Segment Information - Summary of underwriting income or loss by segment (Details) $ in Thousands		3 Months Ended			9 Months Ended
		Sep. 30, 2020 USD ($)		Sep. 30, 2019 USD ($)	Sep. 30, 2020 USD ($) segment		Sep. 30, 2019 USD ($)		Dec. 31, 2019 USD ($)
Segment Reporting Information [Line Items]
Gross premiums written		$ 2,681,032		$ 2,181,121	$ 7,831,554		$ 6,196,809
Premiums ceded		(806,888)		(567,664)	(2,151,853)		(1,613,195)
Net premiums written		1,874,144		1,613,457	5,679,701		4,583,614
Change in unearned premiums		(103,052)		(175,434)	(498,811)		(312,998)
Net premiums earned		1,771,092		1,438,023	5,180,890		4,270,616
Other underwriting income (loss)		5,413		3,326	18,932		18,104
Losses and loss adjustment expenses		(1,216,273)		(802,455)	(3,562,214)		(2,288,530)
Acquisition expenses		(247,942)		(211,120)	(750,014)		(619,057)
Other operating expenses		(215,686)		(196,512)	(659,479)		(596,589)
Underwriting income (loss)		96,604		231,262	228,115		784,544
Net investment income		128,512		161,488	405,150		473,475
Net realized gains (losses)		280,499		61,355	470,127		322,368
Equity in net income (loss) of investment funds accounted for using the equity method		126,735		17,130	57,407		96,533
Other income (loss)		919		1,338	6,327		3,550
Corporate expenses		(16,263)		(15,066)	(51,407)		(47,911)
Transaction costs and other		(1,674)	[1]	(1,995)	(5,246)	[1]	(5,363)	[1]
Amortization of intangible assets		(16,715)		(20,003)	(49,835)		(60,214)
Interest expense		(41,343)		(31,328)	(105,037)		(89,673)
Net foreign exchange gains (losses)		(44,885)		33,124	(11,425)		31,697
Income (loss) before income taxes		512,389		437,305	944,176		1,509,006
Income tax expense (benefit)		(23,707)		(38,116)	(77,779)		(128,474)
Net income (loss)		488,682		399,189	866,397		1,380,532
Amounts attributable to redeemable noncontrolling interests		(1,875)		(6,600)	(4,998)		(15,778)
Amounts attributable to non-redeemable noncontrolling interests		(67,768)		(136)	578		(54,819)
Net income (loss) available to Arch		419,039		392,453	861,977		1,309,935
Preferred dividends		(10,403)		(10,403)	(31,209)		(31,209)
Net income (loss) available to Arch common shareholders		$ 408,636		$ 382,050	$ 830,768		$ 1,278,726
Underwriting Ratios
Loss ratio		68.70%		55.80%	68.80%		53.60%
Acquisition expense ratio		14.00%		14.70%	14.50%		14.50%
Other operating expense ratio		12.20%		13.70%	12.70%		14.00%
Combined ratio		94.90%		84.20%	96.00%		82.10%
Goodwill and intangible assets		$ 713,777		$ 624,500	$ 713,777		$ 624,500		$ 738,083
Other
Segment Reporting Information [Line Items]
Number of segments | segment					2
Gross premiums written	[2]	197,480		249,960	$ 590,309		598,627
Premiums ceded		(50,164)		(94,208)	(150,437)		(178,118)
Net premiums written		147,316		155,752	439,872		420,509
Change in unearned premiums		(1,285)		(29,920)	(22,267)		2,735
Net premiums earned		146,031		125,832	417,605		423,244
Other underwriting income (loss)		546		579	1,547		1,844
Losses and loss adjustment expenses		(115,813)		(96,214)	(331,275)		(318,480)
Acquisition expenses		(24,418)		(23,072)	(68,766)		(81,654)
Other operating expenses		(14,619)		(11,568)	(42,523)		(39,368)
Underwriting income (loss)		(8,273)		(4,443)	(23,412)		(14,414)
Net investment income		28,655		34,614	91,234		102,314
Net realized gains (losses)		69,515		(18,659)	(53,837)		6,167
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		(5,119)		(8,091)	(18,438)		(19,579)
Net foreign exchange gains (losses)		(6,204)		3,330	6,387		2,918
Income (loss) before income taxes		78,574		6,751	1,934		77,406
Income tax expense (benefit)		(69)		0	333		(20)
Net income (loss)		78,505		6,751	2,267		77,386
Amounts attributable to redeemable noncontrolling interests		(993)		(6,600)	(3,125)		(15,778)
Amounts attributable to non-redeemable noncontrolling interests		(67,768)		(136)	578		(54,819)
Net income (loss) available to Arch		9,744		15	(280)		6,789
Preferred dividends		0		0	0		0
Net income (loss) available to Arch common shareholders		$ 9,744		$ 15	$ (280)		$ 6,789
Underwriting Ratios
Loss ratio		79.30%		76.50%	79.30%		75.20%
Acquisition expense ratio		16.70%		18.30%	16.50%		19.30%
Other operating expense ratio		10.00%		9.20%	10.20%		9.30%
Combined ratio		106.00%		104.00%	106.00%		103.80%
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]	2,556,914		2,043,292	$ 7,461,860		5,853,574
Premiums ceded		(830,086)		(585,587)	(2,222,031)		(1,690,469)
Net premiums written		1,726,828		1,457,705	5,239,829		4,163,105
Change in unearned premiums		(101,767)		(145,514)	(476,544)		(315,733)
Net premiums earned		1,625,061		1,312,191	4,763,285		3,847,372
Other underwriting income (loss)		4,867		2,747	17,385		16,260
Losses and loss adjustment expenses		(1,100,460)		(706,241)	(3,230,939)		(1,970,050)
Acquisition expenses		(223,524)		(188,048)	(681,248)		(537,403)
Other operating expenses		(201,067)		(184,944)	(616,956)		(557,221)
Underwriting income (loss)		104,877		235,705	251,527		798,958
Net investment income		99,857		126,874	313,916		371,161
Net realized gains (losses)		210,984		80,014	523,964		316,201
Equity in net income (loss) of investment funds accounted for using the equity method		126,735		17,130	57,407		96,533
Other income (loss)		919		1,338	6,327		3,550
Corporate expenses	[1]	(16,263)		(15,066)	(51,407)		(47,911)
Transaction costs and other	[1]	(1,674)		(1,995)	(5,246)		(5,363)
Amortization of intangible assets		(16,715)		(20,003)	(49,835)		(60,214)
Interest expense		(36,224)		(23,237)	(86,599)		(70,094)
Net foreign exchange gains (losses)		(38,681)		29,794	(17,812)		28,779
Income (loss) before income taxes		433,815		430,554	942,242		1,431,600
Income tax expense (benefit)		(23,638)		(38,116)	(78,112)		(128,454)
Net income (loss)		410,177		392,438	864,130		1,303,146
Amounts attributable to redeemable noncontrolling interests		(882)		0	(1,873)		0
Amounts attributable to non-redeemable noncontrolling interests		0		0	0		0
Net income (loss) available to Arch		409,295		392,438	862,257		1,303,146
Preferred dividends		(10,403)		(10,403)	(31,209)		(31,209)
Net income (loss) available to Arch common shareholders		$ 398,892		$ 382,035	$ 831,048		$ 1,271,937
Underwriting Ratios
Loss ratio		67.70%		53.80%	67.80%		51.20%
Acquisition expense ratio		13.80%		14.30%	14.30%		14.00%
Other operating expense ratio		12.40%		14.10%	13.00%		14.50%
Combined ratio		93.90%		82.20%	95.10%		79.70%
Goodwill and intangible assets		$ 706,127		$ 616,850	$ 706,127		$ 616,850
Sub-Total | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[2]	1,206,328		1,005,874	3,444,335		2,867,753
Premiums ceded		(382,167)		(302,034)	(1,119,165)		(914,751)
Net premiums written		824,161		703,840	2,325,170		1,953,002
Change in unearned premiums		(105,007)		(98,504)	(202,188)		(201,719)
Net premiums earned		719,154		605,336	2,122,982		1,751,283
Other underwriting income (loss)		(31)		0	(31)		0
Losses and loss adjustment expenses		(525,321)		(422,782)	(1,550,632)		(1,168,677)
Acquisition expenses		(102,420)		(91,259)	(317,428)		(265,177)
Other operating expenses		(122,541)		(115,408)	(370,947)		(338,327)
Underwriting income (loss)		$ (31,159)		$ (24,113)	$ (116,056)		$ (20,898)
Underwriting Ratios
Loss ratio		73.00%		69.80%	73.00%		66.70%
Acquisition expense ratio		14.20%		15.10%	15.00%		15.10%
Other operating expense ratio		17.00%		19.10%	17.50%		19.30%
Combined ratio		104.20%		104.00%	105.50%		101.10%
Goodwill and intangible assets		$ 282,146		$ 158,990	$ 282,146		$ 158,990
Sub-Total | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[2]	1,004,590		662,572	2,934,174		1,890,974
Premiums ceded		(400,388)		(226,096)	(967,698)		(627,120)
Net premiums written		604,202		436,476	1,966,476		1,263,854
Change in unearned premiums		(49,704)		(72,621)	(388,321)		(186,450)
Net premiums earned		554,498		363,855	1,578,155		1,077,404
Other underwriting income (loss)		298		(1,208)	1,767		4,393
Losses and loss adjustment expenses		(422,084)		(270,379)	(1,235,586)		(751,147)
Acquisition expenses		(85,388)		(62,393)	(255,516)		(173,504)
Other operating expenses		(41,818)		(32,533)	(125,831)		(102,197)
Underwriting income (loss)		$ 5,506		$ (2,658)	$ (37,011)		$ 54,949
Underwriting Ratios
Loss ratio		76.10%		74.30%	78.30%		69.70%
Acquisition expense ratio		15.40%		17.10%	16.20%		16.10%
Other operating expense ratio		7.50%		8.90%	8.00%		9.50%
Combined ratio		99.00%		100.30%	102.50%		95.30%
Goodwill and intangible assets		$ 20,319		$ 0	$ 20,319		$ 0
Sub-Total | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[2]	346,248		375,092	1,084,337		1,095,607
Premiums ceded		(47,783)		(57,703)	(136,154)		(149,358)
Net premiums written		298,465		317,389	948,183		946,249
Change in unearned premiums		52,944		25,611	113,965		72,436
Net premiums earned		351,409		343,000	1,062,148		1,018,685
Other underwriting income (loss)		4,600		3,955	15,649		11,867
Losses and loss adjustment expenses		(153,055)		(13,080)	(444,721)		(50,226)
Acquisition expenses		(35,716)		(34,396)	(108,304)		(98,722)
Other operating expenses		(36,708)		(37,003)	(120,178)		(116,697)
Underwriting income (loss)		$ 130,530		$ 262,476	$ 404,594		$ 764,907
Underwriting Ratios
Loss ratio		43.60%		3.80%	41.90%		4.90%
Acquisition expense ratio		10.20%		10.00%	10.20%		9.70%
Other operating expense ratio		10.40%		10.80%	11.30%		11.50%
Combined ratio		64.20%		24.60%	63.40%		26.10%
Goodwill and intangible assets		$ 403,662		$ 457,860	$ 403,662		$ 457,860

[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.