other comprehensive income (57) — — — — — — Purchases, issuances, sales and settlements Purchases — — — 5,638 — 5,102 — Issuances — — — — — — — Sales — — — (301) — — — Settlements (3) — — — — — — Transfers in and/or out of Level 3 — — — — — — — Balance at end of period $ 3,424 $ 13 $ 998 $ 73,900 $ 73,678 $ 49,136 $ (466) Six Months Ended June 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) 9 — — 34 (356) (236) (195) Included in other comprehensive income (145) — — — — — 950 Purchases, issuances, sales and settlements Purchases — — — 10,770 — 227 — Issuances — — — — — — — Sales (3) — — — (2,471) — (3) — Settlements (344) — — (2,983) — — — Transfers in and/or out of Level 3 — 3,557 — — — — — Balance at end of period $ 2,867 $ 3,570 $ — $ 33,331 $ 4,392 $ 2,906 $ (16,205) Six Months Ended June 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) (56) — 13 881 4,690 1,826 (5) Included in other comprehensive income 57 — — — — — — Purchases, issuances, sales and settlements Purchases — — — 13,003 — 5,295 — Issuances — — — — — — — Sales — — — (7,087) — — — Settlements (3) — — — — — — Transfers in and/or out of Level 3 — — — — — — — Balance at end of period $ 3,424 $ 13 $ 998 $ 73,900 $ 73,678 $ 49,136 $ (466) (1) Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities. (2) Gains or losses were included in net realized gains (losses). Financial Instruments Disclosed, But Not Carried, At Fair Value The Company uses various financial instruments in the normal course of its business. The carrying values of cash, accrued investment income, receivable for securities sold, certain other assets, payable for securities purchased and certain other liabilities approximated their fair values at June 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	6 Months Ended
	Jun. 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 June 30, 2022 Futures contracts $ 49,695 $ (22,561) $ 2,794,246 Foreign currency forward contracts 9,556 (18,884) 908,192 TBAs — — — Other 62,782 (33,702) 3,849,244 Total $ 122,033 $ (75,147) 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’ and the fair value of liability derivatives are included in ‘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 June 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 June 30, 2022, asset derivatives and liability derivatives of $116.9 million and $75.1 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 June 30, hedging instruments: 2022 2021 Three Months Ended Net realized gains (losses): Futures contracts $ (39,205) $ (54,759) Foreign currency forward contracts (25,638) 1,295 TBAs — — Other (1) 19,159 2,355 Total $ (45,684) $ (51,109) Six Months Ended Net realized gains (losses): Futures contracts $ (85,979) $ (7,321) Foreign currency forward contracts (27,676) (20,776) TBAs (51) — Other (1) 44,311 13,104 Total $ (69,395) $ (14,993) (1) Includes realized gains and losses on swaps, options and other derivatives contracts.

Commitments and Contingencies

Commitments and Contingencies	6 Months Ended
	Jun. 30, 2022
Commitments and Contingencies Disclosure [Abstract]
Commitments and Contingencies	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 $3.5 billion at June 30, 2022, compared to $3.0 billion at December 31, 2021. Interest Paid

Variable Interest Entities and

Variable Interest Entities and Noncontrolling Interests	6 Months Ended
	Jun. 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. 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 for the six months ended June 30, 2021. Non-redeemable noncontrolling interests Through June 30, 2021, the Company accounted for the portion of Somers’s common equity attributable to third party investors in the shareholders’ equity section of its consolidated balance sheets. The portion of Somers’s income or loss attributable to third party investors was recorded in the consolidated statements of income in ‘net (income) loss attributable to noncontrolling interests.’ The following table sets forth activity in the non-redeemable noncontrolling interests: June 30, 2021 Three Months Ended Balance, beginning of period $ 876,864 Additional paid in capital attributable to noncontrolling interests 383 Amounts attributable to noncontrolling interests 41,617 Other comprehensive income (loss) attributable to noncontrolling interests 10 Balance, end of period $ 918,874 Six Months Ended Balance, beginning of year $ 823,007 Additional paid in capital attributable to noncontrolling interests 22,113 Amounts attributable to noncontrolling interests 78,314 Other comprehensive income (loss) attributable to noncontrolling interests (4,560) Balance, end of period $ 918,874 Redeemable noncontrolling interests Through June 30, 2021, the Company accounted for redeemable noncontrolling interests in the mezzanine section of its consolidated balance sheets in accordance with applicable accounting guidance. Such redeemable noncontrolling interests primarily related to the Somers Preference Shares issued in late March 2014 with a par value of $0.01 per share and a liquidation preference of $25.00 per share. The Somers Preference Shares were issued at a discounted amount of $24.50 per share. Through June 30, 2021 preferred dividends, including the accretion of the discount and issuance costs, were included in ‘net (income) loss attributable to noncontrolling interests’ in the Company’s consolidated statements of income. The following table sets forth activity in the redeemable non-controlling interests: June 30, 2022 2021 Three Months Ended Balance, beginning of period $ 9,763 $ 57,670 Accretion of preference share issuance costs — 23 Other (1,304) (160) Balance, end of period $ 8,459 $ 57,533 Six Months Ended Balance, beginning of year $ 9,233 $ 58,548 Accretion of preference share issuance costs — 46 Other (774) (1,061) Balance, end of period $ 8,459 $ 57,533 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: June 30, 2022 2021 Three Months Ended Amounts attributable to non-redeemable noncontrolling interests $ — $ (41,617) Amounts attributable to redeemable noncontrolling interests 399 (1,561) Net (income) loss attributable to noncontrolling interests $ 399 $ (43,178) Six Months Ended Amounts attributable to non-redeemable noncontrolling interests $ — $ (78,314) Amounts attributable to redeemable noncontrolling interests (1,233) (2,416) Net (income) loss attributable to noncontrolling interests $ (1,233) $ (80,730) 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. June 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) $ 61,328 $ (68) $ 274 $ 206 $ — $ 108,368 $ (159) $ 424 $ 265 2018-1 Ltd. (Apr-18) 122,190 (342) 965 623 — 181,136 (528) 1,268 740 2018-3 Ltd. (Oct-18) 244,257 (566) 1,522 956 — 302,563 (1,018) 2,496 1,478 2019-1 Ltd. (Mar-19) 134,972 (127) 988 861 — 181,324 (380) 5,807 5,427 2019-2 Ltd. (Apr-19) 383,737 (426) 5,323 4,897 — 398,316 (515) 3,998 3,483 2019-3 Ltd. (Jul-19) 296,466 (282) 2,154 1,872 — 409,859 (584) 3,190 2,606 2019-4 Ltd. (Oct-19) 312,668 (306) 4,702 4,396 — 411,954 (462) 4,759 4,297 2020-2 Ltd. (Sep-20) 151,543 (58) 1,331 1,273 442 217,766 (177) 1,984 1,807 2020-3 Ltd. (Nov-20) 303,011 (26) 4,388 4,362 10,779 348,818 (128) 5,793 5,665 2020-4 Ltd. (Dec-20) 124,672 23 1,267 1,290 5,900 176,826 (50) 1,630 1,580 2021-1 Ltd. (Mar-21) 519,641 (1,006) 2,771 1,765 48,841 568,986 (303) 3,283 2,980 2021-2 Ltd. (Jun-21) 492,837 (577) 3,505 2,928 85,717 522,807 281 4,124 4,405 2021-3 Ltd. (Sep-21) 507,873 (1,082) 2,878 1,796 131,518 507,873 (411) 3,446 3,035 2022-1 Ltd. (Jan-22) 283,500 (282) 2,020 1,738 33,260 Total $ 3,938,695 $ (5,125) $ 34,088 $ 28,963 $ 316,457 $ 4,336,596 $ (4,434) $ 42,202 $ 37,768 (1) Coverage from a separate panel of reinsurers remaining at June 30, 2022.

Other Comprehensive Income (Los

Other Comprehensive Income (Loss)	6 Months Ended
	Jun. 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 Six Months Ended Details About Line Item That Includes June 30, June 30, AOCI Components Reclassification 2022 2021 2022 2021 Unrealized appreciation (decline) on available-for-sale investments Net realized gains (losses) $ (41,990) $ 64,914 $ (130,630) $ 66,918 Provision for credit losses (25,026) 896 (56,748) (751) Total before tax (67,016) 65,810 (187,378) 66,167 Income tax (expense) benefit 9,306 (5,263) 27,390 (8,317) Net of tax $ (57,710) $ 60,547 $ (159,988) $ 57,850 Before Tax Amount Tax Expense (Benefit) Net of Tax Amount Three Months Ended June 30, 2022 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (676,048) $ (78,043) $ (598,005) Less reclassification of net realized gains (losses) included in net income (67,016) (9,306) (57,710) Foreign currency translation adjustments (68,562) (37) (68,525) Other comprehensive income (loss) $ (677,594) $ (68,774) $ (608,820) Three Months Ended June 30, 2021 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ 91,057 $ 12,486 $ 78,571 Less reclassification of net realized gains (losses) included in net income 65,810 5,263 60,547 Foreign currency translation adjustments 6,392 187 6,205 Other comprehensive income (loss) $ 31,639 $ 7,410 $ 24,229 Six Months Ended June 30, 2022 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (1,460,938) $ (178,578) $ (1,282,360) Less reclassification of net realized gains (losses) included in net income (187,378) (27,390) (159,988) Foreign currency translation adjustments (71,127) 166 (71,293) Other comprehensive income (loss) $ (1,344,687) $ (151,022) $ (1,193,665) Six Months Ended June 30, 2021 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (203,303) $ (20,124) $ (183,179) Less reclassification of net realized gains (losses) included in net income 66,167 8,317 57,850 Foreign currency translation adjustments (22,023) 356 (22,379) Other comprehensive income (loss) $ (291,493) $ (28,085) $ (263,408)

Income Taxes

Income Taxes	6 Months Ended
	Jun. 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 5.3% for the six months ended June 30, 2022, compared to 7.0% for the six months ended June 30, 2021. 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 $411.1 million at June 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 $128.6 million and $141.1 million of income taxes for the six months ended June 30, 2022 and 2021, respectively.

Legal Proceedings

Legal Proceedings	6 Months Ended
	Jun. 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 June 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	6 Months Ended
	Jun. 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 June 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 six months ended June 30, 2022, the Company ceded premiums written related to such transactions of $424.6 million (which includes reinsurance transactions in force as well as those entered into in conjunction with the Merger Agreement). In addition, Somers paid certain acquisition costs and administrative fees to the Company. At June 30, 2022, reinsurance recoverable on unpaid and paid losses from Somers was $964.7 million, with a reinsurance balance payable to Somers of $358.4 million. See note 11, “Variable Interest Entities and Noncontrolling Interests,” 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. As of June 30, 2022, the Company owns $35.0 million in aggregate principal amount of Somers Group Holdings Ltd’s 6.5% senior notes, due July 2, 2029 and approximately 6.6% of Somers’s preference shares.

Basis of Presentation and Rec_2

Basis of Presentation and Recent Accounting Pronouncements (Policies)	6 Months Ended
	Jun. 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	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

Earnings Per Common Share (Tabl

Earnings Per Common Share (Tables)	6 Months Ended
	Jun. 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 Six Months Ended June 30, June 30, 2022 2021 2022 2021 Numerator: Net income (loss) $ 403,945 $ 718,664 $ 601,377 $ 1,194,372 Amounts attributable to noncontrolling interests 399 (43,178) (1,233) (80,730) Net income (loss) available to Arch 404,344 675,486 600,144 1,113,642 Preferred dividends (10,184) (11,666) (20,368) (22,069) Net income (loss) available to Arch common shareholders $ 394,160 $ 663,820 $ 579,776 $ 1,091,573 Denominator: Weighted average common shares and common share equivalents outstanding — basic 369,241,193 397,743,402 371,728,683 399,267,183 Effect of dilutive common share equivalents: Nonvested restricted shares 2,121,678 1,990,729 2,238,267 1,932,929 Stock options (1) 6,590,117 6,751,863 6,938,562 6,487,568 Weighted average common shares and common share equivalents outstanding — diluted 377,952,988 406,485,994 380,905,512 407,687,680 Earnings per common share: Basic $ 1.07 $ 1.67 $ 1.56 $ 2.73 Diluted $ 1.04 $ 1.63 $ 1.52 $ 2.68 (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 second quarter and 2021 second quarter, the number of stock options excluded were 773,163 and 1,974,849, respectively. For the six months ended June 30, 2022 and 2021, the number of stock options excluded were 778,724 and 2,395,749, respectively.

Segment Information (Tables)

Segment Information (Tables)	6 Months Ended
	Jun. 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 June 30, 2022 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 1,705,167 $ 1,793,398 $ 371,896 $ 3,869,727 $ — $ 3,869,727 Premiums ceded (476,910) (630,764) (78,148) (1,185,088) — (1,185,088) Net premiums written 1,228,257 1,162,634 293,748 2,684,639 — 2,684,639 Change in unearned premiums (126,113) (234,635) 1,884 (358,864) — (358,864) Net premiums earned 1,102,144 927,999 295,632 2,325,775 — 2,325,775 Other underwriting income (loss) — 4,526 (1,556) 2,970 — 2,970 Losses and loss adjustment expenses (629,759) (537,578) 64,681 (1,102,656) — (1,102,656) Acquisition expenses (213,688) (189,494) (10,137) (413,319) — (413,319) Other operating expenses (161,088) (66,053) (50,251) (277,392) — (277,392) Underwriting income (loss) $ 97,609 $ 139,400 $ 298,369 535,378 — 535,378 Net investment income 106,392 — 106,392 Net realized gains (losses) (266,579) — (266,579) Equity in net income (loss) of investment funds accounted for using the equity method 58,061 — 58,061 Other income (loss) (11,777) — (11,777) Corporate expenses (2) (27,359) — (27,359) Transaction costs and other (2) (261) — (261) Amortization of intangible assets (27,207) — (27,207) Interest expense (32,795) — (32,795) Net foreign exchange gains (losses) 87,775 — 87,775 Income (loss) before income taxes and income (loss) from operating affiliates 421,628 — 421,628 Income tax (expense) benefit (22,323) — (22,323) Income (loss) from operating affiliates 4,640 — 4,640 Net income (loss) 403,945 — 403,945 Amounts attributable to redeemable noncontrolling interests 399 — 399 Net income (loss) available to Arch 404,344 — 404,344 Preferred dividends (10,184) — (10,184) Net income (loss) available to Arch common shareholders $ 394,160 $ — $ 394,160 Underwriting Ratios Loss ratio 57.1 % 57.9 % (21.9) % 47.4 % — % 47.4 % Acquisition expense ratio 19.4 % 20.4 % 3.4 % 17.8 % — % 17.8 % Other operating expense ratio 14.6 % 7.1 % 17.0 % 11.9 % — % 11.9 % Combined ratio 91.1 % 85.4 % (1.5) % 77.1 % — % 77.1 % Goodwill and intangible assets $ 236,661 $ 166,437 $ 464,916 $ 868,014 $ — $ 868,014 (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 June 30, 2021 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 1,368,867 $ 1,358,020 $ 391,511 $ 3,117,505 $ 240,942 $ 3,286,291 Premiums ceded (405,312) (433,288) (55,665) (893,372) (65,551) (886,767) Net premiums written 963,555 924,732 335,846 2,224,133 175,391 2,399,524 Change in unearned premiums (98,128) (187,708) (1,625) (287,461) 8,846 (278,615) Net premiums earned 865,427 737,024 334,221 1,936,672 184,237 2,120,909 Other underwriting income (loss) — 1,053 4,148 5,201 328 5,529 Losses and loss adjustment expenses (545,880) (463,823) (9,880) (1,019,583) (140,248) (1,159,831) Acquisition expenses (136,852) (133,585) (30,117) (300,554) (34,589) (335,143) Other operating expenses (133,342) (44,695) (48,312) (226,349) (18,594) (244,943) Underwriting income (loss) $ 49,353 $ 95,974 $ 250,060 395,387 (8,866) 386,521 Net investment income 89,430 22,183 111,613 Net realized gains (losses) 163,394 39,513 202,907 Equity in net income (loss) of investment funds accounted for using the equity method 122,186 — 122,186 Other income (loss) 6,852 — 6,852 Corporate expenses (2) (17,175) — (17,175) Transaction costs and other (2) 1,444 (220) 1,224 Amortization of intangible assets (14,388) (898) (15,286) Interest expense (31,439) (4,261) (35,700) Net foreign exchange gains (losses) (17,892) 117 (17,775) Income (loss) before income taxes and income (loss) from operating affiliates 697,799 47,568 745,367 Income tax (expense) benefit (50,953) (226) (51,179) Income (loss) from operating affiliates 24,476 — 24,476 Net income (loss) 671,322 47,342 718,664 Amounts attributable to redeemable noncontrolling interests (580) (981) (1,561) Amounts attributable to nonredeemable noncontrolling interests — (41,617) (41,617) Net income (loss) available to Arch 670,742 4,744 675,486 Preferred dividends (11,666) — (11,666) Net income (loss) available to Arch common shareholders $ 659,076 $ 4,744 $ 663,820 Underwriting Ratios Loss ratio 63.1 % 62.9 % 3.0 % 52.6 % 76.1 % 54.7 % Acquisition expense ratio 15.8 % 18.1 % 9.0 % 15.5 % 18.8 % 15.8 % Other operating expense ratio 15.4 % 6.1 % 14.5 % 11.7 % 10.1 % 11.5 % Combined ratio 94.3 % 87.1 % 26.5 % 79.8 % 105.0 % 82.0 % Goodwill and intangible assets $ 270,262 $ 16,168 $ 370,405 $ 656,835 $ 10,318 $ 667,153 (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.’ Six Months Ended June 30, 2022 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 3,424,772 $ 3,512,340 $ 736,735 $ 7,670,502 $ — $ 7,670,502 Premiums ceded (989,619) (1,210,582) (154,867) (2,351,723) — (2,351,723) Net premiums written 2,435,153 2,301,758 581,868 5,318,779 — 5,318,779 Change in unearned premiums (306,313) (569,359) 3,301 (872,371) — (872,371) Net premiums earned 2,128,840 1,732,399 585,169 4,446,408 — 4,446,408 Other underwriting income (loss) — 5,362 3,505 8,867 — 8,867 Losses and loss adjustment expenses (1,230,498) (992,278) 119,285 (2,103,491) — (2,103,491) Acquisition expenses (409,338) (361,490) (20,650) (791,478) — (791,478) Other operating expenses (327,913) (135,829) (103,593) (567,335) — (567,335) Underwriting income (loss) $ 161,091 $ 248,164 $ 583,716 $ 992,971 $ — $ 992,971 Net investment income 186,828 — 186,828 Net realized gains (losses) (558,993) — (558,993) Equity in net income (loss) of investment funds accounted for using the equity method 94,366 — 94,366 Other income (loss) (20,802) — (20,802) Corporate expenses (2) (59,294) — (59,294) Transaction costs and other (2) (658) — (658) Amortization of intangible assets (54,374) — (54,374) Interest expense (65,503) — (65,503) Net foreign exchange gains (losses) 91,620 — 91,620 Income (loss) before income taxes and income (loss) from operating affiliates 606,161 — 606,161 Income tax (expense) benefit (33,942) — (33,942) Income (loss) from operating affiliates 29,158 — 29,158 Net income (loss) 601,377 — 601,377 Amounts attributable to redeemable noncontrolling interests (1,233) — (1,233) Net income (loss) available to Arch 600,144 — 600,144 Preferred dividends (20,368) — (20,368) Net income (loss) available to Arch common shareholders $ 579,776 $ — $ 579,776 Underwriting Ratios Loss ratio 57.8 % 57.3 % (20.4) % 47.3 % — % 47.3 % Acquisition expense ratio 19.2 % 20.9 % 3.5 % 17.8 % — % 17.8 % Other operating expense ratio 15.4 % 7.8 % 17.7 % 12.8 % — % 12.8 % Combined ratio 92.4 % 86.0 % 0.8 % 77.9 % — % 77.9 % (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. (2) Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’ Six Months Ended June 30, 2021 Insurance Reinsurance Mortgage Sub-Total Other Total Gross premiums written (1) $ 2,784,753 $ 2,829,080 $ 782,757 $ 6,394,798 $ 457,465 $ 6,683,497 Premiums ceded (826,359) (905,236) (111,716) (1,841,519) (102,763) (1,775,516) Net premiums written 1,958,394 1,923,844 671,041 4,553,279 354,702 4,907,981 Change in unearned premiums (273,493) (541,920) (503) (815,916) (22,734) (838,650) Net premiums earned 1,684,901 1,381,924 670,538 3,737,363 331,968 4,069,331 Other underwriting income (loss) — (145) 11,045 10,900 739 11,639 Losses and loss adjustment expenses (1,081,627) (948,693) (73,569) (2,103,889) (259,042) (2,362,931) Acquisition expenses (265,074) (251,610) (60,199) (576,883) (62,741) (639,624) Other operating expenses (270,455) (105,209) (97,443) (473,107) (32,869) (505,976) Underwriting income (loss) $ 67,745 $ 76,267 $ 450,372 $ 594,384 $ (21,945) $ 572,439 Net investment income 168,159 42,310 210,469 Net realized gains (losses) 264,730 80,638 345,368 Equity in net income (loss) of investment funds accounted for using the equity method 193,872 — 193,872 Other income (loss) 5,111 — 5,111 Corporate expenses (2) (40,643) — (40,643) Transaction costs and other (2) 243 (935) (692) Amortization of intangible assets (28,790) (898) (29,688) Interest expense (65,636) (8,410) (74,046) Net foreign exchange gains (losses) 3,613 (1,325) 2,288 Income (loss) before income taxes and income (loss) from operating affiliates 1,095,043 89,435 1,184,478 Income tax (expense) benefit (89,805) (234) (90,039) Income (loss) from operating affiliates 99,933 — 99,933 Net income (loss) 1,105,171 89,201 1,194,372 Amounts attributable to redeemable noncontrolling interests (463) (1,953) (2,416) Amounts attributable to nonredeemable noncontrolling interests — (78,314) (78,314) Net income (loss) available to Arch 1,104,708 8,934 1,113,642 Preferred dividends (22,069) — (22,069) Net income (loss) available to Arch common shareholders $ 1,082,639 $ 8,934 $ 1,091,573 Underwriting Ratios Loss ratio 64.2 % 68.7 % 11.0 % 56.3 % 78.0 % 58.1 % Acquisition expense ratio 15.7 % 18.2 % 9.0 % 15.4 % 18.9 % 15.7 % Other operating expense ratio 16.1 % 7.6 % 14.5 % 12.7 % 9.9 % 12.4 % Combined ratio 96.0 % 94.5 % 34.5 % 84.4 % 106.8 % 86.2 % (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)	6 Months Ended
	Jun. 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 Six Months Ended June 30, June 30, 2022 2021 2022 2021 Reserve for losses and loss adjustment expenses at beginning of period $ 18,109,107 $ 16,443,952 $ 17,757,156 $ 16,513,929 Unpaid losses and loss adjustment expenses recoverable 5,709,998 3,916,650 5,599,231 4,314,855 Net reserve for losses and loss adjustment expenses at beginning of period 12,399,109 12,527,302 12,157,925 12,199,074 Net incurred losses and loss adjustment expenses relating to losses occurring in: Current year 1,273,882 1,219,081 2,416,529 2,463,853 Prior years (171,226) (59,250) (313,038) (100,922) Total net incurred losses and loss adjustment expenses 1,102,656 1,159,831 2,103,491 2,362,931 Retroactive reinsurance transactions (1) — — — (183,893) Net foreign exchange (gains) losses and other (248,655) 135,847 (281,295) 88,970 Net paid losses and loss adjustment expenses relating to losses occurring in: Current year (166,466) (164,441) (237,272) (223,425) Prior years (578,668) (607,911) (1,234,873) (1,193,029) Total net paid losses and loss adjustment expenses (745,134) (772,352) (1,472,145) (1,416,454) Net reserve for losses and loss adjustment expenses at end of period 12,507,976 13,050,628 12,507,976 13,050,628 Unpaid losses and loss adjustment expenses recoverable 5,686,348 4,146,020 5,686,348 4,146,020 Reserve for losses and loss adjustment expenses at end of period $ 18,194,324 $ 17,196,648 $ 18,194,324 $ 17,196,648 (1) 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”).

Allowance for Expected Credit_2

Allowance for Expected Credit Losses (Tables)	6 Months Ended
	Jun. 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 June 30, 2022 Balance at beginning of period $ 3,223,504 $ 39,073 Change for provision of expected credit losses (1) (903) Balance at end of period $ 3,634,182 $ 38,170 Three Months Ended June 30, 2021 Balance at beginning of period $ 2,618,175 $ 36,111 Change for provision of expected credit losses (1) (132) Balance at end of period $ 2,866,578 $ 35,979 Six Months Ended June 30, 2022 Balance at beginning of period $ 2,633,280 $ 39,958 Change for provision of expected credit losses (1) (1,788) Balance at end of period $ 3,634,182 $ 38,170 Six Months Ended June 30, 2021 Balance at beginning of period $ 2,064,586 $ 37,781 Change for provision of expected credit losses (1) (1,802) Balance at end of period $ 2,866,578 $ 35,979 (1) Amounts deemed uncollectible are written-off in operating expenses. For the 2022 second quarter and 2021 second quarter, amounts written off were $3.3 million and $1.1 million, respectively. For the six months ended June 30, 2022 and 2021 period, amounts written off were $4.8 million and $1.2 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 June 30, 2022 Balance at beginning of period $ 5,941,000 $ 18,483 Change for provision of expected credit losses (3,743) Balance at end of period $ 5,938,511 $ 14,740 Three Months Ended June 30, 2021 Balance at beginning of period $ 4,041,076 $ 10,872 Change for provision of expected credit losses 157 Balance at end of period $ 4,314,515 $ 11,029 Six Months Ended June 30, 2022 Balance at beginning of period $ 5,880,735 $ 13,230 Change for provision of expected credit losses 1,510 Balance at end of period $ 5,938,511 $ 14,740 Six Months Ended June 30, 2021 Balance at beginning of period $ 4,500,802 $ 11,636 Change for provision of expected credit losses (607) Balance at end of period $ 4,314,515 $ 11,029
Ceded credit risk	The following table summarizes the Company’s reinsurance recoverables on paid and unpaid losses (not including ceded unearned premiums): June 30, December 31 2022 2021 Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses $ 5,938,511 $ 5,880,735 % due from carriers with A.M. Best rating of “A-” or better 69.3 % 69.7 % % due from all other rated carriers 0.1 % 0.1 % % due from all other carriers with no A.M. Best rating (1) 30.6 % 30.2 % Largest balance due from any one carrier as % of total shareholders’ equity 7.8 % 6.7 % (1) At June 30, 2022 and December 31, 2021 over 93% 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 June 30, 2022 Balance at beginning of period $ 1,810,199 $ 3,731 Change for provision of expected credit losses (726) Balance at end of period $ 1,758,018 $ 3,005 Three Months Ended June 30, 2021 Balance at beginning of period $ 1,919,655 $ 5,853 Change for provision of expected credit losses (1,382) Balance at end of period 1,882,948 $ 4,471 Six Months Ended June 30, 2022 Balance at beginning of period $ 1,828,691 $ 3,437 Change for provision of expected credit losses (432) Balance at end of period $ 1,758,018 $ 3,005 Six Months Ended June 30, 2021 Balance at beginning of period $ 1,986,924 $ 8,638 Change for provision of expected credit losses (4,167) Balance at end of period 1,882,948 $ 4,471

Investment Information (Tables)

Investment Information (Tables)	6 Months Ended
	Jun. 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 June 30, 2022 Fixed maturities: Corporate bonds $ 7,288,555 $ 32,021 $ (655,664) $ (38,494) $ 7,950,692 Mortgage backed securities 698,168 4,427 (55,898) — 749,639 Municipal bonds 417,380 4,129 (18,936) (298) 432,485 Commercial mortgage backed securities 1,023,088 1,533 (42,056) (3,594) 1,067,205 U.S. government and government agencies 4,368,150 25,112 (240,786) — 4,583,824 Non-U.S. government securities 2,181,943 16,175 (163,724) (1,335) 2,330,827 Asset backed securities 1,607,745 1,001 (80,267) (14,689) 1,701,700 Total 17,585,029 84,398 (1,257,331) (58,410) 18,816,372 Short-term investments 2,227,874 2,458 (1,257) — 2,226,673 Total $ 19,812,903 $ 86,856 $ (1,258,588) $ (58,410) $ 21,043,045 December 31, 2021 Fixed maturities: Corporate bonds $ 6,553,333 $ 104,170 $ (69,194) $ (2,037) $ 6,520,394 Mortgage backed securities 408,477 2,825 (5,410) (48) 411,110 Municipal bonds 404,666 18,724 (1,409) (2) 387,353 Commercial mortgage backed securities 1,046,484 1,740 (3,117) (6) 1,047,867 U.S. government and government agencies 4,772,764 10,076 (45,967) — 4,808,655 Non-U.S. government securities 2,120,294 54,048 (34,749) (82) 2,101,077 Asset backed securities 2,692,091 6,540 (11,108) (708) 2,697,367 Total 17,998,109 198,123 (170,954) (2,883) 17,973,823 Short-term investments 1,734,716 568 (590) — 1,734,738 Total $ 19,732,825 $ 198,691 $ (171,544) $ (2,883) $ 19,708,561
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 June 30, 2022 Fixed maturities: Corporate bonds $ 6,583,215 $ (580,235) $ 489,098 $ (75,429) $ 7,072,313 $ (655,664) Mortgage backed securities 595,485 (46,415) 61,751 (9,483) 657,236 (55,898) Municipal bonds 271,481 (17,908) 8,876 (1,028) 280,357 (18,936) Commercial mortgage backed securities 973,212 (42,056) — — 973,212 (42,056) U.S. government and government agencies 4,029,550 (235,510) 69,596 (5,276) 4,099,146 (240,786) Non-U.S. government securities 1,929,278 (148,781) 103,969 (14,943) 2,033,247 (163,724) Asset backed securities 1,292,087 (73,575) 136,119 (6,692) 1,428,206 (80,267) Total 15,674,308 (1,144,480) 869,409 (112,851) 16,543,717 (1,257,331) Short-term investments 505,798 (1,257) — — 505,798 (1,257) Total $ 16,180,106 $ (1,145,737) $ 869,409 $ (112,851) $ 17,049,515 $ (1,258,588) December 31, 2021 Fixed maturities: Corporate bonds $ 3,639,582 $ (63,938) $ 98,867 $ (5,256) $ 3,738,449 $ (69,194) Mortgage backed securities 222,176 (3,545) 46,809 (1,865) 268,985 (5,410) Municipal bonds 26,665 (385) 16,361 (1,024) 43,026 (1,409) Commercial mortgage backed securities 675,603 (2,805) 5,908 (312) 681,511 (3,117) U.S. government and government agencies 4,211,621 (44,180) 33,373 (1,787) 4,244,994 (45,967) Non-U.S. government securities 1,511,301 (31,983) 62,957 (2,766) 1,574,258 (34,749) Asset backed securities 1,667,002 (9,853) 33,082 (1,255) 1,700,084 (11,108) Total 11,953,950 (156,689) 297,357 (14,265) 12,251,307 (170,954) Short-term investments 284,733 (590) — — 284,733 (590) Total $ 12,238,683 $ (157,279) $ 297,357 $ (14,265) $ 12,536,040 $ (171,544)
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. June 30, 2022 December 31, 2021 Maturity Estimated Amortized Estimated Amortized Due in one year or less $ 412,194 $ 414,752 $ 300,889 $ 299,772 Due after one year through five years 9,423,547 9,927,876 8,355,255 8,339,387 Due after five years through 10 years 4,070,099 4,512,685 4,689,155 4,684,393 Due after 10 years 350,188 442,515 505,758 493,927 14,256,028 15,297,828 13,851,057 13,817,479 Mortgage backed securities 698,168 749,639 408,477 411,110 Commercial mortgage backed securities 1,023,088 1,067,205 1,046,484 1,047,867 Asset backed securities 1,607,745 1,701,700 2,692,091 2,697,367 Total $ 17,585,029 $ 18,816,372 $ 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: June 30, December 31, Fixed maturities $ 525,451 $ 416,698 Other investments 1,054,771 1,432,553 Short-term investments 39,657 97,806 Equity securities 14,489 26,493 Total $ 1,634,368 $ 1,973,550 The following table summarizes the Company’s other investments, as detailed in the previous table, by strategy: June 30, December 31, Lending $ 427,812 $ 536,345 Investment grade fixed income 221,484 147,810 Term loan investments 152,277 484,950 Private equity 124,282 91,126 Energy 74,234 81,692 Credit related funds 54,682 70,278 Infrastructure — 20,352 Total $ 1,054,771 $ 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: June 30, December 31, Credit related funds $ 1,119,711 $ 1,022,334 Private equity 646,904 436,042 Real estate 455,044 396,395 Lending 447,028 376,649 Equities 350,587 395,090 Infrastructure 231,816 230,070 Energy 115,514 119,141 Fixed income 129,737 101,890 Total $ 3,496,341 $ 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: June 30, December 31, Investments accounted for using the equity method (1) 3,496,341 3,077,611 Investments accounted for using the fair value option (2) 128,826 170,595 Total $ 3,625,167 $ 3,248,206 (1) Aggregate unfunded commitments were $3.0 billion at June 30, 2022, compared to $2.6 billion at December 31, 2021. (2) Aggregate unfunded commitments were $21.7 million at June 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: June 30, 2022 2021 Three Months Ended Fixed maturities $ 105,342 $ 88,625 Term loans 401 16,879 Equity securities 6,121 8,584 Short-term investments 4,120 1,138 Other (1) 7,583 19,950 Gross investment income 123,567 135,176 Investment expenses (17,175) (23,563) Net investment income $ 106,392 $ 111,613 Six Months Ended Fixed maturities $ 187,395 $ 179,251 Term loans 2,018 31,607 Equity securities 12,359 14,234 Short-term investments 6,695 1,745 Other (1) 18,042 34,305 Gross investment income 226,509 261,142 Investment expenses (39,681) (50,673) Net investment income $ 186,828 $ 210,469
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: June 30, 2022 2021 Three Months Ended Available for sale securities: Gross gains on investment sales $ 15,186 $ 115,541 Gross losses on investment sales (57,176) (50,627) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities (39,255) 10,912 Other investments (21,710) 60,884 Equity securities (2,124) 5,492 Short-term investments (2,008) (104) Equity securities, at fair value: Net realized gains (losses) on sales during the period 16,879 33,570 Net unrealized gains (losses) on equity securities still held at reporting date (106,375) 65,847 Allowance for credit losses: Investments related (25,026) 896 Underwriting related 842 1,381 Derivative instruments (1) (45,684) (51,109) Other (128) 10,224 Net realized gains (losses) $ (266,579) $ 202,907 Six Months Ended Available for sale securities: Gross gains on investment sales $ 34,893 $ 180,543 Gross losses on investment sales (165,523) (113,625) Change in fair value of assets and liabilities accounted for using the fair value option: Fixed maturities (69,844) 27,465 Other investments (17,321) 107,739 Equity securities (5,437) 7,557 Short-term investments (2,157) 632 Equity securities, at fair value: Net realized gains (losses) on sales during the period 82,090 71,419 Net unrealized gains (losses) on equity securities still held at reporting date (282,570) 85,555 Allowance for credit losses: Investments related (56,748) (752) Underwriting related (3,444) 6,649 Derivative instruments (1) (69,395) (14,993) Other (3,537) (12,821) Net realized gains (losses) $ (558,993) $ 345,368 (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 June 30, 2022 Balance at beginning of period $ 6,998 $ 106 $ 27,041 $ 34,145 Additions for current-period provision for expected credit losses 4,788 252 13,466 18,506 Additions (reductions) for previously recognized expected credit losses 6,705 (60) (205) 6,440 Reductions due to disposals (208) — (473) (681) Balance at end of period $ 18,283 $ 298 $ 39,829 $ 58,410 Three Months Ended June 30, 2021 Balance at beginning of period $ 1,207 $ 2 $ 2,621 $ 3,830 Additions for current-period provision for expected credit losses 52 — 7 59 Additions (reductions) for previously recognized expected credit losses (383) 4 (412) (791) Reductions due to disposals (117) — (857) (974) Balance at end of period $ 759 $ 6 $ 1,359 $ 2,124 Six Months Ended June 30, 2022 Balance at beginning of period $ 802 $ 2 $ 2,079 $ 2,883 Additions for current-period provision for expected credit losses 10,778 347 38,616 49,741 Additions (reductions) for previously recognized expected credit losses 7,192 (51) (220) 6,921 Reductions due to disposals (489) — (646) (1,135) Balance at end of period $ 18,283 $ 298 $ 39,829 $ 58,410 Six Months Ended June 30, 2021 Balance at beginning of period $ 1,490 $ 11 $ 896 $ 2,397 Additions for current-period provision for expected credit losses 234 — 2,428 2,662 Additions (reductions) for previously recognized expected credit losses (765) (5) (952) (1,722) Reductions due to disposals (200) — (1,013) (1,213) Balance at end of period $ 759 $ 6 $ 1,359 $ 2,124 (1) Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.
Summary of restricted assets	The following table details the value of the Company’s restricted assets: June 30, December 31, Assets used for collateral or guarantees: Affiliated transactions $ 4,193,561 $ 4,223,955 Third party agreements 2,953,800 2,721,160 Deposits with U.S. regulatory authorities 781,024 798,100 Deposits with non-U.S. regulatory authorities 485,341 506,517 Total restricted assets $ 8,413,726 $ 8,249,732
Reconciliation of cash and restricted cash	The following table details reconciliation of cash and restricted cash within the Consolidated Balance Sheets: June 30, December 31, Cash $ 813,548 $ 858,668 Restricted cash (included in ‘other assets’) $ 414,683 $ 456,103 Cash and restricted cash $ 1,228,231 $ 1,314,771

Fair Value (Tables)

Fair Value (Tables)	6 Months Ended
	Jun. 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 June 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 $ 7,288,555 $ — $ 7,284,985 $ 3,570 Mortgage backed securities 698,168 — 698,168 — Municipal bonds 417,380 — 417,380 — Commercial mortgage backed securities 1,023,088 — 1,023,088 — U.S. government and government agencies 4,368,150 4,341,399 26,751 — Non-U.S. government securities 2,181,943 — 2,181,943 — Asset backed securities 1,607,745 — 1,604,878 2,867 Total 17,585,029 4,341,399 13,237,193 6,437 Short-term investments 2,227,874 2,049,235 178,639 — Equity securities, at fair value 772,689 736,343 33,440 2,906 Derivative instruments (2) 122,033 — 122,033 — Residential mortgage loans 3,929 — 3,929 — Fair value option: Corporate bonds 522,707 — 522,707 — Non-U.S. government bonds 611 — 611 — Asset backed securities 2,133 — 2,133 — Short-term investments 39,657 886 38,771 — Equity securities 14,489 10,097 — 4,392 Other investments 178,461 — 145,130 33,331 Other investments measured at net asset value (1) 876,310 Total 1,634,368 10,983 709,352 37,723 Total assets measured at fair value $ 22,345,922 $ 7,137,960 $ 14,284,586 $ 47,066 Liabilities measured at fair value: Other liabilities $ (16,205) $ — $ — $ (16,205) Derivative instruments (2) (75,147) — (75,147) — Total liabilities measured at fair value $ (91,352) $ — $ (75,147) $ (16,205) (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 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 June 30, 2022 Balance at beginning of period $ 3,152 $ 3,570 $ — $ 22,602 $ 4,511 $ 2,768 $ (17,591) Total gains or (losses) (realized/unrealized) Included in earnings (2) (1) — — 27 (119) (89) (97) Included in other comprehensive income (85) — — — — — 1,483 Purchases, issuances, sales and settlements Purchases — — — 10,702 — 227 — Issuances — — — — — — — Sales — — — — — — — Settlements (199) — — — — — — Transfers in and/or out of Level 3 — — — — — — — Balance at end of period $ 2,867 $ 3,570 $ — $ 33,331 $ 4,392 $ 2,906 $ (16,205) Three Months Ended June 30, 2021 Balance at beginning of period $ 3,472 $ 13 $ 989 $ 67,930 $ 71,176 $ 43,112 $ (465) Total gains or (losses) (realized/unrealized) Included in earnings (2) 12 — 9 633 2,502 922 (1) Included in other comprehensive income (57) — — — — — — Purchases, issuances, sales and settlements Purchases — — — 5,638 — 5,102 — Issuances — — — — — — — Sales — — — (301) — — — Settlements (3) — — — — — — Transfers in and/or out of Level 3 — — — — — — — Balance at end of period $ 3,424 $ 13 $ 998 $ 73,900 $ 73,678 $ 49,136 $ (466) Six Months Ended June 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) 9 — — 34 (356) (236) (195) Included in other comprehensive income (145) — — — — — 950 Purchases, issuances, sales and settlements Purchases — — — 10,770 — 227 — Issuances — — — — — — — Sales (3) — — — (2,471) — (3) — Settlements (344) — — (2,983) — — — Transfers in and/or out of Level 3 — 3,557 — — — — — Balance at end of period $ 2,867 $ 3,570 $ — $ 33,331 $ 4,392 $ 2,906 $ (16,205) Six Months Ended June 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) (56) — 13 881 4,690 1,826 (5) Included in other comprehensive income 57 — — — — — — Purchases, issuances, sales and settlements Purchases — — — 13,003 — 5,295 — Issuances — — — — — — — Sales — — — (7,087) — — — Settlements (3) — — — — — — Transfers in and/or out of Level 3 — — — — — — — Balance at end of period $ 3,424 $ 13 $ 998 $ 73,900 $ 73,678 $ 49,136 $ (466) (1) Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

Derivative Instruments (Tables)

Derivative Instruments (Tables)	6 Months Ended
	Jun. 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 June 30, 2022 Futures contracts $ 49,695 $ (22,561) $ 2,794,246 Foreign currency forward contracts 9,556 (18,884) 908,192 TBAs — — — Other 62,782 (33,702) 3,849,244 Total $ 122,033 $ (75,147) 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’ and the fair value of liability derivatives are included in ‘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 June 30, hedging instruments: 2022 2021 Three Months Ended Net realized gains (losses): Futures contracts $ (39,205) $ (54,759) Foreign currency forward contracts (25,638) 1,295 TBAs — — Other (1) 19,159 2,355 Total $ (45,684) $ (51,109) Six Months Ended Net realized gains (losses): Futures contracts $ (85,979) $ (7,321) Foreign currency forward contracts (27,676) (20,776) TBAs (51) — Other (1) 44,311 13,104 Total $ (69,395) $ (14,993) (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)	6 Months Ended
	Jun. 30, 2022
Noncontrolling Interest [Abstract]
Activity in non-redeemable noncontrolling interests	The following table sets forth activity in the non-redeemable noncontrolling interests: June 30, 2021 Three Months Ended Balance, beginning of period $ 876,864 Additional paid in capital attributable to noncontrolling interests 383 Amounts attributable to noncontrolling interests 41,617 Other comprehensive income (loss) attributable to noncontrolling interests 10 Balance, end of period $ 918,874 Six Months Ended Balance, beginning of year $ 823,007 Additional paid in capital attributable to noncontrolling interests 22,113 Amounts attributable to noncontrolling interests 78,314 Other comprehensive income (loss) attributable to noncontrolling interests (4,560) Balance, end of period $ 918,874
Activity in redeemable noncontrolling interests	The following table sets forth activity in the redeemable non-controlling interests: June 30, 2022 2021 Three Months Ended Balance, beginning of period $ 9,763 $ 57,670 Accretion of preference share issuance costs — 23 Other (1,304) (160) Balance, end of period $ 8,459 $ 57,533 Six Months Ended Balance, beginning of year $ 9,233 $ 58,548 Accretion of preference share issuance costs — 46 Other (774) (1,061) Balance, end of period $ 8,459 $ 57,533
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: June 30, 2022 2021 Three Months Ended Amounts attributable to non-redeemable noncontrolling interests $ — $ (41,617) Amounts attributable to redeemable noncontrolling interests 399 (1,561) Net (income) loss attributable to noncontrolling interests $ 399 $ (43,178) Six Months Ended Amounts attributable to non-redeemable noncontrolling interests $ — $ (78,314) Amounts attributable to redeemable noncontrolling interests (1,233) (2,416) Net (income) loss attributable to noncontrolling interests $ (1,233) $ (80,730)
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. June 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) $ 61,328 $ (68) $ 274 $ 206 $ — $ 108,368 $ (159) $ 424 $ 265 2018-1 Ltd. (Apr-18) 122,190 (342) 965 623 — 181,136 (528) 1,268 740 2018-3 Ltd. (Oct-18) 244,257 (566) 1,522 956 — 302,563 (1,018) 2,496 1,478 2019-1 Ltd. (Mar-19) 134,972 (127) 988 861 — 181,324 (380) 5,807 5,427 2019-2 Ltd. (Apr-19) 383,737 (426) 5,323 4,897 — 398,316 (515) 3,998 3,483 2019-3 Ltd. (Jul-19) 296,466 (282) 2,154 1,872 — 409,859 (584) 3,190 2,606 2019-4 Ltd. (Oct-19) 312,668 (306) 4,702 4,396 — 411,954 (462) 4,759 4,297 2020-2 Ltd. (Sep-20) 151,543 (58) 1,331 1,273 442 217,766 (177) 1,984 1,807 2020-3 Ltd. (Nov-20) 303,011 (26) 4,388 4,362 10,779 348,818 (128) 5,793 5,665 2020-4 Ltd. (Dec-20) 124,672 23 1,267 1,290 5,900 176,826 (50) 1,630 1,580 2021-1 Ltd. (Mar-21) 519,641 (1,006) 2,771 1,765 48,841 568,986 (303) 3,283 2,980 2021-2 Ltd. (Jun-21) 492,837 (577) 3,505 2,928 85,717 522,807 281 4,124 4,405 2021-3 Ltd. (Sep-21) 507,873 (1,082) 2,878 1,796 131,518 507,873 (411) 3,446 3,035 2022-1 Ltd. (Jan-22) 283,500 (282) 2,020 1,738 33,260 Total $ 3,938,695 $ (5,125) $ 34,088 $ 28,963 $ 316,457 $ 4,336,596 $ (4,434) $ 42,202 $ 37,768 (1) Coverage from a separate panel of reinsurers remaining at June 30, 2022.

Other Comprehensive Income (L_2

Other Comprehensive Income (Loss) (Tables)	6 Months Ended
	Jun. 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 Six Months Ended Details About Line Item That Includes June 30, June 30, AOCI Components Reclassification 2022 2021 2022 2021 Unrealized appreciation (decline) on available-for-sale investments Net realized gains (losses) $ (41,990) $ 64,914 $ (130,630) $ 66,918 Provision for credit losses (25,026) 896 (56,748) (751) Total before tax (67,016) 65,810 (187,378) 66,167 Income tax (expense) benefit 9,306 (5,263) 27,390 (8,317) Net of tax $ (57,710) $ 60,547 $ (159,988) $ 57,850
Schedule of comprehensive income (loss)	Before Tax Amount Tax Expense (Benefit) Net of Tax Amount Three Months Ended June 30, 2022 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (676,048) $ (78,043) $ (598,005) Less reclassification of net realized gains (losses) included in net income (67,016) (9,306) (57,710) Foreign currency translation adjustments (68,562) (37) (68,525) Other comprehensive income (loss) $ (677,594) $ (68,774) $ (608,820) Three Months Ended June 30, 2021 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ 91,057 $ 12,486 $ 78,571 Less reclassification of net realized gains (losses) included in net income 65,810 5,263 60,547 Foreign currency translation adjustments 6,392 187 6,205 Other comprehensive income (loss) $ 31,639 $ 7,410 $ 24,229 Six Months Ended June 30, 2022 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (1,460,938) $ (178,578) $ (1,282,360) Less reclassification of net realized gains (losses) included in net income (187,378) (27,390) (159,988) Foreign currency translation adjustments (71,127) 166 (71,293) Other comprehensive income (loss) $ (1,344,687) $ (151,022) $ (1,193,665) Six Months Ended June 30, 2021 Unrealized appreciation (decline) in value of investments: Unrealized holding gains (losses) arising during period $ (203,303) $ (20,124) $ (183,179) Less reclassification of net realized gains (losses) included in net income 66,167 8,317 57,850 Foreign currency translation adjustments (22,023) 356 (22,379) Other comprehensive income (loss) $ (291,493) $ (28,085) $ (263,408)

Basis of Presentation and Rec_3

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

Share Transactions - Share repu

Share Transactions - Share repurchases (Details) - Common shares shares in Millions, $ in Millions	6 Months Ended
	Jun. 30, 2022 USD ($) shares
Class of Stock [Line Items]
Cumulative number of shares acquired since inception of share repurchase program | shares	433.3
Aggregate purchase price of shares acquired since inception of share repurchase program	$ 5,860
Treasury stock, shares acquired (shares) | shares	12.7
Shares repurchased for treasury	$ 575.7
Remaining authorized repurchase amount	$ 606.6

Share Transactions - Long-Term

Share Transactions - Long-Term Incentive and Share Award Plan (Details) - 2022 Long-term incentive and share award plan - shares	Jun. 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	6 Months Ended
	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Class of Stock [Line Items]
Proceeds from issuance of preferred shares, net		$ 0	$ 485,821
Depositary Series G Preferred Stock
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
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%

Earnings Per Common Share (Deta

Earnings Per Common Share (Details) - USD ($) $ / shares in Units, $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Numerator:
Net income (loss)		$ 403,945	$ 718,664	$ 601,377	$ 1,194,372
Amounts attributable to noncontrolling interests		399	(43,178)	(1,233)	(80,730)
Net income available to Arch		404,344	675,486	600,144	1,113,642
Preferred dividends		(10,184)	(11,666)	(20,368)	(22,069)
Net income (loss) available to Arch common shareholders		$ 394,160	$ 663,820	$ 579,776	$ 1,091,573
Denominator:
Weighted average common shares outstanding — basic		369,241,193	397,743,402	371,728,683	399,267,183
Effect of dilutive common share equivalents:
Nonvested restricted shares		2,121,678	1,990,729	2,238,267	1,932,929
Stock options	[1]	6,590,117	6,751,863	6,938,562	6,487,568
Weighted average common shares and common share equivalents outstanding — diluted		377,952,988	406,485,994	380,905,512	407,687,680
Earnings per common share:
Basic (per share)		$ 1.07	$ 1.67	$ 1.56	$ 2.73
Diluted (per share)		$ 1.04	$ 1.63	$ 1.52	$ 2.68
Stock options
Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]
Antidilutive securities excluded from computation of earnings per common share (shares)		773,163	1,974,849	778,724	2,395,749
[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 second quarter and 2021 second quarter, the number of stock options excluded were 773,163 and 1,974,849, respectively. For the six months ended June 30, 2022 and 2021, the number of stock options excluded were 778,724 and 2,395,749, respectively.

Segment Information - Summary o

Segment Information - Summary of underwriting income or loss by segment (Details) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2022 USD ($)	Jun. 30, 2021 USD ($)	Jun. 30, 2022 USD ($) segment	Jun. 30, 2021 USD ($)	Dec. 31, 2021 USD ($)
Segment Reporting Information [Line Items]
Gross premiums written		$ 3,869,727	$ 3,286,291	$ 7,670,502	$ 6,683,497
Premiums ceded		(1,185,088)	(886,767)	(2,351,723)	(1,775,516)
Net premiums written		2,684,639	2,399,524	5,318,779	4,907,981
Change in unearned premiums		(358,864)	(278,615)	(872,371)	(838,650)
Net premiums earned		2,325,775	2,120,909	4,446,408	4,069,331
Other underwriting income (loss)		2,970	5,529	8,867	11,639
Losses and loss adjustment expenses		(1,102,656)	(1,159,831)	(2,103,491)	(2,362,931)
Acquisition expenses		(413,319)	(335,143)	(791,478)	(639,624)
Other operating expenses		(277,392)	(244,943)	(567,335)	(505,976)
Underwriting income (loss)		535,378	386,521	992,971	572,439
Net investment income		106,392	111,613	186,828	210,469
Net realized gains (losses)		(266,579)	202,907	(558,993)	345,368
Equity in net income (loss) of investment funds accounted for using the equity method		58,061	122,186	94,366	193,872
Other income (loss)		(11,777)	6,852	(20,802)	5,111
Corporate expenses		(27,359)	(17,175)	(59,294)	(40,643)
Transaction costs and other		(261)	1,224	(658)	(692)
Amortization of intangible assets		(27,207)	(15,286)	(54,374)	(29,688)
Interest expense		(32,795)	(35,700)	(65,503)	(74,046)
Net foreign exchange gains (losses)		87,775	(17,775)	91,620	2,288
Income (loss) before income taxes and income (loss) from operating affiliates		421,628	745,367	606,161	1,184,478
Income tax expense (benefit)		(22,323)	(51,179)	(33,942)	(90,039)
Income (loss) from operating affiliates		4,640	24,476	29,158	99,933
Net income (loss)		403,945	718,664	601,377	1,194,372
Amounts attributable to redeemable noncontrolling interests		399	(1,561)	(1,233)	(2,416)
Amounts attributable to non-redeemable noncontrolling interests		0	(41,617)	0	(78,314)
Net income (loss) available to Arch		404,344	675,486	600,144	1,113,642
Preferred dividends		(10,184)	(11,666)	(20,368)	(22,069)
Net income (loss) available to Arch common shareholders		$ 394,160	$ 663,820	$ 579,776	$ 1,091,573
Underwriting Ratios
Loss ratio		47.40%	54.70%	47.30%	58.10%
Acquisition expense ratio		17.80%	15.80%	17.80%	15.70%
Other operating expense ratio		11.90%	11.50%	12.80%	12.40%
Combined ratio		77.10%	82%	77.90%	86.20%
Goodwill and intangible assets		$ 868,014	$ 667,153	$ 868,014	$ 667,153	$ 944,983
Operating segments | Underwriting Segments
Segment Reporting Information [Line Items]
Number of segments | segment				3
Gross premiums written	[1]	3,869,727	3,117,505	$ 7,670,502	6,394,798
Premiums ceded		(1,185,088)	(893,372)	(2,351,723)	(1,841,519)
Net premiums written		2,684,639	2,224,133	5,318,779	4,553,279
Change in unearned premiums		(358,864)	(287,461)	(872,371)	(815,916)
Net premiums earned		2,325,775	1,936,672	4,446,408	3,737,363
Other underwriting income (loss)		2,970	5,201	8,867	10,900
Losses and loss adjustment expenses		(1,102,656)	(1,019,583)	(2,103,491)	(2,103,889)
Acquisition expenses		(413,319)	(300,554)	(791,478)	(576,883)
Other operating expenses		(277,392)	(226,349)	(567,335)	(473,107)
Underwriting income (loss)		535,378	395,387	992,971	594,384
Net investment income		106,392	89,430	186,828	168,159
Net realized gains (losses)		(266,579)	163,394	(558,993)	264,730
Equity in net income (loss) of investment funds accounted for using the equity method		58,061	122,186	94,366	193,872
Other income (loss)		(11,777)	6,852	(20,802)	5,111
Corporate expenses	[2]	(27,359)	(17,175)	(59,294)	(40,643)
Transaction costs and other	[2]	(261)	1,444	(658)	243
Amortization of intangible assets		(27,207)	(14,388)	(54,374)	(28,790)
Interest expense		(32,795)	(31,439)	(65,503)	(65,636)
Net foreign exchange gains (losses)		87,775	(17,892)	91,620	3,613
Income (loss) before income taxes and income (loss) from operating affiliates		421,628	697,799	606,161	1,095,043
Income tax expense (benefit)		(22,323)	(50,953)	(33,942)	(89,805)
Income (loss) from operating affiliates		4,640	24,476	29,158	99,933
Net income (loss)		403,945	671,322	601,377	1,105,171
Amounts attributable to redeemable noncontrolling interests		399	(580)	(1,233)	(463)
Amounts attributable to non-redeemable noncontrolling interests			0		0
Net income (loss) available to Arch		404,344	670,742	600,144	1,104,708
Preferred dividends		(10,184)	(11,666)	(20,368)	(22,069)
Net income (loss) available to Arch common shareholders		$ 394,160	$ 659,076	$ 579,776	$ 1,082,639
Underwriting Ratios
Loss ratio		47.40%	52.60%	47.30%	56.30%
Acquisition expense ratio		17.80%	15.50%	17.80%	15.40%
Other operating expense ratio		11.90%	11.70%	12.80%	12.70%
Combined ratio		77.10%	79.80%	77.90%	84.40%
Goodwill and intangible assets		$ 868,014	$ 656,835	$ 868,014	$ 656,835
Operating segments | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,705,167	1,368,867	3,424,772	2,784,753
Premiums ceded		(476,910)	(405,312)	(989,619)	(826,359)
Net premiums written		1,228,257	963,555	2,435,153	1,958,394
Change in unearned premiums		(126,113)	(98,128)	(306,313)	(273,493)
Net premiums earned		1,102,144	865,427	2,128,840	1,684,901
Other underwriting income (loss)		0	0	0	0
Losses and loss adjustment expenses		(629,759)	(545,880)	(1,230,498)	(1,081,627)
Acquisition expenses		(213,688)	(136,852)	(409,338)	(265,074)
Other operating expenses		(161,088)	(133,342)	(327,913)	(270,455)
Underwriting income (loss)		$ 97,609	$ 49,353	$ 161,091	$ 67,745
Underwriting Ratios
Loss ratio		57.10%	63.10%	57.80%	64.20%
Acquisition expense ratio		19.40%	15.80%	19.20%	15.70%
Other operating expense ratio		14.60%	15.40%	15.40%	16.10%
Combined ratio		91.10%	94.30%	92.40%	96%
Goodwill and intangible assets		$ 236,661	$ 270,262	$ 236,661	$ 270,262
Operating segments | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,793,398	1,358,020	3,512,340	2,829,080
Premiums ceded		(630,764)	(433,288)	(1,210,582)	(905,236)
Net premiums written		1,162,634	924,732	2,301,758	1,923,844
Change in unearned premiums		(234,635)	(187,708)	(569,359)	(541,920)
Net premiums earned		927,999	737,024	1,732,399	1,381,924
Other underwriting income (loss)		4,526	1,053	5,362	(145)
Losses and loss adjustment expenses		(537,578)	(463,823)	(992,278)	(948,693)
Acquisition expenses		(189,494)	(133,585)	(361,490)	(251,610)
Other operating expenses		(66,053)	(44,695)	(135,829)	(105,209)
Underwriting income (loss)		$ 139,400	$ 95,974	$ 248,164	$ 76,267
Underwriting Ratios
Loss ratio		57.90%	62.90%	57.30%	68.70%
Acquisition expense ratio		20.40%	18.10%	20.90%	18.20%
Other operating expense ratio		7.10%	6.10%	7.80%	7.60%
Combined ratio		85.40%	87.10%	86%	94.50%
Goodwill and intangible assets		$ 166,437	$ 16,168	$ 166,437	$ 16,168
Operating segments | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[1]	371,896	391,511	736,735	782,757
Premiums ceded		(78,148)	(55,665)	(154,867)	(111,716)
Net premiums written		293,748	335,846	581,868	671,041
Change in unearned premiums		1,884	(1,625)	3,301	(503)
Net premiums earned		295,632	334,221	585,169	670,538
Other underwriting income (loss)		(1,556)	4,148	3,505	11,045
Losses and loss adjustment expenses		64,681	(9,880)	119,285	(73,569)
Acquisition expenses		(10,137)	(30,117)	(20,650)	(60,199)
Other operating expenses		(50,251)	(48,312)	(103,593)	(97,443)
Underwriting income (loss)		$ 298,369	$ 250,060	$ 583,716	$ 450,372
Underwriting Ratios
Loss ratio		(21.90%)	3%	(20.40%)	11%
Acquisition expense ratio		3.40%	9%	3.50%	9%
Other operating expense ratio		17%	14.50%	17.70%	14.50%
Combined ratio		(1.50%)	26.50%	0.80%	34.50%
Goodwill and intangible assets		$ 464,916	$ 370,405	$ 464,916	$ 370,405
Operating segments | Corporate and Other Segments
Segment Reporting Information [Line Items]
Number of segments | segment				2
Gross premiums written	[1]	0	240,942	$ 0	457,465
Premiums ceded		0	(65,551)	0	(102,763)
Net premiums written		0	175,391	0	354,702
Change in unearned premiums		0	8,846	0	(22,734)
Net premiums earned		0	184,237	0	331,968
Other underwriting income (loss)		0	328	0	739
Losses and loss adjustment expenses		0	(140,248)	0	(259,042)
Acquisition expenses		0	(34,589)	0	(62,741)
Other operating expenses		0	(18,594)	0	(32,869)
Underwriting income (loss)		0	(8,866)	0	(21,945)
Net investment income		0	22,183	0	42,310
Net realized gains (losses)		0	39,513	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	(220)	0	(935)
Amortization of intangible assets		0	(898)	0	(898)
Interest expense		0	(4,261)	0	(8,410)
Net foreign exchange gains (losses)		0	117	0	(1,325)
Income (loss) before income taxes and income (loss) from operating affiliates		0	47,568	0	89,435
Income tax expense (benefit)		0	(226)	0	(234)
Income (loss) from operating affiliates		0	0	0	0
Net income (loss)		0	47,342	0	89,201
Amounts attributable to redeemable noncontrolling interests		0	(981)	0	(1,953)
Amounts attributable to non-redeemable noncontrolling interests			(41,617)		(78,314)
Net income (loss) available to Arch		0	4,744	0	8,934
Preferred dividends		0	0	0	0
Net income (loss) available to Arch common shareholders		$ 0	$ 4,744	$ 0	$ 8,934
Underwriting Ratios
Loss ratio		0%	76.10%	0%	78%
Acquisition expense ratio		0%	18.80%	0%	18.90%
Other operating expense ratio		0%	10.10%	0%	9.90%
Combined ratio		0%	105%	0%	106.80%
Goodwill and intangible assets		$ 0	$ 10,318	$ 0	$ 10,318
[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		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 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		$ 18,109,107	$ 16,443,952	$ 17,757,156	$ 16,513,929
Unpaid losses and loss adjustment expenses recoverable		5,709,998	3,916,650	5,599,231	4,314,855
Net reserve for losses and loss adjustment expenses at beginning of period		12,399,109	12,527,302	12,157,925	12,199,074
Net incurred losses and loss adjustment expenses relating to losses occurring in:
Current year		1,273,882	1,219,081	2,416,529	2,463,853
Prior years		(171,226)	(59,250)	(313,038)	(100,922)
Total net incurred losses and loss adjustment expenses		1,102,656	1,159,831	2,103,491	2,362,931
Retroactive reinsurance transaction	[1]	0	0	0	(183,893)
Net foreign exchange (gains) losses and other		(248,655)	135,847	(281,295)	88,970
Net paid losses and loss adjustment expenses relating to losses occurring in:
Current year		(166,466)	(164,441)	(237,272)	(223,425)
Prior years		(578,668)	(607,911)	(1,234,873)	(1,193,029)
Total net paid losses and loss adjustment expenses		(745,134)	(772,352)	(1,472,145)	(1,416,454)
Net reserve for losses and loss adjustment expenses at end of period		12,507,976	13,050,628	12,507,976	13,050,628
Unpaid losses and loss adjustment expenses recoverable		5,686,348	4,146,020	5,686,348	4,146,020
Reserve for losses and loss adjustment expenses at end of period		$ 18,194,324	$ 17,196,648	$ 18,194,324	$ 17,196,648
[1]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		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 171,226	$ 59,250	$ 313,038	$ 100,922
Operating segments | Insurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 6,700	$ 4,000	$ 14,000	$ 8,100
Percentage of prior year development	0.60%	0.50%	0.70%	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)	$ 14,300		$ 33,200	$ 49,400
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)		$ 7,100		21,600
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)		6,700		9,300
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)	12,200	10,700	30,800	18,600
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)		(24,500)		(45,400)
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)			5,200	(12,600)
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)	(6,300)		(13,600)	(11,200)
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)		(20,100)	(6,100)	(20,100)
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)	2,600		5,500
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)		5,600	(7,600)
Operating segments | Insurance | Long tailed lines | Executive assurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	(5,700)
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)	(7,500)		(19,200)
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)		28,500		53,500
Operating segments | Reinsurance
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 46,400	$ 20,500	$ 78,900	$ 47,300
Percentage of prior year development	5%	2.80%	4.60%	3.40%
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)			$ 74,900	$ 67,200
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)	$ 6,300	$ (17,100)	9,700	(39,600)
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)	31,600		47,400	28,800
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)	13,100	61,600	18,000	78,200
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)	4,200	4,000	14,900
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)	(8,000)	(33,200)	(10,900)	(24,800)
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)		(34,200)
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)	54,400	53,700	89,700	72,100
Operating segments | Mortgage
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)	$ 118,100	$ 43,100	$ 220,200	$ 54,000
Percentage of prior year development	39.90%	12.90%	37.60%	8.10%
Operating segments | Other
Causes of Increase (Decrease) in Liability for Unpaid Claims and Claims Adjustment Expense [Line Items]
Prior year development favorable (unfavorable)		$ (8,300)		$ (8,400)

Allowance for Expected Credit_3

Allowance for Expected Credit Losses - Premiums receivable (Details) - USD ($) $ in Thousands		3 Months Ended		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Credit Loss [Abstract]
Balance at beginning of period		$ 3,223,504	$ 2,618,175	$ 2,633,280	$ 2,064,586
Balance at end of period		3,634,182	2,866,578	3,634,182	2,866,578
Allowance for Expected Credit Losses
Balance at beginning of period		39,073	36,111	39,958	37,781
Change for provision of expected credit losses	[1]	(903)	(132)	(1,788)	(1,802)
Balance at end of period		38,170	35,979	38,170	35,979
Write-offs charged against the allowance		$ 3,300	$ 1,100	$ 4,800	$ 1,200
[1]Amounts deemed uncollectible are written-off in operating expenses. For the 2022 second quarter and 2021 second quarter, amounts written off were $3.3 million and $1.1 million, respectively. For the six months ended June 30, 2022 and 2021 period, amounts written off were $4.8 million and $1.2 million, respectively.

Allowance for Expected Credit_4

Allowance for Expected Credit Losses - Reinsurance recoverables (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Credit Loss [Abstract]
Balance at beginning of period	$ 5,941,000	$ 4,041,076	$ 5,880,735	$ 4,500,802
Balance at end of period	5,938,511	4,314,515	5,938,511	4,314,515
Allowance for Expected Credit Losses
Balance at beginning of period	18,483	10,872	13,230	11,636
Change for provision of expected credit losses	(3,743)	157	1,510	(607)
Balance at end of period	$ 14,740	$ 11,029	$ 14,740	$ 11,029

Allowance for Expected Credit_5

Allowance for Expected Credit Losses - Ceded credit risk (Details) - USD ($) $ in Thousands		6 Months Ended	12 Months Ended
		Jun. 30, 2022	Dec. 31, 2021	Mar. 31, 2022	Jun. 30, 2021	Mar. 31, 2021	Dec. 31, 2020
Ceded Credit Risk [Line Items]
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses		$ 5,938,511	$ 5,880,735	$ 5,941,000	$ 4,314,515	$ 4,041,076	$ 4,500,802
Reinsurance recoverable | Reinsurer concentration risk | AM Best A minus Or Better Rating
Ceded Credit Risk [Line Items]
Concentration risk percentage		69.30%	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]	30.60%	30.20%
Reinsurance recoverable | Reinsurer concentration risk | Not Rated | Reinsurance trusts or letters of credit
Ceded Credit Risk [Line Items]
Concentration risk percentage		93%	91%
Stockholders' equity | Reinsurer concentration risk | Largest Balance Due From Any One Carrier
Ceded Credit Risk [Line Items]
Concentration risk percentage		7.80%	6.70%
[1]At June 30, 2022 and December 31, 2021 over 93% 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		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Credit Loss [Abstract]
Balance at beginning of period	$ 1,810,199	$ 1,919,655	$ 1,828,691	$ 1,986,924
Balance at end of period	1,758,018	1,882,948	1,758,018	1,882,948
Allowance for Expected Credit Losses
Balance at beginning of period	3,731	5,853	3,437	8,638
Change for provision of expected credit losses	(726)	(1,382)	(432)	(4,167)
Balance at end of period	$ 3,005	$ 4,471	$ 3,005	$ 4,471

Investment Information - Summar

Investment Information - Summary of available for sale securities (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Mar. 31, 2022	Dec. 31, 2021	Jun. 30, 2021	Mar. 31, 2021	Dec. 31, 2020
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	$ 19,812,903		$ 19,732,825
Gross Unrealized Gains	86,856		198,691
Gross Unrealized Losses	(1,258,588)		(171,544)
Allowance for Expected Credit Losses	(58,410)	$ (34,145)	(2,883)	$ (2,124)	$ (3,830)	$ (2,397)
Cost or Amortized Cost	21,043,045		19,708,561
Municipal bonds
Debt Securities, Available-for-sale [Line Items]
Allowance for Expected Credit Losses	(298)	$ (106)	(2)	$ (6)	$ (2)	$ (11)
Fixed maturities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	17,585,029		17,998,109
Gross Unrealized Gains	84,398		198,123
Gross Unrealized Losses	(1,257,331)		(170,954)
Allowance for Expected Credit Losses	(58,410)		(2,883)
Cost or Amortized Cost	18,816,372		17,973,823
Fixed maturities | Corporate bonds
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	7,288,555		6,553,333
Gross Unrealized Gains	32,021		104,170
Gross Unrealized Losses	(655,664)		(69,194)
Allowance for Expected Credit Losses	(38,494)		(2,037)
Cost or Amortized Cost	7,950,692		6,520,394
Fixed maturities | Mortgage backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	698,168		408,477
Gross Unrealized Gains	4,427		2,825
Gross Unrealized Losses	(55,898)		(5,410)
Allowance for Expected Credit Losses	0		(48)
Cost or Amortized Cost	749,639		411,110
Fixed maturities | Municipal bonds
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	417,380		404,666
Gross Unrealized Gains	4,129		18,724
Gross Unrealized Losses	(18,936)		(1,409)
Allowance for Expected Credit Losses	(298)		(2)
Cost or Amortized Cost	432,485		387,353
Fixed maturities | Commercial mortgage backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	1,023,088		1,046,484
Gross Unrealized Gains	1,533		1,740
Gross Unrealized Losses	(42,056)		(3,117)
Allowance for Expected Credit Losses	(3,594)		(6)
Cost or Amortized Cost	1,067,205		1,047,867
Fixed maturities | US government and government agencies
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	4,368,150		4,772,764
Gross Unrealized Gains	25,112		10,076
Gross Unrealized Losses	(240,786)		(45,967)
Allowance for Expected Credit Losses	0		0
Cost or Amortized Cost	4,583,824		4,808,655
Fixed maturities | Non-US government securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	2,181,943		2,120,294
Gross Unrealized Gains	16,175		54,048
Gross Unrealized Losses	(163,724)		(34,749)
Allowance for Expected Credit Losses	(1,335)		(82)
Cost or Amortized Cost	2,330,827		2,101,077
Fixed maturities | Asset backed securities
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	1,607,745		2,692,091
Gross Unrealized Gains	1,001		6,540
Gross Unrealized Losses	(80,267)		(11,108)
Allowance for Expected Credit Losses	(14,689)		(708)
Cost or Amortized Cost	1,701,700		2,697,367
Short-term investments
Debt Securities, Available-for-sale [Line Items]
Estimated Fair Value	2,227,874		1,734,716
Gross Unrealized Gains	2,458		568
Gross Unrealized Losses	(1,257)		(590)
Allowance for Expected Credit Losses	0		0
Cost or Amortized Cost	$ 2,226,673		$ 1,734,738

Investment Information - Aging

Investment Information - Aging of available for sale securities in an unrealized loss position (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	$ 16,180,106	$ 12,238,683
Estimated Fair Value - 12 Months or More	869,409	297,357
Estimated Fair Value	17,049,515	12,536,040
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(1,145,737)	(157,279)
Gross Unrealized Losses - 12 Months or More	(112,851)	(14,265)
Gross Unrealized Losses	(1,258,588)	(171,544)
Fixed maturities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	15,674,308	11,953,950
Estimated Fair Value - 12 Months or More	869,409	297,357
Estimated Fair Value	16,543,717	12,251,307
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(1,144,480)	(156,689)
Gross Unrealized Losses - 12 Months or More	(112,851)	(14,265)
Gross Unrealized Losses	(1,257,331)	(170,954)
Fixed maturities | Corporate bonds
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	6,583,215	3,639,582
Estimated Fair Value - 12 Months or More	489,098	98,867
Estimated Fair Value	7,072,313	3,738,449
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(580,235)	(63,938)
Gross Unrealized Losses - 12 Months or More	(75,429)	(5,256)
Gross Unrealized Losses	(655,664)	(69,194)
Fixed maturities | Mortgage backed securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	595,485	222,176
Estimated Fair Value - 12 Months or More	61,751	46,809
Estimated Fair Value	657,236	268,985
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(46,415)	(3,545)
Gross Unrealized Losses - 12 Months or More	(9,483)	(1,865)
Gross Unrealized Losses	(55,898)	(5,410)
Fixed maturities | Municipal bonds
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	271,481	26,665
Estimated Fair Value - 12 Months or More	8,876	16,361
Estimated Fair Value	280,357	43,026
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(17,908)	(385)
Gross Unrealized Losses - 12 Months or More	(1,028)	(1,024)
Gross Unrealized Losses	(18,936)	(1,409)
Fixed maturities | Commercial mortgage backed securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	973,212	675,603
Estimated Fair Value - 12 Months or More	0	5,908
Estimated Fair Value	973,212	681,511
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(42,056)	(2,805)
Gross Unrealized Losses - 12 Months or More	0	(312)
Gross Unrealized Losses	(42,056)	(3,117)
Fixed maturities | US government and government agencies
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	4,029,550	4,211,621
Estimated Fair Value - 12 Months or More	69,596	33,373
Estimated Fair Value	4,099,146	4,244,994
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(235,510)	(44,180)
Gross Unrealized Losses - 12 Months or More	(5,276)	(1,787)
Gross Unrealized Losses	(240,786)	(45,967)
Fixed maturities | Non-US government securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	1,929,278	1,511,301
Estimated Fair Value - 12 Months or More	103,969	62,957
Estimated Fair Value	2,033,247	1,574,258
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(148,781)	(31,983)
Gross Unrealized Losses - 12 Months or More	(14,943)	(2,766)
Gross Unrealized Losses	(163,724)	(34,749)
Fixed maturities | Asset backed securities
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	1,292,087	1,667,002
Estimated Fair Value - 12 Months or More	136,119	33,082
Estimated Fair Value	1,428,206	1,700,084
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(73,575)	(9,853)
Gross Unrealized Losses - 12 Months or More	(6,692)	(1,255)
Gross Unrealized Losses	(80,267)	(11,108)
Short-term investments
Debt Securities, Available-for-sale, Unrealized Loss Position, Estimated Fair Value [Abstract]
Estimated Fair Value - Less than 12 Months	505,798	284,733
Estimated Fair Value - 12 Months or More	0	0
Estimated Fair Value	505,798	284,733
Debt Securities, Available-for-sale, Unrealized Loss Position, Accumulated Loss [Abstract]
Gross Unrealized Losses - Less than 12 Months	(1,257)	(590)
Gross Unrealized Losses - 12 Months or More	0	0
Gross Unrealized Losses	$ (1,257)	$ (590)

Investment Information - Maturi

Investment Information - Maturity profile of available for sale securities) (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Estimated Fair Value
Estimated Fair Value	$ 19,812,903	$ 19,732,825
Amortized Cost
Cost or Amortized Cost	21,043,045	19,708,561
Fixed maturities
Estimated Fair Value
Due in one year or less	412,194	300,889
Due after one year through five years	9,423,547	8,355,255
Due after five years through 10 years	4,070,099	4,689,155
Due after 10 years	350,188	505,758
Single maturity date	14,256,028	13,851,057
Estimated Fair Value	17,585,029	17,998,109
Amortized Cost
Due in one year or less	414,752	299,772
Due after one year through five years	9,927,876	8,339,387
Due after five years through 10 years	4,512,685	4,684,393
Due after 10 years	442,515	493,927
Single maturity date	15,297,828	13,817,479
Cost or Amortized Cost	18,816,372	17,973,823
Fixed maturities | Mortgage backed securities
Estimated Fair Value
Securities without single maturity date	698,168	408,477
Estimated Fair Value	698,168	408,477
Amortized Cost
Securities without single maturity date	749,639	411,110
Cost or Amortized Cost	749,639	411,110
Fixed maturities | Commercial mortgage backed securities
Estimated Fair Value
Securities without single maturity date	1,023,088	1,046,484
Estimated Fair Value	1,023,088	1,046,484
Amortized Cost
Securities without single maturity date	1,067,205	1,047,867
Cost or Amortized Cost	1,067,205	1,047,867
Fixed maturities | Asset backed securities
Estimated Fair Value
Securities without single maturity date	1,607,745	2,692,091
Estimated Fair Value	1,607,745	2,692,091
Amortized Cost
Securities without single maturity date	1,701,700	2,697,367
Cost or Amortized Cost	$ 1,701,700	$ 2,697,367

Investment Information - Other

Investment Information - Other investments (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Schedule Of Other Investments [Line Items]
Other investments, at fair value	$ 1,634,368	$ 1,973,550
Fixed maturities
Schedule Of Other Investments [Line Items]
Other investments, at fair value	525,451	416,698
Other investments
Schedule Of Other Investments [Line Items]
Other investments, at fair value	1,054,771	1,432,553
Other investments | Lending
Schedule Of Other Investments [Line Items]
Other investments, at fair value	427,812	536,345
Other investments | Investment grade fixed income
Schedule Of Other Investments [Line Items]
Other investments, at fair value	221,484	147,810
Other investments | Term loan investments
Schedule Of Other Investments [Line Items]
Other investments, at fair value	152,277	484,950
Other investments | Private equity
Schedule Of Other Investments [Line Items]
Other investments, at fair value	124,282	91,126
Other investments | Energy
Schedule Of Other Investments [Line Items]
Other investments, at fair value	74,234	81,692
Other investments | Credit related funds
Schedule Of Other Investments [Line Items]
Other investments, at fair value	54,682	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	39,657	97,806
Equity securities
Schedule Of Other Investments [Line Items]
Other investments, at fair value	$ 14,489	$ 26,493

Investment Information - Equity

Investment Information - Equity method investments (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 3,496,341	$ 3,077,611
Credit related funds
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	1,119,711	1,022,334
Private equity
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	646,904	436,042
Real estate
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	455,044	396,395
Lending
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	447,028	376,649
Equity securities
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	350,587	395,090
Infrastructure
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	231,816	230,070
Energy
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	115,514	119,141
Fixed income
Schedule of Equity Method Investments [Line Items]
Investments accounted for using the equity method	$ 129,737	$ 101,890

Investment Information - Limite

Investment Information - Limited partnership interests (Details) - USD ($) $ in Thousands		Jun. 30, 2022	Dec. 31, 2021
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss		$ 3,625,167	$ 3,248,206
Aggregate unfunded commitments		3,500,000	3,000,000
Equity method investments
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss	[1]	3,496,341	3,077,611
Aggregate unfunded commitments		3,000,000	2,600,000
Fair value option
Schedule of Equity Method Investments [Line Items]
Maximum Exposure to Loss	[2]	128,826	170,595
Aggregate unfunded commitments		$ 21,700	$ 18,800
[1]Aggregate unfunded commitments were $3.0 billion at June 30, 2022, compared to $2.6 billion at December 31, 2021.[2]Aggregate unfunded commitments were $21.7 million at June 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		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Net investment income:
Gross investment income		$ 123,567	$ 135,176	$ 226,509	$ 261,142
Investment expenses		(17,175)	(23,563)	(39,681)	(50,673)
Net investment income		106,392	111,613	186,828	210,469
Fixed maturities
Net investment income:
Gross investment income		105,342	88,625	187,395	179,251
Term loans
Net investment income:
Gross investment income		401	16,879	2,018	31,607
Equity securities
Net investment income:
Gross investment income		6,121	8,584	12,359	14,234
Short-term investments
Net investment income:
Gross investment income		4,120	1,138	6,695	1,745
Other
Net investment income:
Gross investment income	[1]	$ 7,583	$ 19,950	$ 18,042	$ 34,305
[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		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Available for sale securities:
Available for sale securities, gross gains on investment sales		$ 15,186	$ 115,541	$ 34,893	$ 180,543
Available for sale securities, gross losses on investment sales		(57,176)	(50,627)	(165,523)	(113,625)
Equity securities, at fair value:
Net realized gains (losses) on sales during the period		16,879	33,570	82,090	71,419
Net unrealized gains (losses) on equity securities still held at reporting date		(106,375)	65,847	(282,570)	85,555
Allowance for credit losses:
Allowance for credit losses - investments related		(25,026)	896	(56,748)	(752)
Allowance for credit losses - underwriting related		842	1,381	(3,444)	6,649
Derivative instruments	[1]	(45,684)	(51,109)	(69,395)	(14,993)
Other		(128)	10,224	(3,537)	(12,821)
Net realized gains (losses)		(266,579)	202,907	(558,993)	345,368
Fixed maturities
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		(39,255)	10,912	(69,844)	27,465
Other investments
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		(21,710)	60,884	(17,321)	107,739
Equity securities
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		(2,124)	5,492	(5,437)	7,557
Short-term investments
Available for sale securities:
Change in fair value of assets and liabilities accounted for using the fair value option		$ (2,008)	$ (104)	$ (2,157)	$ 632
[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		6 Months Ended		12 Months Ended
	Jun. 30, 2022 USD ($)	Jun. 30, 2021 USD ($)	Jun. 30, 2022 USD ($)	Jun. 30, 2021 USD ($)	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	$ 967,603		$ 967,603		$ 1,135,655
Income (loss) from operating affiliates	$ 4,640	$ 24,476	$ 29,158	$ 99,933
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	$ 536,000		$ 536,000		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	$ 309,600		$ 309,600		375,700
Operating affiliate, gain on acquisition					$ 95,700
Issued Shares Excluding Treasury Stock | Coface
Schedule of Equity Method Investments [Line Items]
Percentage ownership	30.09%		30.09%
Greysbridge Holdings Ltd | Kelso And Company
Schedule of Equity Method Investments [Line Items]
Percentage ownership							30%
Greysbridge Holdings Ltd | Warburg Pincus LLC
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		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Allowance for expected credit losses
Balance at beginning of period		$ 34,145	$ 3,830	$ 2,883	$ 2,397
Additions for current-period provision for expected credit losses		18,506	59	49,741	2,662
Additions (reductions) for previously recognized expected credit losses		6,440	(791)	6,921	(1,722)
Reductions due to disposals		(681)	(974)	(1,135)	(1,213)
Balance at end of period		58,410	2,124	58,410	2,124
Structured securities
Allowance for expected credit losses
Balance at beginning of period	[1]	6,998	1,207	802	1,490
Additions for current-period provision for expected credit losses	[1]	4,788	52	10,778	234
Additions (reductions) for previously recognized expected credit losses	[1]	6,705	(383)	7,192	(765)
Reductions due to disposals	[1]	(208)	(117)	(489)	(200)
Balance at end of period	[1]	18,283	759	18,283	759
Municipal bonds
Allowance for expected credit losses
Balance at beginning of period		106	2	2	11
Additions for current-period provision for expected credit losses		252	0	347	0
Additions (reductions) for previously recognized expected credit losses		(60)	4	(51)	(5)
Reductions due to disposals		0	0	0	0
Balance at end of period		298	6	298	6
Corporate bonds
Allowance for expected credit losses
Balance at beginning of period		27,041	2,621	2,079	896
Additions for current-period provision for expected credit losses		13,466	7	38,616	2,428
Additions (reductions) for previously recognized expected credit losses		(205)	(412)	(220)	(952)
Reductions due to disposals		(473)	(857)	(646)	(1,013)
Balance at end of period		$ 39,829	$ 1,359	$ 39,829	$ 1,359
[1]Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

Investment Information - Restri

Investment Information - Restricted assets (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Restricted Assets [Line Items]
Restricted assets	$ 8,413,726	$ 8,249,732
Collateral or guarantees - affiliated transactions
Restricted Assets [Line Items]
Restricted assets	4,193,561	4,223,955
Collateral or guarantees - third party agreements
Restricted Assets [Line Items]
Restricted assets	2,953,800	2,721,160
Deposits with US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	781,024	798,100
Deposits with non-US regulatory authorities
Restricted Assets [Line Items]
Restricted assets	$ 485,341	$ 506,517

Investment Information - Cash a

Investment Information - Cash and restricted cash (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021	Jun. 30, 2021	Dec. 31, 2020
Disclosure Investment Information [Abstract]
Cash	$ 813,548	$ 858,668
Restricted cash (included in ‘other assets’)	414,683	456,103
Cash and restricted cash	$ 1,228,231	$ 1,314,771	$ 1,818,463	$ 1,290,544

Investment Information - Narrat

Investment Information - Narrative (Details) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022 USD ($) lots	Jun. 30, 2021 USD ($)	Jun. 30, 2022 USD ($) lots	Jun. 30, 2021 USD ($)	Dec. 31, 2021 USD ($) lots
Continuous unrealized loss, qualitative disclosures:
Number of positions in an unrealized loss position (lots) | lots	8,360		8,360		4,700
Total number of positions (lots) | lots	10,440		10,440		10,240
Largest single loss	$ 5,700		$ 5,700		$ 1,100
Narrative items:
Equity securities, at fair value	772,689		772,689		$ 1,804,170
Equity in net (loss) income of investment funds accounted for using the equity method	$ 58,061	$ 122,186	$ 94,366	$ 193,872
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		Jun. 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		$ 7,137,960	$ 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		4,341,399	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		4,341,399	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		2,049,235	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		736,343	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		10,983	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		886	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		10,097	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		14,284,586	14,923,923
Liabilities measured at fair value		(75,147)	(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		(75,147)	(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		3,929	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		13,237,193	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		7,284,985	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		698,168	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		417,380	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		1,023,088	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		26,751	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		2,181,943	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		1,604,878	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		178,639	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		33,440	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		122,033	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		709,352	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		522,707	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		611	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		2,133	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		38,771	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		0	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		145,130	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		47,066	39,007
Liabilities measured at fair value		(16,205)	(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		(16,205)	(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		6,437	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		3,570	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		2,867	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		2,906	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		37,723	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		4,392	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		33,331	27,981
Estimated Fair Value
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets measured at fair value		22,345,922	23,687,513
Liabilities measured at fair value		(91,352)	(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		(16,205)	(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		(75,147)	(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		3,929	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		17,585,029	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		7,288,555	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		698,168	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		417,380	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		1,023,088	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		4,368,150	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		2,181,943	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		1,607,745	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		2,227,874	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		772,689	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		122,033	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		1,634,368	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		522,707	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		611	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		2,133	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		39,657	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		14,489	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		178,461	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]	$ 876,310	$ 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		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Other liabilities
Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		$ (17,591)	$ (465)	$ (16,960)	$ (461)
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(97)	(1)	(195)	(5)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		1,483	0	950	0
Purchases, issuances, sales and settlements
Purchases		0	0	0	0
Issuances		0	0	0	0
Sales		0	0	0	0
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		(16,205)	(466)	(16,205)	(466)
Available for sale | Structured securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period	[2]	3,152	3,472	3,347	3,426
Total gains or (losses) (realized/unrealized) - included in earnings	[1],[2]	(1)	12	9	(56)
Total gains or (losses) (realized/unrealized) - included in other comprehensive income	[2]	(85)	(57)	(145)	57
Purchases, issuances, sales and settlements
Purchases	[2]	0	0	0	0
Issuances	[2]	0	0	0	0
Sales	[2]	0	0	0	0
Settlements	[2]	(199)	(3)	(344)	(3)
Transfers in and/or out of Level 3	[2]	0	0	0	0
Balance at end of period	[2]	2,867	3,424	2,867	3,424
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]	0	0	0	0
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	0	0	0
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	0	3,557	0
Balance at end of period		3,570	13	3,570	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	989	0	985
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	0	9	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	0	0	0
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		0	998	0	998
Fair value option | Other investments
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		22,602	67,930	27,981	67,103
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	27	633	34	881
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		10,702	5,638	10,770	13,003
Issuances		0	0	0	0
Sales		0	(301)	(2,471)	(7,087)
Settlements		0	0	(2,983)	0
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		33,331	73,900	33,331	73,900
Fair value option | Equity securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		4,511	71,176	4,748	68,988
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(119)	2,502	(356)	4,690
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	0	0	0
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		4,392	73,678	4,392	73,678
Equity securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]
Balance at beginning of period		2,768	43,112	2,918	42,015
Total gains or (losses) (realized/unrealized) - included in earnings	[1]	(89)	922	(236)	1,826
Total gains or (losses) (realized/unrealized) - included in other comprehensive income		0	0	0	0
Purchases, issuances, sales and settlements
Purchases		227	5,102	227	5,295
Issuances		0	0	0	0
Sales		0	0	(3)	0
Settlements		0	0	0	0
Transfers in and/or out of Level 3		0	0	0	0
Balance at end of period		$ 2,906	$ 49,136	$ 2,906	$ 49,136
[1]Gains or losses were included in net realized gains (losses).[2]Includes asset backed securities, mortgage backed securities and commercial mortgage backed securities.

Fair Value - Narrative (Details

Fair Value - Narrative (Details) - USD ($) $ in Thousands	Jun. 30, 2022	Dec. 31, 2021
Fair Value Disclosures [Abstract]
Total assets and liabilities measured at fair value	$ 22,400,000	$ 23,800,000
Total assets and liabilities measured at fair value priced using non-binding broker quotes	$ 10,900	$ 7,700
Total assets and liabilities measured at fair value priced using non-binding broker quotes (percentage)	0%	0%
Senior notes	$ 2,724,896	$ 2,724,394
Estimated fair value of senior notes	$ 2,600,000	$ 3,300,000

Derivative Instruments - Fair v

Derivative Instruments - Fair value and notional amount of derivatives (Details) - USD ($) $ in Thousands		Jun. 30, 2022	Dec. 31, 2021
Derivative offsetting
Derivative assets subject to master netting agreements		$ 116,900	$ 122,300
Derivative liabilities subject to master netting agreements		75,100	53,900
Not designated as hedging instrument
Derivative [Line Items]
Asset derivatives - fair value		122,033	127,121
Liability derivatives - fair value		(75,147)	(54,224)
Not designated as hedging instrument | Futures contracts
Derivative [Line Items]
Net derivatives - notional value	[1]	2,794,246	2,826,564
Not designated as hedging instrument | Futures contracts | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	49,695	34,999
Not designated as hedging instrument | Futures contracts | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	(22,561)	(9,808)
Not designated as hedging instrument | Foreign currency forward contracts
Derivative [Line Items]
Net derivatives - notional value	[1]	908,192	915,962
Not designated as hedging instrument | Foreign currency forward contracts | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	9,556	7,734
Not designated as hedging instrument | Foreign currency forward contracts | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	(18,884)	(11,390)
Not designated as hedging instrument | TBAs
Derivative [Line Items]
Net derivatives - notional value	[1]	0	11,227
Not designated as hedging instrument | TBAs | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	0	11,227
Not designated as hedging instrument | TBAs | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	0	0
Not designated as hedging instrument | Other
Derivative [Line Items]
Net derivatives - notional value	[1]	3,849,244	3,736,773
Not designated as hedging instrument | Other | Other assets
Derivative [Line Items]
Asset derivatives - fair value	[2]	62,782	73,161
Not designated as hedging instrument | Other | Other liabilities
Derivative [Line Items]
Liability derivatives - fair value	[2]	$ (33,702)	$ (33,026)
[1]Represents the absolute notional value of all outstanding contracts, consisting of long and short positions.[2]The fair value of asset derivatives are included in ‘other assets’ and the fair value of liability derivatives are included in ‘other liabilities.’

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		6 Months Ended
		Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments	[1]	$ (45,684)	$ (51,109)	$ (69,395)	$ (14,993)
Not designated as hedging instrument
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(45,684)	(51,109)	(69,395)	(14,993)
Not designated as hedging instrument | Futures contracts
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(39,205)	(54,759)	(85,979)	(7,321)
Not designated as hedging instrument | Foreign currency forward contracts
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		(25,638)	1,295	(27,676)	(20,776)
Not designated as hedging instrument | TBAs
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments		0	0	(51)	0
Not designated as hedging instrument | Other
Net realized gains (losses) on derivative instruments
Net realized gains (losses) on derivative instruments	[2]	$ 19,159	$ 2,355	$ 44,311	$ 13,104
[1]See note 9 for information on the Company’s derivative instruments.

Commitments and Contingencies (

Commitments and Contingencies (Details) - USD ($) $ in Millions		6 Months Ended
	Apr. 07, 2022	Jun. 30, 2022	Jun. 30, 2021	Dec. 31, 2021
Commitments and Contingencies Disclosure [Abstract]
Investment commitments		$ 3,500		$ 3,000
Interest paid on senior notes and other borrowings		64.6	$ 74.7
Credit Agreement
Line of Credit Facility [Line Items]
Maximum borrowing capacity	$ 925
Credit facility term	5 years
Optional increased capacity	$ 1,300
Secured Facility
Line of Credit Facility [Line Items]
Maximum borrowing capacity	425	425
Revolving credit agreement borrowings		333.4
Remaining capacity		91.6
Unsecured Facility
Line of Credit Facility [Line Items]
Maximum borrowing capacity	$ 500
Secured Letters of Credit | Barbican Group Holdings Limited
Line of Credit Facility [Line Items]
Revolving credit agreement borrowings		23.6
Unsecured Letters of Credit | Barbican Group Holdings Limited
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
	Mar. 31, 2014	Jun. 30, 2022	Jun. 30, 2021	Jul. 01, 2021
Variable Interest Entity [Line Items]
Net cash provided by (used for) operating activities		$ 1,453,968	$ 1,612,572
Net cash provided by (used for) investing activities		(815,602)	(1,093,678)
Net cash (used for) provided by financing activities		$ (682,116)	22,415
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 - Non-redeemable noncontrolling interests (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Noncontrolling Interest [Line Items]
Amounts attributable to noncontrolling interests	$ 0	$ 41,617	$ 0	$ 78,314
Other comprehensive (income) loss attributable to noncontrolling interests	0	10	0	(4,560)
Non-redeemable noncontrolling interests, end of period	$ 0	918,874	$ 0	918,874
Somers Holdings Ltd
Noncontrolling Interest [Line Items]
Non-redeemable noncontrolling interests, beginning of period		876,864		823,007
Additional paid in capital attributable to noncontrolling interests		383		22,113
Amounts attributable to noncontrolling interests		41,617		78,314
Other comprehensive (income) loss attributable to noncontrolling interests		10		(4,560)
Non-redeemable noncontrolling interests, end of period		$ 918,874		$ 918,874

Variable Interest Entities an_5

Variable Interest Entities and Noncontrolling Interests - Redeemable noncontrolling interests (Details) - USD ($) $ / shares in Units, $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021	Mar. 31, 2014
Redeemable Noncontrolling Interest [Line Items]
Redeemable noncontrolling interests, beginning of period			$ 9,233
Redeemable noncontrolling interests, end of period	$ 8,459		8,459
Somers Holdings Ltd
Redeemable Noncontrolling Interest [Line Items]
Redeemable noncontrolling interests, beginning of period	9,763	$ 57,670	9,233	$ 58,548
Accretion of preference share issuance costs	0	23	0	46
Other	(1,304)	(160)	(774)	(1,061)
Redeemable noncontrolling interests, end of period	$ 8,459	$ 57,533	$ 8,459	$ 57,533
Cumulative redeemable preference shares | Somers Holdings Ltd
Redeemable Noncontrolling Interest [Line Items]
Par value per share					$ 0.01
Liquidation preference per share					25
Issue price per share					$ 24.50

Variable Interest Entities an_6

Variable Interest Entities and Noncontrolling Interests - Income or loss attributable to third party investors (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Noncontrolling Interest [Abstract]
Amounts attributable to non-redeemable noncontrolling interests	$ 0	$ (41,617)	$ 0	$ (78,314)
Amounts attributable to redeemable noncontrolling interests	399	(1,561)	(1,233)	(2,416)
Net (income) loss attributable to noncontrolling interests	$ 399	$ (43,178)	$ (1,233)	$ (80,730)

Variable Interest Entities an_7

Variable Interest Entities and Noncontrolling Interests - Other variable interest entity disclosures (Details) - USD ($) $ in Thousands		Jun. 30, 2022	Dec. 31, 2021
Variable Interest Entity [Line Items]
Total VIE Assets		$ 45,719,194	$ 45,100,945
Maximum Exposure to Loss, Total		3,625,167	3,248,206
Variable Interest Entity, Not Primary Beneficiary
Variable Interest Entity [Line Items]
Total VIE Assets		3,938,695	4,336,596
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(5,125)	(4,434)
Maximum Exposure to Loss - Off-Balance Sheet		34,088	42,202
Maximum Exposure to Loss, Total		28,963	37,768
Remaining Coverage, Amount		316,457
Variable Interest Entity, Not Primary Beneficiary | 2017-1 Ltd. (Oct-17)
Variable Interest Entity [Line Items]
Total VIE Assets		61,328	108,368
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(68)	(159)
Maximum Exposure to Loss - Off-Balance Sheet		274	424
Maximum Exposure to Loss, Total		206	265
Variable Interest Entity, Not Primary Beneficiary | 2018-1 Ltd. (Apr-18)
Variable Interest Entity [Line Items]
Total VIE Assets		122,190	181,136
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(342)	(528)
Maximum Exposure to Loss - Off-Balance Sheet		965	1,268
Maximum Exposure to Loss, Total		623	740
Variable Interest Entity, Not Primary Beneficiary | 2018-3 Ltd. (Oct-18)
Variable Interest Entity [Line Items]
Total VIE Assets		244,257	302,563
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(566)	(1,018)
Maximum Exposure to Loss - Off-Balance Sheet		1,522	2,496
Maximum Exposure to Loss, Total		956	1,478
Variable Interest Entity, Not Primary Beneficiary | 2019-1 Ltd. (Mar-19)
Variable Interest Entity [Line Items]
Total VIE Assets		134,972	181,324
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(127)	(380)
Maximum Exposure to Loss - Off-Balance Sheet		988	5,807
Maximum Exposure to Loss, Total		861	5,427
Variable Interest Entity, Not Primary Beneficiary | 2019-2 Ltd. (Apr-19)
Variable Interest Entity [Line Items]
Total VIE Assets		383,737	398,316
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(426)	(515)
Maximum Exposure to Loss - Off-Balance Sheet		5,323	3,998
Maximum Exposure to Loss, Total		4,897	3,483
Variable Interest Entity, Not Primary Beneficiary | 2019-3 Ltd. (Jul-19)
Variable Interest Entity [Line Items]
Total VIE Assets		296,466	409,859
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(282)	(584)
Maximum Exposure to Loss - Off-Balance Sheet		2,154	3,190
Maximum Exposure to Loss, Total		1,872	2,606
Variable Interest Entity, Not Primary Beneficiary | 2019-4 Ltd. (Oct-19)
Variable Interest Entity [Line Items]
Total VIE Assets		312,668	411,954
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(306)	(462)
Maximum Exposure to Loss - Off-Balance Sheet		4,702	4,759
Maximum Exposure to Loss, Total		4,396	4,297
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-2 Ltd (Sep-20)
Variable Interest Entity [Line Items]
Total VIE Assets		151,543	217,766
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(58)	(177)
Maximum Exposure to Loss - Off-Balance Sheet		1,331	1,984
Maximum Exposure to Loss, Total		1,273	1,807
Remaining Coverage, Amount	[1]	442
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-3 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		303,011	348,818
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(26)	(128)
Maximum Exposure to Loss - Off-Balance Sheet		4,388	5,793
Maximum Exposure to Loss, Total		4,362	5,665
Remaining Coverage, Amount	[1]	10,779
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2020-4 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		124,672	176,826
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		23	(50)
Maximum Exposure to Loss - Off-Balance Sheet		1,267	1,630
Maximum Exposure to Loss, Total		1,290	1,580
Remaining Coverage, Amount	[1]	5,900
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-1 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		519,641	568,986
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(1,006)	(303)
Maximum Exposure to Loss - Off-Balance Sheet		2,771	3,283
Maximum Exposure to Loss, Total		1,765	2,980
Remaining Coverage, Amount	[1]	48,841
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-2 Ltd. (Jun-21)
Variable Interest Entity [Line Items]
Total VIE Assets		492,837	522,807
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(577)	281
Maximum Exposure to Loss - Off-Balance Sheet		3,505	4,124
Maximum Exposure to Loss, Total		2,928	4,405
Remaining Coverage, Amount	[1]	85,717
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2021-3 Ltd
Variable Interest Entity [Line Items]
Total VIE Assets		507,873	507,873
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(1,082)	(411)
Maximum Exposure to Loss - Off-Balance Sheet		2,878	3,446
Maximum Exposure to Loss, Total		1,796	$ 3,035
Remaining Coverage, Amount	[1]	131,518
Variable Interest Entity, Not Primary Beneficiary | Bellemeade 2022-1 Ltd.
Variable Interest Entity [Line Items]
Total VIE Assets		283,500
Maximum Exposure to Loss - On-Balance Sheet (Asset) Liability		(282)
Maximum Exposure to Loss - Off-Balance Sheet		2,020
Maximum Exposure to Loss, Total		1,738
Remaining Coverage, Amount	[1]	$ 33,260
[1]Coverage from a separate panel of reinsurers remaining at June 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		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Reclassification Adjustment out of Accumulated Other Comprehensive Income [Line Items]
Provision for credit losses	$ (25,026)	$ 896	$ (56,748)	$ (752)
Income tax expense	(22,323)	(51,179)	(33,942)	(90,039)
Net of tax	403,945	718,664	601,377	1,194,372
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)	(41,990)	64,914	(130,630)	66,918
Provision for credit losses	(25,026)	896	(56,748)	(751)
Income (loss) before income taxes and income (loss) from operating affiliates	(67,016)	65,810	(187,378)	66,167
Income tax expense	9,306	(5,263)	27,390	(8,317)
Net of tax	$ (57,710)	$ 60,547	$ (159,988)	$ 57,850

Other Comprehensive Income (L_4

Other Comprehensive Income (Loss) - Components of other comprehensive income (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021
Before tax amount:
Unrealized holding gains (losses) arising during period, before tax	$ (676,048)	$ 91,057	$ (1,460,938)	$ (203,303)
Less reclassification of net realized gains included in net income, before tax	(67,016)	65,810	(187,378)	66,167
Foreign currency translation adjustments, before tax	(68,562)	6,392	(71,127)	(22,023)
Other comprehensive income (loss), before tax	(677,594)	31,639	(1,344,687)	(291,493)
Tax expense (benefit):
Unrealized holding gains (losses) arising during period, tax	(78,043)	12,486	(178,578)	(20,124)
Less reclassification of net realized gains included in net income, tax	(9,306)	5,263	(27,390)	8,317
Foreign currency translation adjustments, tax	(37)	187	166	356
Other comprehensive income (loss), tax	(68,774)	7,410	(151,022)	(28,085)
Net of tax amount:
Unrealized holding gains (losses) arising during period, net of tax	(598,005)	78,571	(1,282,360)	(183,179)
Less reclassification of net realized gains included in net income, net of tax	(57,710)	60,547	(159,988)	57,850
Foreign currency translation adjustments, net of tax	(68,525)	6,205	(71,293)	(22,379)
Net current period other comprehensive income (loss)	$ (608,820)	$ 24,229	$ (1,193,665)	$ (263,408)

Income Taxes (Details)

Income Taxes (Details) - USD ($) $ in Millions	6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Dec. 31, 2021
Income Tax Disclosure [Abstract]
Effective tax rate on income before income taxes (percentage)	5.30%	7%
Net deferred tax asset	$ 411.1		$ 194
Income taxes paid	$ 128.6	$ 141.1

Transactions With Related Par_2

Transactions With Related Parties (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Jun. 30, 2022	Jun. 30, 2021	Jun. 30, 2022	Jun. 30, 2021	Mar. 31, 2022	Dec. 31, 2021	Jul. 01, 2021	Mar. 31, 2021	Jan. 01, 2021	Dec. 31, 2020
Related Party Transaction [Line Items]
Premiums ceded	$ 1,185,088	$ 886,767	$ 2,351,723	$ 1,775,516
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	5,938,511	$ 4,314,515	5,938,511	$ 4,314,515	$ 5,941,000	$ 5,880,735		$ 4,041,076		$ 4,500,802
Reinsurance balances payable	1,634,700		1,634,700			$ 1,583,253
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			424,600
Reinsurance recoverable on unpaid and paid losses and loss adjustment expenses	964,700		964,700
Reinsurance balances payable	358,400		358,400
Senior notes, face amount	$ 35,000		$ 35,000
Senior notes, stated percentage	6.50%		6.50%
Operating affiliates | Somers Holdings Ltd | Non-cumulative preferred shares
Related Party Transaction [Line Items]
Percentage ownership	6.60%		6.60%