Segment Information - Summary of underwriting income or loss by segment (Details) $ in Thousands		3 Months Ended
		Mar. 31, 2021 USD ($) segment	Mar. 31, 2020 USD ($)	Dec. 31, 2020 USD ($)
Segment Reporting Information [Line Items]
Gross premiums written		$ 3,397,206	$ 2,832,830
Premiums ceded		(888,749)	(695,584)
Net premiums written		2,508,457	2,137,246
Change in unearned premiums		(560,035)	(392,802)
Net premiums earned		1,948,422	1,744,444
Other underwriting income (loss)		6,110	6,852
Losses and loss adjustment expenses		(1,203,100)	(1,115,419)
Acquisition expenses		(304,481)	(247,283)
Other operating expenses		(261,033)	(234,544)
Underwriting income (loss)		185,918	154,050
Net investment income		98,856	145,153
Net realized gains (losses)		142,461	(366,960)
Equity in net income (loss) of investment funds accounted for using the equity method		71,686	(4,209)
Other income (loss)		(1,741)	32
Corporate expenses		(23,468)	(18,201)
Transaction costs and other		(1,916)	(2,595)
Amortization of intangible assets		(14,402)	(16,631)
Interest expense		(38,346)	(32,555)
Net foreign exchange gains (losses)		20,063	72,671
Income (loss) before income taxes and income (loss) from operating affiliates		439,111	(69,245)
Income tax expense (benefit)		(38,860)	(27,945)
Income (loss) from operating affiliates		75,457	8,516
Net income (loss)		475,708	(88,674)
Amounts attributable to redeemable noncontrolling interests		(855)	(1,153)
Amounts attributable to non-redeemable noncontrolling interests		(36,697)	233,944
Net income (loss) available to Arch		438,156	144,117
Preferred dividends		(10,403)	(10,403)
Net income (loss) available to Arch common shareholders		$ 427,753	$ 133,714
Underwriting Ratios
Loss ratio		61.70%	63.90%
Acquisition expense ratio		15.60%	14.20%
Other operating expense ratio		13.40%	13.40%
Combined ratio		90.70%	91.50%
Goodwill and intangible assets		$ 679,509	$ 705,450	$ 692,863
Other
Segment Reporting Information [Line Items]
Number of segments | segment		2
Gross premiums written	[1]	$ 216,523	234,902
Premiums ceded		(37,212)	(48,202)
Net premiums written		179,311	186,700
Change in unearned premiums		(31,580)	(46,661)
Net premiums earned		147,731	140,039
Other underwriting income (loss)		411	133
Losses and loss adjustment expenses		(118,794)	(110,676)
Acquisition expenses		(28,152)	(21,804)
Other operating expenses		(14,275)	(13,702)
Underwriting income (loss)		(13,079)	(6,010)
Net investment income		20,127	32,125
Net realized gains (losses)		41,125	(294,851)
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]	(715)	0
Amortization of intangible assets		0	0
Interest expense		(4,149)	(7,310)
Net foreign exchange gains (losses)		(1,442)	9,364
Income (loss) before income taxes and income (loss) from operating affiliates		41,867	(266,682)
Income tax expense (benefit)		(8)	0
Income (loss) from operating affiliates		0	0
Net income (loss)		41,859	(266,682)
Amounts attributable to redeemable noncontrolling interests		(972)	(1,096)
Amounts attributable to non-redeemable noncontrolling interests		(36,697)	233,944
Net income (loss) available to Arch		4,190	(33,834)
Preferred dividends		0	0
Net income (loss) available to Arch common shareholders		$ 4,190	$ (33,834)
Underwriting Ratios
Loss ratio		80.40%	79.00%
Acquisition expense ratio		19.10%	15.60%
Other operating expense ratio		9.70%	9.80%
Combined ratio		109.20%	104.40%
Goodwill and intangible assets		$ 7,650	$ 7,650
Underwriting segments
Segment Reporting Information [Line Items]
Number of segments | segment		3
Gross premiums written	[1]	$ 3,277,293	2,698,537
Premiums ceded		(948,147)	(747,991)
Net premiums written		2,329,146	1,950,546
Change in unearned premiums		(528,455)	(346,141)
Net premiums earned		1,800,691	1,604,405
Other underwriting income (loss)		5,699	6,719
Losses and loss adjustment expenses		(1,084,306)	(1,004,743)
Acquisition expenses		(276,329)	(225,479)
Other operating expenses		(246,758)	(220,842)
Underwriting income (loss)		198,997	160,060
Net investment income		78,729	113,028
Net realized gains (losses)		101,336	(72,109)
Equity in net income (loss) of investment funds accounted for using the equity method		71,686	(4,209)
Other income (loss)		(1,741)	32
Corporate expenses	[2]	(23,468)	(18,201)
Transaction costs and other	[2]	(1,201)	(2,595)
Amortization of intangible assets		(14,402)	(16,631)
Interest expense		(34,197)	(25,245)
Net foreign exchange gains (losses)		21,505	63,307
Income (loss) before income taxes and income (loss) from operating affiliates		397,244	197,437
Income tax expense (benefit)		(38,852)	(27,945)
Income (loss) from operating affiliates		75,457	8,516
Net income (loss)		433,849	178,008
Amounts attributable to redeemable noncontrolling interests		117	(57)
Amounts attributable to non-redeemable noncontrolling interests		0	0
Net income (loss) available to Arch		433,966	177,951
Preferred dividends		(10,403)	(10,403)
Net income (loss) available to Arch common shareholders		$ 423,563	$ 167,548
Underwriting Ratios
Loss ratio		60.20%	62.60%
Acquisition expense ratio		15.30%	14.10%
Other operating expense ratio		13.70%	13.80%
Combined ratio		89.20%	90.50%
Goodwill and intangible assets		$ 671,859	$ 697,800
Underwriting segments | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,415,886	1,207,645
Premiums ceded		(421,047)	(378,897)
Net premiums written		994,839	828,748
Change in unearned premiums		(175,365)	(112,829)
Net premiums earned		819,474	715,919
Other underwriting income (loss)		0	0
Losses and loss adjustment expenses		(535,747)	(507,108)
Acquisition expenses		(128,222)	(107,337)
Other operating expenses		(137,113)	(129,649)
Underwriting income (loss)		$ 18,392	$ (28,175)
Underwriting Ratios
Loss ratio		65.40%	70.80%
Acquisition expense ratio		15.60%	15.00%
Other operating expense ratio		16.70%	18.10%
Combined ratio		97.70%	103.90%
Goodwill and intangible assets		$ 276,211	$ 268,296
Underwriting segments | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,471,060	1,122,519
Premiums ceded		(471,948)	(325,339)
Net premiums written		999,112	797,180
Change in unearned premiums		(354,212)	(253,720)
Net premiums earned		644,900	543,460
Other underwriting income (loss)		(1,198)	2,120
Losses and loss adjustment expenses		(484,870)	(430,069)
Acquisition expenses		(118,025)	(79,606)
Other operating expenses		(60,514)	(45,297)
Underwriting income (loss)		$ (19,707)	$ (9,392)
Underwriting Ratios
Loss ratio		75.20%	79.10%
Acquisition expense ratio		18.30%	14.60%
Other operating expense ratio		9.40%	8.30%
Combined ratio		102.90%	102.00%
Goodwill and intangible assets		$ 17,807	$ 2,516
Underwriting segments | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[1]	391,246	368,945
Premiums ceded		(56,051)	(44,327)
Net premiums written		335,195	324,618
Change in unearned premiums		1,122	20,408
Net premiums earned		336,317	345,026
Other underwriting income (loss)		6,897	4,599
Losses and loss adjustment expenses		(63,689)	(67,566)
Acquisition expenses		(30,082)	(38,536)
Other operating expenses		(49,131)	(45,896)
Underwriting income (loss)		$ 200,312	$ 197,627
Underwriting Ratios
Loss ratio		18.90%	19.60%
Acquisition expense ratio		8.90%	11.20%
Other operating expense ratio		14.60%	13.30%
Combined ratio		42.40%	44.10%
Goodwill and intangible assets		$ 377,841	$ 426,988

[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.’