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%	82.00%	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%	96.00%
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%	86.00%	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%)	3.00%	(20.40%)	11.00%
Acquisition expense ratio		3.40%	9.00%	3.50%	9.00%
Other operating expense ratio		17.00%	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		0.00%	76.10%	0.00%	78.00%
Acquisition expense ratio		0.00%	18.80%	0.00%	18.90%
Other operating expense ratio		0.00%	10.10%	0.00%	9.90%
Combined ratio		0.00%	105.00%	0.00%	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.’