Segment Information - Summary of underwriting income or loss by segment (Details) $ in Thousands		3 Months Ended			6 Months Ended
		Jun. 30, 2020 USD ($)		Jun. 30, 2019 USD ($)	Jun. 30, 2020 USD ($) segment		Jun. 30, 2019 USD ($)		Dec. 31, 2019 USD ($)
Segment Reporting Information [Line Items]
Gross premiums written		$ 2,317,692		$ 1,937,809	$ 5,150,522		$ 4,015,688
Premiums ceded		(649,381)		(492,911)	(1,344,965)		(1,045,531)
Net premiums written		1,668,311		1,444,898	3,805,557		2,970,157
Change in unearned premiums		(2,957)		18,829	(395,759)		(137,564)
Net premiums earned		1,665,354		1,463,727	3,409,798		2,832,593
Other underwriting income		6,667		5,953	13,519		14,778
Losses and loss adjustment expenses		(1,230,522)		(767,543)	(2,345,941)		(1,486,075)
Acquisition expenses, net		(254,789)		(210,089)	(502,072)		(407,937)
Other operating expenses		(209,249)		(198,914)	(443,793)		(400,077)
Underwriting income (loss)		(22,539)		293,134	131,511		553,282
Net investment income		131,485		155,038	276,638		311,987
Net realized gains (losses)		556,588		120,757	189,628		261,013
Equity in net income (loss) of investment funds accounted for using the equity method		(65,119)		32,536	(69,328)		79,403
Other income (loss)		(3,140)		1,129	5,408		2,212
Corporate expenses		(16,943)		(16,073)	(35,144)		(32,845)
Transaction costs and other		(977)	[1]	(2,178)	(3,572)	[1]	(3,368)	[1]
Amortization of intangible assets		(16,489)		(19,794)	(33,120)		(40,211)
Interest expense		(31,139)		(29,280)	(63,694)		(58,345)
Net foreign exchange gains (losses)		(39,211)		(4,952)	33,460		(1,427)
Income (loss) before income taxes		492,516		530,317	431,787		1,071,701
Income tax expense		(26,127)		(44,472)	(54,072)		(90,358)
Net income (loss)		466,389		485,845	377,715		981,343
Dividends attributable to redeemable noncontrolling interests		(1,970)		(4,590)	(3,123)		(9,178)
Amounts attributable to non-redeemable noncontrolling interests		(165,598)		(12,301)	68,346		(54,683)
Net income (loss) available to Arch		298,821		468,954	442,938		917,482
Preferred dividends		(10,403)		(10,403)	(20,806)		(20,806)
Net income available to Arch common shareholders		$ 288,418		$ 458,551	$ 422,132		$ 896,676
Underwriting Ratios
Loss ratio		73.90%		52.40%	68.80%		52.50%
Acquisition expense ratio		15.30%		14.40%	14.70%		14.40%
Other operating expense ratio		12.60%		13.60%	13.00%		14.10%
Combined ratio		101.80%		80.40%	96.50%		81.00%
Goodwill and intangible assets		$ 688,490		$ 641,010	$ 688,490		$ 641,010		$ 738,083
Other
Segment Reporting Information [Line Items]
Number of segments | segment					2
Gross premiums written	[2]	157,927		161,978	$ 392,829		348,667
Premiums ceded		(52,071)		(42,608)	(100,273)		(83,910)
Net premiums written		105,856		119,370	292,556		264,757
Change in unearned premiums		25,679		31,948	(20,982)		32,655
Net premiums earned		131,535		151,318	271,574		297,412
Other underwriting income		868		673	1,001		1,265
Losses and loss adjustment expenses		(104,786)		(111,416)	(215,462)		(222,266)
Acquisition expenses, net		(22,544)		(29,556)	(44,348)		(58,582)
Other operating expenses		(14,202)		(15,612)	(27,904)		(27,800)
Underwriting income (loss)		(9,129)		(4,593)	(15,139)		(9,971)
Net investment income		30,454		32,000	62,579		67,700
Net realized gains (losses)		171,499		(4,306)	(123,352)		24,826
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	[1]	0		0	0		0
Transaction costs and other	[1]	0		0	0		0
Amortization of intangible assets		0		0	0		0
Interest expense		(6,009)		(5,905)	(13,319)		(11,488)
Net foreign exchange gains (losses)		3,227		1,238	12,591		(412)
Income (loss) before income taxes		190,042		18,434	(76,640)		70,655
Income tax expense		402		(20)	402		(20)
Net income (loss)		190,444		18,414	(76,238)		70,635
Dividends attributable to redeemable noncontrolling interests		(1,036)		(4,590)	(2,132)		(9,178)
Amounts attributable to non-redeemable noncontrolling interests		(165,598)		(12,301)	68,346		(54,683)
Net income (loss) available to Arch		23,810		1,523	(10,024)		6,774
Preferred dividends		0		0	0		0
Net income available to Arch common shareholders		$ 23,810		$ 1,523	$ (10,024)		$ 6,774
Underwriting Ratios
Loss ratio		79.70%		73.60%	79.30%		74.70%
Acquisition expense ratio		17.10%		19.50%	16.30%		19.70%
Other operating expense ratio		10.80%		10.30%	10.30%		9.30%
Combined ratio		107.60%		103.40%	105.90%		103.70%
Goodwill and intangible assets		$ 7,650		$ 7,650	$ 7,650		$ 7,650
Sub-Total
Segment Reporting Information [Line Items]
Number of segments | segment					3
Gross premiums written	[2]	2,206,410		1,829,829	$ 4,904,947		3,810,282
Premiums ceded		(643,955)		(504,301)	(1,391,946)		(1,104,882)
Net premiums written		1,562,455		1,325,528	3,513,001		2,705,400
Change in unearned premiums		(28,636)		(13,119)	(374,777)		(170,219)
Net premiums earned		1,533,819		1,312,409	3,138,224		2,535,181
Other underwriting income		5,799		5,280	12,518		13,513
Losses and loss adjustment expenses		(1,125,736)		(656,127)	(2,130,479)		(1,263,809)
Acquisition expenses, net		(232,245)		(180,533)	(457,724)		(349,355)
Other operating expenses		(195,047)		(183,302)	(415,889)		(372,277)
Underwriting income (loss)		(13,410)		297,727	146,650		563,253
Net investment income		101,031		123,038	214,059		244,287
Net realized gains (losses)		385,089		125,063	312,980		236,187
Equity in net income (loss) of investment funds accounted for using the equity method		(65,119)		32,536	(69,328)		79,403
Other income (loss)		(3,140)		1,129	5,408		2,212
Corporate expenses	[1]	(16,943)		(16,073)	(35,144)		(32,845)
Transaction costs and other	[1]	(977)		(2,178)	(3,572)		(3,368)
Amortization of intangible assets		(16,489)		(19,794)	(33,120)		(40,211)
Interest expense		(25,130)		(23,375)	(50,375)		(46,857)
Net foreign exchange gains (losses)		(42,438)		(6,190)	20,869		(1,015)
Income (loss) before income taxes		302,474		511,883	508,427		1,001,046
Income tax expense		(26,529)		(44,452)	(54,474)		(90,338)
Net income (loss)		275,945		467,431	453,953		910,708
Dividends attributable to redeemable noncontrolling interests		(934)		0	(991)		0
Amounts attributable to non-redeemable noncontrolling interests		0		0	0		0
Net income (loss) available to Arch		275,011		467,431	452,962		910,708
Preferred dividends		(10,403)		(10,403)	(20,806)		(20,806)
Net income available to Arch common shareholders		$ 264,608		$ 457,028	$ 432,156		$ 889,902
Underwriting Ratios
Loss ratio		73.40%		50.00%	67.90%		49.90%
Acquisition expense ratio		15.10%		13.80%	14.60%		13.80%
Other operating expense ratio		12.70%		14.00%	13.30%		14.70%
Combined ratio		101.20%		77.80%	95.80%		78.40%
Goodwill and intangible assets		$ 680,840		$ 633,360	$ 680,840		$ 633,360
Sub-Total | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[2]	1,030,362		919,925	2,238,007		1,861,879
Premiums ceded		(358,101)		(292,095)	(736,998)		(612,717)
Net premiums written		672,261		627,830	1,501,009		1,249,162
Change in unearned premiums		15,648		(35,388)	(97,181)		(103,215)
Net premiums earned		687,909		592,442	1,403,828		1,145,947
Other underwriting income		0		0	0		0
Losses and loss adjustment expenses		(518,203)		(389,172)	(1,025,311)		(745,895)
Acquisition expenses, net		(107,671)		(91,094)	(215,008)		(173,918)
Other operating expenses		(118,757)		(109,523)	(248,406)		(222,919)
Underwriting income (loss)		$ (56,722)		$ 2,653	$ (84,897)		$ 3,215
Underwriting Ratios
Loss ratio		75.30%		65.70%	73.00%		65.10%
Acquisition expense ratio		15.70%		15.40%	15.30%		15.20%
Other operating expense ratio		17.30%		18.50%	17.70%		19.50%
Combined ratio		108.30%		99.60%	106.00%		99.80%
Goodwill and intangible assets		$ 263,086		$ 157,440	$ 263,086		$ 157,440
Sub-Total | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[2]	807,065		545,547	1,929,584		1,228,402
Premiums ceded		(241,971)		(169,457)	(567,310)		(401,024)
Net premiums written		565,094		376,090	1,362,274		827,378
Change in unearned premiums		(84,897)		(8,906)	(338,617)		(113,829)
Net premiums earned		480,197		367,184	1,023,657		713,549
Other underwriting income		(651)		1,224	1,469		5,601
Losses and loss adjustment expenses		(383,433)		(240,958)	(813,502)		(480,768)
Acquisition expenses, net		(90,522)		(56,785)	(170,128)		(111,111)
Other operating expenses		(38,716)		(33,960)	(84,013)		(69,664)
Underwriting income (loss)		$ (33,125)		$ 36,705	$ (42,517)		$ 57,607
Underwriting Ratios
Loss ratio		79.80%		65.60%	79.50%		67.40%
Acquisition expense ratio		18.90%		15.50%	16.60%		15.60%
Other operating expense ratio		8.10%		9.20%	8.20%		9.80%
Combined ratio		106.80%		90.30%	104.30%		92.80%
Goodwill and intangible assets		$ 2,516		$ 0	$ 2,516		$ 0
Sub-Total | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[2]	369,144		364,465	738,089		720,515
Premiums ceded		(44,044)		(42,857)	(88,371)		(91,655)
Net premiums written		325,100		321,608	649,718		628,860
Change in unearned premiums		40,613		31,175	61,021		46,825
Net premiums earned		365,713		352,783	710,739		675,685
Other underwriting income		6,450		4,056	11,049		7,912
Losses and loss adjustment expenses		(224,100)		(25,997)	(291,666)		(37,146)
Acquisition expenses, net		(34,052)		(32,654)	(72,588)		(64,326)
Other operating expenses		(37,574)		(39,819)	(83,470)		(79,694)
Underwriting income (loss)		$ 76,437		$ 258,369	$ 274,064		$ 502,431
Underwriting Ratios
Loss ratio		61.30%		7.40%	41.00%		5.50%
Acquisition expense ratio		9.30%		9.30%	10.20%		9.50%
Other operating expense ratio		10.30%		11.30%	11.70%		11.80%
Combined ratio		80.90%		28.00%	62.90%		26.80%
Goodwill and intangible assets		$ 415,238		$ 475,920	$ 415,238		$ 475,920

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

[2] 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.