Segment Information - Summary of underwriting income or loss by segment (Details) $ in Thousands		3 Months Ended		9 Months Ended
		Sep. 30, 2022 USD ($)	Sep. 30, 2021 USD ($)	Sep. 30, 2022 USD ($) segment	Sep. 30, 2021 USD ($)	Dec. 31, 2021 USD ($)
Segment Reporting Information [Line Items]
Gross premiums written		$ 3,860,683	$ 3,207,415	$ 11,531,185	$ 9,890,912
Premiums ceded		(1,136,909)	(1,131,486)	(3,488,632)	(2,907,002)
Net premiums written		2,723,774	2,075,929	8,042,553	6,983,910
Change in unearned premiums		(253,024)	(146,592)	(1,125,395)	(985,242)
Net premiums earned		2,470,750	1,929,337	6,917,158	5,998,668
Other underwriting income (loss)		3,077	7,274	11,944	18,913
Losses and loss adjustment expenses		(1,682,696)	(1,226,019)	(3,786,187)	(3,588,950)
Acquisition expenses		(447,587)	(306,015)	(1,239,065)	(945,639)
Other operating expenses		(274,747)	(230,832)	(842,082)	(736,808)
Underwriting income (loss)		68,797	173,745	1,061,768	746,184
Net investment income		128,640	88,195	315,468	298,664
Net realized gains (losses)		(183,673)	(25,040)	(742,666)	320,328
Equity in net income (loss) of investment funds accounted for using the equity method		(18,861)	105,398	75,505	299,270
Other income (loss)		(13,684)	(3,960)	(34,486)	1,151
Corporate expenses		(17,634)	(18,636)	(76,928)	(59,279)
Transaction costs and other		(76)	(1,036)	(734)	(1,728)
Amortization of intangible assets		(26,104)	(20,135)	(80,478)	(49,823)
Interest expense		(33,063)	(33,176)	(98,566)	(107,222)
Net foreign exchange gains (losses)		90,509	36,078	182,129	38,366
Income (loss) before income taxes and income (loss) from operating affiliates		(5,149)	301,433	601,012	1,485,911
Income tax expense (benefit)		14,900	(4,137)	(19,042)	(94,176)
Income (loss) from operating affiliates		8,507	124,119	37,665	224,052
Net income (loss)		18,258	421,415	619,635	1,615,787
Amounts attributable to redeemable noncontrolling interests		(1,157)	(1,473)	(2,390)	(3,889)
Amounts attributable to non-redeemable noncontrolling interests		0	0	0	(78,314)
Net income (loss) available to Arch		17,101	419,942	617,245	1,533,584
Preferred dividends		(10,184)	(16,090)	(30,552)	(38,159)
Loss on redemption of preferred shares		0	(15,101)	0	(15,101)
Net income (loss) available to Arch common shareholders		$ 6,917	$ 388,751	$ 586,693	$ 1,480,324
Underwriting Ratios
Loss ratio		68.10%	63.50%	54.70%	59.80%
Acquisition expense ratio		18.10%	15.90%	17.90%	15.80%
Other operating expense ratio		11.10%	12.00%	12.20%	12.30%
Combined ratio		97.30%	91.40%	84.80%	87.90%
Goodwill and intangible assets		$ 806,655	$ 963,322	$ 806,655	$ 963,322	$ 944,983
Operating segments | Underwriting Segments
Segment Reporting Information [Line Items]
Number of segments | segment				3
Gross premiums written	[1]	3,860,683	3,207,415	$ 11,531,185	9,602,213
Premiums ceded		(1,136,909)	(1,131,486)	(3,488,632)	(2,973,005)
Net premiums written		2,723,774	2,075,929	8,042,553	6,629,208
Change in unearned premiums		(253,024)	(146,592)	(1,125,395)	(962,508)
Net premiums earned		2,470,750	1,929,337	6,917,158	5,666,700
Other underwriting income (loss)		3,077	7,274	11,944	18,174
Losses and loss adjustment expenses		(1,682,696)	(1,226,019)	(3,786,187)	(3,329,908)
Acquisition expenses		(447,587)	(306,015)	(1,239,065)	(882,898)
Other operating expenses		(274,747)	(230,832)	(842,082)	(703,939)
Underwriting income (loss)		68,797	173,745	1,061,768	768,129
Net investment income		128,640	88,195	315,468	256,354
Net realized gains (losses)		(183,673)	(25,040)	(742,666)	239,690
Equity in net income (loss) of investment funds accounted for using the equity method		(18,861)	105,398	75,505	299,270
Other income (loss)		(13,684)	(3,960)	(34,486)	1,151
Corporate expenses	[2]	(17,634)	(18,636)	(76,928)	(59,279)
Transaction costs and other	[2]	(76)	(1,036)	(734)	(793)
Amortization of intangible assets		(26,104)	(20,135)	(80,478)	(48,925)
Interest expense		(33,063)	(33,176)	(98,566)	(98,812)
Net foreign exchange gains (losses)		90,509	36,078	182,129	39,691
Income (loss) before income taxes and income (loss) from operating affiliates		(5,149)	301,433	601,012	1,396,476
Income tax expense (benefit)		14,900	(4,137)	(19,042)	(93,942)
Income (loss) from operating affiliates		8,507	124,119	37,665	224,052
Net income (loss)		18,258	421,415	619,635	1,526,586
Amounts attributable to redeemable noncontrolling interests		(1,157)	(1,473)	(2,390)	(1,936)
Amounts attributable to non-redeemable noncontrolling interests					0
Net income (loss) available to Arch		17,101	419,942	617,245	1,524,650
Preferred dividends		(10,184)	(16,090)	(30,552)	(38,159)
Loss on redemption of preferred shares			(15,101)		(15,101)
Net income (loss) available to Arch common shareholders		$ 6,917	$ 388,751	$ 586,693	$ 1,471,390
Underwriting Ratios
Loss ratio		68.10%	63.50%	54.70%	58.80%
Acquisition expense ratio		18.10%	15.90%	17.90%	15.60%
Other operating expense ratio		11.10%	12.00%	12.20%	12.40%
Combined ratio		97.30%	91.40%	84.80%	86.80%
Goodwill and intangible assets		$ 806,655	$ 963,322	$ 806,655	$ 963,322
Operating segments | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,862,026	1,596,619	5,286,798	4,381,372
Premiums ceded		(493,267)	(442,806)	(1,482,886)	(1,269,165)
Net premiums written		1,368,759	1,153,813	3,803,912	3,112,207
Change in unearned premiums		(181,851)	(215,143)	(488,164)	(488,636)
Net premiums earned		1,186,908	938,670	3,315,748	2,623,571
Other underwriting income (loss)		0	0	0	0
Losses and loss adjustment expenses		(822,663)	(668,630)	(2,053,161)	(1,750,257)
Acquisition expenses		(232,469)	(152,467)	(641,807)	(417,541)
Other operating expenses		(165,499)	(138,931)	(493,412)	(409,386)
Underwriting income (loss)		$ (33,723)	$ (21,358)	$ 127,368	$ 46,387
Underwriting Ratios
Loss ratio		69.30%	71.20%	61.90%	66.70%
Acquisition expense ratio		19.60%	16.20%	19.40%	15.90%
Other operating expense ratio		13.90%	14.80%	14.90%	15.60%
Combined ratio		102.80%	102.20%	96.20%	98.20%
Goodwill and intangible assets		$ 224,525	$ 261,103	$ 224,525	$ 261,103
Operating segments | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,639,061	1,251,760	5,151,401	4,080,840
Premiums ceded		(560,225)	(630,371)	(1,770,807)	(1,535,607)
Net premiums written		1,078,836	621,389	3,380,594	2,545,233
Change in unearned premiums		(77,062)	57,313	(646,421)	(484,607)
Net premiums earned		1,001,774	678,702	2,734,173	2,060,626
Other underwriting income (loss)		452	3,293	5,814	3,148
Losses and loss adjustment expenses		(927,911)	(545,846)	(1,920,189)	(1,494,539)
Acquisition expenses		(208,425)	(129,450)	(569,915)	(381,060)
Other operating expenses		(62,777)	(45,647)	(198,606)	(150,856)
Underwriting income (loss)		$ (196,887)	$ (38,948)	$ 51,277	$ 37,319
Underwriting Ratios
Loss ratio		92.60%	80.40%	70.20%	72.50%
Acquisition expense ratio		20.80%	19.10%	20.80%	18.50%
Other operating expense ratio		6.30%	6.70%	7.30%	7.30%
Combined ratio		119.70%	106.20%	98.30%	98.30%
Goodwill and intangible assets		$ 140,800	$ 176,128	$ 140,800	$ 176,128
Operating segments | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[1]	362,409	360,934	1,099,144	1,143,691
Premiums ceded		(86,230)	(60,207)	(241,097)	(171,923)
Net premiums written		276,179	300,727	858,047	971,768
Change in unearned premiums		5,889	11,238	9,190	10,735
Net premiums earned		282,068	311,965	867,237	982,503
Other underwriting income (loss)		2,625	3,981	6,130	15,026
Losses and loss adjustment expenses		67,878	(11,543)	187,163	(85,112)
Acquisition expenses		(6,693)	(24,098)	(27,343)	(84,297)
Other operating expenses		(46,471)	(46,254)	(150,064)	(143,697)
Underwriting income (loss)		$ 299,407	$ 234,051	$ 883,123	$ 684,423
Underwriting Ratios
Loss ratio		(24.10%)	3.70%	(21.60%)	8.70%
Acquisition expense ratio		2.40%	7.70%	3.20%	8.60%
Other operating expense ratio		16.50%	14.80%	17.30%	14.60%
Combined ratio		(5.20%)	26.20%	(1.10%)	31.90%
Goodwill and intangible assets		$ 441,330	$ 526,091	$ 441,330	$ 526,091
Operating segments | Corporate and Other Segments
Segment Reporting Information [Line Items]
Number of segments | segment				2
Gross premiums written	[1]	0	0	$ 0	457,465
Premiums ceded		0	0	0	(102,763)
Net premiums written		0	0	0	354,702
Change in unearned premiums		0	0	0	(22,734)
Net premiums earned		0	0	0	331,968
Other underwriting income (loss)		0	0	0	739
Losses and loss adjustment expenses		0	0	0	(259,042)
Acquisition expenses		0	0	0	(62,741)
Other operating expenses		0	0	0	(32,869)
Underwriting income (loss)		0	0	0	(21,945)
Net investment income		0	0	0	42,310
Net realized gains (losses)		0	0	0	80,638
Equity in net income (loss) of investment funds accounted for using the equity method		0	0	0	0
Other income (loss)		0	0	0	0
Corporate expenses	[2]	0	0	0	0
Transaction costs and other	[2]	0	0	0	(935)
Amortization of intangible assets		0	0	0	(898)
Interest expense		0	0	0	(8,410)
Net foreign exchange gains (losses)		0	0	0	(1,325)
Income (loss) before income taxes and income (loss) from operating affiliates		0	0	0	89,435
Income tax expense (benefit)		0	0	0	(234)
Income (loss) from operating affiliates		0	0	0	0
Net income (loss)		0	0	0	89,201
Amounts attributable to redeemable noncontrolling interests		0	0	0	(1,953)
Amounts attributable to non-redeemable noncontrolling interests					(78,314)
Net income (loss) available to Arch		0	0	0	8,934
Preferred dividends		0	0	0	0
Loss on redemption of preferred shares			0		0
Net income (loss) available to Arch common shareholders		$ 0	$ 0	$ 0	$ 8,934
Underwriting Ratios
Loss ratio		0.00%	0.00%	0.00%	78.00%
Acquisition expense ratio		0.00%	0.00%	0.00%	18.90%
Other operating expense ratio		0.00%	0.00%	0.00%	9.90%
Combined ratio		0.00%	0.00%	0.00%	106.80%
Goodwill and intangible assets		$ 0	$ 0	$ 0	$ 0

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

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