Segment Information - Analysis of underwriting income by segment and reconciliation to net income available to common shareholders (Details) $ in Thousands		12 Months Ended
		Dec. 31, 2022 USD ($) segment	Dec. 31, 2021 USD ($)		Dec. 31, 2020 USD ($)
Segment Reporting Information [Line Items]
Gross premiums written		$ 15,326,447	$ 12,752,487		$ 10,088,068
Premiums ceded		(4,249,258)	(3,734,150)		(2,650,352)
Net premiums written		11,077,189	9,018,337		7,437,716
Change in unearned premiums		(1,399,112)	(936,039)		(445,781)
Net premiums earned		9,678,077	8,082,298		6,991,935
Other underwriting income		13,227	22,073		26,784
Losses and loss adjustment expenses		(5,027,517)	(4,584,803)		(4,689,599)
Acquisition expenses, net		(1,739,580)	(1,303,178)		(1,004,842)
Other operating expenses		(1,128,175)	(998,595)		(875,176)
Underwriting income (loss)		1,796,032	1,217,795		449,102
Net investment income		496,547	389,118		519,608
Net realized gains (losses)		(662,734)	379,845		823,460
Equity in net income (loss) of investment funds accounted for using the equity method		115,856	366,402		146,693
Other income (loss)		(26,165)	10,244		29
Corporate expenses		(94,390)	(77,119)		(68,492)
Transaction costs and other		(1,092)	(2,038)		(13,496)
Amortization of intangible assets		(106,200)	(82,955)		(69,031)
Interest expense		(130,266)	(139,470)		(143,456)
Net foreign exchange gains (losses)		100,905	41,529		(83,634)
Income before income taxes and income (loss) from operating affiliates		1,488,493	2,103,351		1,560,783
Income tax (expense) benefit		(79,961)	(128,582)		(111,838)
Income (loss) from operating affiliates		73,891	264,693		16,766
Net income (loss)		1,482,423	2,239,462		1,465,711
Amounts attributable to redeemable noncontrolling interests		(5,490)	(4,299)		(7,114)
Amounts attributable to nonredeemable noncontrolling interests		0	(78,314)		(53,076)
Net income available to Arch		1,476,933	2,156,849		1,405,521
Preferred share dividends		(40,736)	(48,343)		(41,612)
Loss on redemption of preferred shares		0	(15,101)		0
Net income (loss) available to Arch common shareholders		$ 1,436,197	$ 2,093,405		$ 1,363,909
Underwriting Ratios
Loss ratio		51.90%	56.70%		67.10%
Acquisition expense ratio		18.00%	16.10%		14.40%
Other operating expense ratio		11.70%	12.40%		12.50%
Combined ratio		81.60%	85.20%		94.00%
Goodwill and intangible assets		$ 804,289	$ 944,983		$ 692,863
Total investable assets		28,065,497	27,442,153		29,513,907
Total assets		47,990,507	45,100,945		43,282,297
Total liabilities		$ 35,069,605	31,545,816		29,294,856
Operating segments | Underwriting Segments
Segment Reporting Information [Line Items]
Number of segments | segment		3
Gross premiums written	[1]	$ 15,326,447	12,463,788		9,632,691
Premiums ceded		(4,249,258)	(3,800,153)		(2,732,564)
Net premiums written		11,077,189	8,663,635		6,900,127
Change in unearned premiums		(1,399,112)	(913,305)		(468,543)
Net premiums earned		9,678,077	7,750,330		6,431,584
Other underwriting income		13,227	21,334		24,739
Losses and loss adjustment expenses		(5,027,517)	(4,325,761)		(4,249,117)
Acquisition expenses, net		(1,739,580)	(1,240,437)		(906,771)
Other operating expenses		(1,128,175)	(965,726)		(819,366)
Underwriting income (loss)		1,796,032	1,239,740		481,069
Net investment income		496,547	346,808		401,908
Net realized gains (losses)		(662,734)	299,207		813,781
Equity in net income (loss) of investment funds accounted for using the equity method		115,856	366,402		146,693
Other income (loss)		(26,165)	10,244		29
Corporate expenses		(94,390)	(77,119)		(68,492)
Transaction costs and other		(1,092)	(1,103)		(9,456)
Amortization of intangible assets		(106,200)	(82,057)		(69,031)
Interest expense		(130,266)	(131,060)		(120,214)
Net foreign exchange gains (losses)		100,905	42,854		(80,161)
Income before income taxes and income (loss) from operating affiliates		1,488,493	2,013,916		1,496,126
Income tax (expense) benefit		(79,961)	(128,348)		(111,812)
Income (loss) from operating affiliates		73,891	264,693		16,766
Net income (loss)		1,482,423	2,150,261		1,401,080
Amounts attributable to redeemable noncontrolling interests		(5,490)	(2,346)		(2,997)
Amounts attributable to nonredeemable noncontrolling interests			0		0
Net income available to Arch		1,476,933	2,147,915		1,398,083
Preferred share dividends		(40,736)	(48,343)		(41,612)
Loss on redemption of preferred shares			(15,101)
Net income (loss) available to Arch common shareholders		$ 1,436,197	$ 2,084,471		$ 1,356,471
Underwriting Ratios
Loss ratio		51.90%	55.80%		66.10%
Acquisition expense ratio		18.00%	16.00%		14.10%
Other operating expense ratio		11.70%	12.50%		12.70%
Combined ratio		81.60%	84.30%		92.90%
Goodwill and intangible assets		$ 804,289	$ 944,983		$ 685,213
Total investable assets		28,065,497	27,442,153		26,856,295
Total assets		47,990,507	45,100,945		39,791,983
Total liabilities		35,069,605	31,545,816		26,789,149
Operating segments | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	6,930,864	5,867,734		4,688,562
Premiums ceded	[2]	(1,910,222)	(1,719,541)		(1,525,655)
Net premiums written		5,020,642	4,148,193		3,162,907
Change in unearned premiums		(461,307)	(521,725)		(291,487)
Net premiums earned		4,559,335	3,626,468		2,871,420
Other underwriting income		0	0		(31)
Losses and loss adjustment expenses		(2,782,945)	(2,344,365)		(2,092,453)
Acquisition expenses, net		(885,866)	(606,265)		(418,483)
Other operating expenses		(665,472)	(558,906)		(489,153)
Underwriting income (loss)		$ 225,052	$ 116,932		$ (128,700)
Underwriting Ratios
Loss ratio		61.00%	64.60%		72.90%
Acquisition expense ratio		19.40%	16.70%		14.60%
Other operating expense ratio		14.60%	15.40%		17.00%
Combined ratio		95.00%	96.70%		104.50%
Goodwill and intangible assets		$ 228,532	$ 256,434		$ 280,978
Operating segments | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[1]	6,948,438	5,093,930		3,472,086
Premiums ceded	[2]	(2,024,462)	(1,839,556)		(1,014,716)
Net premiums written		4,923,976	3,254,374		2,457,370
Change in unearned premiums		(964,595)	(413,931)		(295,141)
Net premiums earned		3,959,381	2,840,443		2,162,229
Other underwriting income		4,871	3,669		4,454
Losses and loss adjustment expenses		(2,568,843)	(1,924,719)		(1,628,320)
Acquisition expenses, net		(813,555)	(536,754)		(354,048)
Other operating expenses		(267,531)	(212,810)		(168,011)
Underwriting income (loss)		$ 314,323	$ 169,829		$ 16,304
Underwriting Ratios
Loss ratio		64.90%	67.80%		75.30%
Acquisition expense ratio		20.50%	18.90%		16.40%
Other operating expense ratio		6.80%	7.50%		7.80%
Combined ratio		92.20%	94.20%		99.50%
Goodwill and intangible assets		$ 144,846	$ 183,523		$ 18,963
Operating segments | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[1]	1,454,971	1,507,825		1,473,999
Premiums ceded	[2]	(322,400)	(246,757)		(194,149)
Net premiums written		1,132,571	1,261,068		1,279,850
Change in unearned premiums		26,790	22,351		118,085
Net premiums earned		1,159,361	1,283,419		1,397,935
Other underwriting income		8,356	17,665		20,316
Losses and loss adjustment expenses		324,271	(56,677)		(528,344)
Acquisition expenses, net		(40,159)	(97,418)		(134,240)
Other operating expenses		(195,172)	(194,010)		(162,202)
Underwriting income (loss)		$ 1,256,657	$ 952,979		$ 593,465
Underwriting Ratios
Loss ratio		(28.00%)	4.40%		37.80%
Acquisition expense ratio		3.50%	7.60%		9.60%
Other operating expense ratio		16.80%	15.10%		11.60%
Combined ratio		(7.70%)	27.10%		59.00%
Goodwill and intangible assets		$ 430,911	$ 505,026		$ 385,272
Operating segments | Other
Segment Reporting Information [Line Items]
Number of segments | segment		2
Gross premiums written	[1]	$ 0	457,465		728,546
Premiums ceded		0	(102,763)	[2]	(190,957)	[2]
Net premiums written		0	354,702		537,589
Change in unearned premiums		0	(22,734)		22,762
Net premiums earned		0	331,968		560,351
Other underwriting income		0	739		2,045
Losses and loss adjustment expenses		0	(259,042)		(440,482)
Acquisition expenses, net		0	(62,741)		(98,071)
Other operating expenses		0	(32,869)		(55,810)
Underwriting income (loss)		0	(21,945)		(31,967)
Net investment income		0	42,310		117,700
Net realized gains (losses)		0	80,638		9,679
Equity in net income (loss) of investment funds accounted for using the equity method		0	0		0
Other income (loss)		0	0		0
Corporate expenses		0	0		0
Transaction costs and other		0	(935)		(4,040)
Amortization of intangible assets		0	(898)		0
Interest expense		0	(8,410)		(23,242)
Net foreign exchange gains (losses)		0	(1,325)		(3,473)
Income before income taxes and income (loss) from operating affiliates		0	89,435		64,657
Income tax (expense) benefit		0	(234)		(26)
Income (loss) from operating affiliates		0	0		0
Net income (loss)		0	89,201		64,631
Amounts attributable to redeemable noncontrolling interests		0	(1,953)		(4,117)
Amounts attributable to nonredeemable noncontrolling interests		0	(78,314)		(53,076)
Net income available to Arch		0	8,934		7,438
Preferred share dividends		0	0		0
Loss on redemption of preferred shares			0
Net income (loss) available to Arch common shareholders		$ 0	$ 8,934		$ 7,438
Underwriting Ratios
Loss ratio		0.00%	78.00%		78.60%
Acquisition expense ratio		0.00%	18.90%		17.50%
Other operating expense ratio		0.00%	9.90%		10.00%
Combined ratio		0.00%	106.80%		106.10%
Goodwill and intangible assets		$ 0	$ 0		$ 7,650
Total investable assets		0	0		2,657,612
Total assets		0	0		3,490,314
Total liabilities		$ 0	$ 0		$ 2,505,707

[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 amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. 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.