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Segment Information - Summary of underwriting income or loss by segment (Details)
$ in Millions
 3 Months Ended 6 Months Ended
Jun. 30, 2023
USD ($)
Jun. 30, 2022
USD ($)
Jun. 30, 2023
USD ($)
segment
Jun. 30, 2022
USD ($)
Dec. 31, 2022
USD ($)
Segment Reporting Information [Line Items]          
Number of segments | segment     3    
Gross premiums written $ 4,845 $ 3,870 $ 9,625 $ 7,671  
Premiums ceded (1,417) (1,185) (2,773) (2,352)  
Net premiums written 3,428 2,685 6,852 5,319  
Change in unearned premiums (463) (359) (1,004) (872)  
Net premiums earned 2,965 2,326 5,848 4,447  
Other underwriting income 6 3 16 9  
Losses and loss adjustment expenses (1,491) (1,103) (2,962) (2,104)  
Acquisition expenses (561) (413) (1,094) (791)  
Other operating expenses (313) (277) (632) (567)  
Underwriting income (loss) 606 536 1,176 994  
Net investment income 242 106 441 186  
Net realized gains (losses) (123) (267) (106) (559)  
Equity in net income (loss) of investment funds accounted for using the equity method 69 58 117 94  
Other income (loss) 3 (12) 14 (21)  
Corporate expenses [1] (20) (28) (49) (60)  
Transaction costs and other [1] (1) 0 (2) 0  
Amortization of intangible assets (24) (27) (47) (54)  
Interest expense (33) (33) (65) (66)  
Net foreign exchange gains (losses) (5) 88 (23) 92  
Income (loss) before income taxes and income (loss) from operating affiliates 714 421 1,456 606  
Income tax expense (benefit) (67) (22) (131) (34)  
Income (loss) from operating affiliates 22 5 61 30  
Net income (loss) 669 404 1,386 602  
Net (income) loss attributable to noncontrolling interests 2 0 0 (2)  
Net income (loss) available to Arch 671 404 1,386 600  
Preferred dividends (10) (10) (20) (20)  
Net income (loss) available to Arch common shareholders $ 661 $ 394 $ 1,366 $ 580  
Underwriting Ratios          
Loss ratio 50.30% 47.40% 50.60% 47.30%  
Acquisition expense ratio 18.90% 17.80% 18.70% 17.80%  
Other operating expense ratio 10.60% 11.90% 10.80% 12.80%  
Combined ratio 79.80% 77.10% 80.10% 77.90%  
Goodwill and intangible assets $ 775 $ 868 $ 775 $ 868 $ 804
Operating segments | Insurance          
Segment Reporting Information [Line Items]          
Gross premiums written [2] 1,955 1,705 3,934 3,425  
Premiums ceded (501) (477) (1,043) (990)  
Net premiums written 1,454 1,228 2,891 2,435  
Change in unearned premiums (126) (126) (306) (306)  
Net premiums earned 1,328 1,102 2,585 2,129  
Other underwriting income 0 0 0 0  
Losses and loss adjustment expenses (761) (630) (1,464) (1,231)  
Acquisition expenses (264) (214) (509) (410)  
Other operating expenses (195) (161) (390) (328)  
Underwriting income (loss) $ 108 $ 97 $ 222 $ 160  
Underwriting Ratios          
Loss ratio 57.30% 57.10% 56.60% 57.80%  
Acquisition expense ratio 19.90% 19.40% 19.70% 19.20%  
Other operating expense ratio 14.70% 14.60% 15.10% 15.40%  
Combined ratio 91.90% 91.10% 91.40% 92.40%  
Goodwill and intangible assets $ 228 $ 237 $ 228 $ 237  
Operating segments | Reinsurance          
Segment Reporting Information [Line Items]          
Gross premiums written [2] 2,544 1,793 5,004 3,512  
Premiums ceded (835) (630) (1,569) (1,210)  
Net premiums written 1,709 1,163 3,435 2,302  
Change in unearned premiums (366) (235) (762) (570)  
Net premiums earned 1,343 928 2,673 1,732  
Other underwriting income 3 5 7 6  
Losses and loss adjustment expenses (743) (538) (1,509) (992)  
Acquisition expenses (290) (189) (571) (361)  
Other operating expenses (68) (66) (142) (136)  
Underwriting income (loss) $ 245 $ 140 $ 458 $ 249  
Underwriting Ratios          
Loss ratio 55.30% 57.90% 56.50% 57.30%  
Acquisition expense ratio 21.60% 20.40% 21.30% 20.90%  
Other operating expense ratio 5.00% 7.10% 5.30% 7.80%  
Combined ratio 81.90% 85.40% 83.10% 86.00%  
Goodwill and intangible assets $ 146 $ 166 $ 146 $ 166  
Operating segments | Mortgage          
Segment Reporting Information [Line Items]          
Gross premiums written [2] 347 372 690 737  
Premiums ceded (82) (78) (164) (155)  
Net premiums written 265 294 526 582  
Change in unearned premiums 29 2 64 4  
Net premiums earned 294 296 590 586  
Other underwriting income 3 (2) 9 3  
Losses and loss adjustment expenses 13 65 11 119  
Acquisition expenses (7) (10) (14) (20)  
Other operating expenses (50) (50) (100) (103)  
Underwriting income (loss) $ 253 $ 299 $ 496 $ 585  
Underwriting Ratios          
Loss ratio (4.50%) (21.90%) (1.90%) (20.40%)  
Acquisition expense ratio 2.40% 3.40% 2.40% 3.50%  
Other operating expense ratio 17.10% 17.00% 17.00% 17.70%  
Combined ratio 15.00% (1.50%) 17.50% 0.80%  
Goodwill and intangible assets $ 401 $ 465 $ 401 $ 465  
[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.