Segment Information - Summary of underwriting income or loss by segment (Details) $ in Millions		3 Months Ended		9 Months Ended
		Sep. 30, 2023 USD ($)	Sep. 30, 2022 USD ($)	Sep. 30, 2023 USD ($) segment	Sep. 30, 2022 USD ($)	Dec. 31, 2022 USD ($)
Segment Reporting Information [Line Items]
Number of segments | segment				3
Gross premiums written		$ 4,527	$ 3,861	$ 14,152	$ 11,532
Premiums ceded		(1,172)	(1,137)	(3,945)	(3,489)
Net premiums written		3,355	2,724	10,207	8,043
Change in unearned premiums		(107)	(253)	(1,111)	(1,125)
Net premiums earned		3,248	2,471	9,096	6,918
Other underwriting income		5	3	21	12
Losses and loss adjustment expenses		(1,647)	(1,683)	(4,609)	(3,787)
Acquisition expenses		(575)	(448)	(1,669)	(1,239)
Other operating expenses		(310)	(275)	(942)	(842)
Underwriting income (loss)		721	68	1,897	1,062
Net investment income		269	129	710	315
Net realized gains (losses)		(248)	(184)	(354)	(743)
Equity in net income (loss) of investment funds accounted for using the equity method		59	(19)	176	75
Other income (loss)		(4)	(14)	10	(35)
Corporate expenses	[1]	(20)	(18)	(69)	(78)
Transaction costs and other	[1]	0	0	(2)	0
Amortization of intangible assets		(24)	(26)	(71)	(80)
Interest expense		(34)	(33)	(99)	(99)
Net foreign exchange gains (losses)		22	91	(1)	183
Income (loss) before income taxes and income (loss) from operating affiliates		741	(6)	2,197	600
Income tax expense (benefit)		(72)	15	(203)	(19)
Income (loss) from operating affiliates		54	9	115	39
Net income (loss)		723	18	2,109	620
Net (income) loss attributable to noncontrolling interests		0	(1)	0	(3)
Net income (loss) available to Arch		723	17	2,109	617
Preferred dividends		(10)	(10)	(30)	(30)
Net income (loss) available to Arch common shareholders		$ 713	$ 7	$ 2,079	$ 587
Underwriting Ratios
Loss ratio		50.70%	68.10%	50.70%	54.70%
Acquisition expense ratio		17.70%	18.10%	18.30%	17.90%
Other operating expense ratio		9.50%	11.10%	10.40%	12.20%
Combined ratio		77.90%	97.30%	79.40%	84.80%
Goodwill and intangible assets		$ 739	$ 807	$ 739	$ 807	$ 804
Operating segments | Insurance
Segment Reporting Information [Line Items]
Gross premiums written	[2]	2,043	1,862	5,977	5,287
Premiums ceded		(521)	(493)	(1,564)	(1,483)
Net premiums written		1,522	1,369	4,413	3,804
Change in unearned premiums		(110)	(182)	(416)	(488)
Net premiums earned		1,412	1,187	3,997	3,316
Other underwriting income		0	0	0	0
Losses and loss adjustment expenses		(812)	(823)	(2,276)	(2,054)
Acquisition expenses		(269)	(233)	(778)	(643)
Other operating expenses		(202)	(165)	(592)	(493)
Underwriting income (loss)		$ 129	$ (34)	$ 351	$ 126
Underwriting Ratios
Loss ratio		57.50%	69.30%	57.00%	61.90%
Acquisition expense ratio		19.10%	19.60%	19.50%	19.40%
Other operating expense ratio		14.30%	13.90%	14.80%	14.90%
Combined ratio		90.90%	102.80%	91.30%	96.20%
Goodwill and intangible assets		$ 220	$ 225	$ 220	$ 225
Operating segments | Reinsurance
Segment Reporting Information [Line Items]
Gross premiums written	[2]	2,138	1,639	7,142	5,151
Premiums ceded		(576)	(560)	(2,145)	(1,770)
Net premiums written		1,562	1,079	4,997	3,381
Change in unearned premiums		(19)	(77)	(781)	(647)
Net premiums earned		1,543	1,002	4,216	2,734
Other underwriting income		2	0	9	6
Losses and loss adjustment expenses		(870)	(928)	(2,379)	(1,920)
Acquisition expenses		(304)	(208)	(875)	(569)
Other operating expenses		(61)	(63)	(203)	(199)
Underwriting income (loss)		$ 310	$ (197)	$ 768	$ 52
Underwriting Ratios
Loss ratio		56.40%	92.60%	56.40%	70.20%
Acquisition expense ratio		19.70%	20.80%	20.70%	20.80%
Other operating expense ratio		3.90%	6.30%	4.80%	7.30%
Combined ratio		80.00%	119.70%	81.90%	98.30%
Goodwill and intangible assets		$ 132	$ 141	$ 132	$ 141
Operating segments | Mortgage
Segment Reporting Information [Line Items]
Gross premiums written	[2]	347	362	1,037	1,099
Premiums ceded		(76)	(86)	(240)	(241)
Net premiums written		271	276	797	858
Change in unearned premiums		22	6	86	10
Net premiums earned		293	282	883	868
Other underwriting income		3	3	12	6
Losses and loss adjustment expenses		35	68	46	187
Acquisition expenses		(2)	(7)	(16)	(27)
Other operating expenses		(47)	(47)	(147)	(150)
Underwriting income (loss)		$ 282	$ 299	$ 778	$ 884
Underwriting Ratios
Loss ratio		(12.10%)	(24.10%)	(5.30%)	(21.60%)
Acquisition expense ratio		0.60%	2.40%	1.80%	3.20%
Other operating expense ratio		16.20%	16.50%	16.70%	17.30%
Combined ratio		4.70%	(5.20%)	13.20%	(1.10%)
Goodwill and intangible assets		$ 387	$ 441	$ 387	$ 441

[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.