Segment Information - Summary of underwriting income or loss by segment (Details) $ in Thousands		3 Months Ended
		Mar. 31, 2022 USD ($) segment	Mar. 31, 2021 USD ($)	Dec. 31, 2021 USD ($)
Segment Reporting Information [Line Items]
Gross premiums written		$ 3,800,775	$ 3,397,206
Premiums ceded		(1,166,635)	(888,749)
Net premiums written		2,634,140	2,508,457
Change in unearned premiums		(513,507)	(560,035)
Net premiums earned		2,120,633	1,948,422
Other underwriting income (loss)		5,897	6,110
Losses and loss adjustment expenses		(1,000,835)	(1,203,100)
Acquisition expenses		(378,159)	(304,481)
Other operating expenses		(289,943)	(261,033)
Underwriting income (loss)		457,593	185,918
Net investment income		80,436	98,856
Net realized gains (losses)		(292,414)	142,461
Equity in net income (loss) of investment funds accounted for using the equity method		36,305	71,686
Other income (loss)		(9,025)	(1,741)
Corporate expenses		(31,935)	(23,468)
Transaction costs and other		(397)	(1,916)
Amortization of intangible assets		(27,167)	(14,402)
Interest expense		(32,708)	(38,346)
Net foreign exchange gains (losses)		3,845	20,063
Income (loss) before income taxes and income (loss) from operating affiliates		184,533	439,111
Income tax expense (benefit)		(11,619)	(38,860)
Income (loss) from operating affiliates		24,518	75,457
Net income (loss)		197,432	475,708
Amounts attributable to redeemable noncontrolling interests		(1,632)	(855)
Amounts attributable to non-redeemable noncontrolling interests		0	(36,697)
Net income (loss) available to Arch		195,800	438,156
Preferred dividends		(10,184)	(10,403)
Net income (loss) available to Arch common shareholders		$ 185,616	$ 427,753
Underwriting Ratios
Loss ratio		47.20%	61.70%
Acquisition expense ratio		17.80%	15.60%
Other operating expense ratio		13.70%	13.40%
Combined ratio		78.70%	90.70%
Goodwill and intangible assets		$ 926,427	$ 679,509	$ 944,983
Operating segments | Underwriting Segments
Segment Reporting Information [Line Items]
Number of segments | segment		3
Gross premiums written	[1]	$ 3,800,775	3,277,293
Premiums ceded		(1,166,635)	(948,147)
Net premiums written		2,634,140	2,329,146
Change in unearned premiums		(513,507)	(528,455)
Net premiums earned		2,120,633	1,800,691
Other underwriting income (loss)		5,897	5,699
Losses and loss adjustment expenses		(1,000,835)	(1,084,306)
Acquisition expenses		(378,159)	(276,329)
Other operating expenses		(289,943)	(246,758)
Underwriting income (loss)		457,593	198,997
Net investment income		80,436	78,729
Net realized gains (losses)		(292,414)	101,336
Equity in net income (loss) of investment funds accounted for using the equity method		36,305	71,686
Other income (loss)		(9,025)	(1,741)
Corporate expenses	[2]	(31,935)	(23,468)
Transaction costs and other	[2]	(397)	(1,201)
Amortization of intangible assets		(27,167)	(14,402)
Interest expense		(32,708)	(34,197)
Net foreign exchange gains (losses)		3,845	21,505
Income (loss) before income taxes and income (loss) from operating affiliates		184,533	397,244
Income tax expense (benefit)		(11,619)	(38,852)
Income (loss) from operating affiliates		24,518	75,457
Net income (loss)		197,432	433,849
Amounts attributable to redeemable noncontrolling interests		(1,632)	117
Amounts attributable to non-redeemable noncontrolling interests			0
Net income (loss) available to Arch		195,800	433,966
Preferred dividends		(10,184)	(10,403)
Net income (loss) available to Arch common shareholders		$ 185,616	$ 423,563
Underwriting Ratios
Loss ratio		47.20%	60.20%
Acquisition expense ratio		17.80%	15.30%
Other operating expense ratio		13.70%	13.70%
Combined ratio		78.70%	89.20%
Goodwill and intangible assets		$ 926,427	$ 671,859
Operating segments | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,719,605	1,415,886
Premiums ceded		(512,709)	(421,047)
Net premiums written		1,206,896	994,839
Change in unearned premiums		(180,200)	(175,365)
Net premiums earned		1,026,696	819,474
Other underwriting income (loss)		0	0
Losses and loss adjustment expenses		(600,739)	(535,747)
Acquisition expenses		(195,650)	(128,222)
Other operating expenses		(166,825)	(137,113)
Underwriting income (loss)		$ 63,482	$ 18,392
Underwriting Ratios
Loss ratio		58.50%	65.40%
Acquisition expense ratio		19.10%	15.60%
Other operating expense ratio		16.20%	16.70%
Combined ratio		93.80%	97.70%
Goodwill and intangible assets		$ 249,423	$ 276,211
Operating segments | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,718,942	1,471,060
Premiums ceded		(579,818)	(471,948)
Net premiums written		1,139,124	999,112
Change in unearned premiums		(334,724)	(354,212)
Net premiums earned		804,400	644,900
Other underwriting income (loss)		836	(1,198)
Losses and loss adjustment expenses		(454,700)	(484,870)
Acquisition expenses		(171,996)	(118,025)
Other operating expenses		(69,776)	(60,514)
Underwriting income (loss)		$ 108,764	$ (19,707)
Underwriting Ratios
Loss ratio		56.50%	75.20%
Acquisition expense ratio		21.40%	18.30%
Other operating expense ratio		8.70%	9.40%
Combined ratio		86.60%	102.90%
Goodwill and intangible assets		$ 183,675	$ 17,807
Operating segments | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[1]	364,839	391,246
Premiums ceded		(76,719)	(56,051)
Net premiums written		288,120	335,195
Change in unearned premiums		1,417	1,122
Net premiums earned		289,537	336,317
Other underwriting income (loss)		5,061	6,897
Losses and loss adjustment expenses		54,604	(63,689)
Acquisition expenses		(10,513)	(30,082)
Other operating expenses		(53,342)	(49,131)
Underwriting income (loss)		$ 285,347	$ 200,312
Underwriting Ratios
Loss ratio		(18.90%)	18.90%
Acquisition expense ratio		3.60%	8.90%
Other operating expense ratio		18.40%	14.60%
Combined ratio		3.10%	42.40%
Goodwill and intangible assets		$ 493,329	$ 377,841
Operating segments | Corporate and Other Segments
Segment Reporting Information [Line Items]
Number of segments | segment		2
Gross premiums written	[1]	$ 0	216,523
Premiums ceded		0	(37,212)
Net premiums written		0	179,311
Change in unearned premiums		0	(31,580)
Net premiums earned		0	147,731
Other underwriting income (loss)		0	411
Losses and loss adjustment expenses		0	(118,794)
Acquisition expenses		0	(28,152)
Other operating expenses		0	(14,275)
Underwriting income (loss)		0	(13,079)
Net investment income		0	20,127
Net realized gains (losses)		0	41,125
Equity in net income (loss) of investment funds accounted for using the equity method		0	0
Other income (loss)		0	0
Corporate expenses	[2]	0	0
Transaction costs and other	[2]	0	(715)
Amortization of intangible assets		0	0
Interest expense		0	(4,149)
Net foreign exchange gains (losses)		0	(1,442)
Income (loss) before income taxes and income (loss) from operating affiliates		0	41,867
Income tax expense (benefit)		0	(8)
Income (loss) from operating affiliates		0	0
Net income (loss)		0	41,859
Amounts attributable to redeemable noncontrolling interests		0	(972)
Amounts attributable to non-redeemable noncontrolling interests			(36,697)
Net income (loss) available to Arch		0	4,190
Preferred dividends		0	0
Net income (loss) available to Arch common shareholders		$ 0	$ 4,190
Underwriting Ratios
Loss ratio		0.00%	80.40%
Acquisition expense ratio		0.00%	19.10%
Other operating expense ratio		0.00%	9.70%
Combined ratio		0.00%	109.20%
Goodwill and intangible assets		$ 0	$ 7,650

[1] Certain amounts included in the gross premiums written of each segment are related to intersegment transactions. Accordingly, the sum of gross premiums written for each segment does not agree to the total gross premiums written as shown in the table above due to the elimination of intersegment transactions in the total.

[2] Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’