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Segment Information - Summary of underwriting income or loss by segment (Details)
$ in Millions
 3 Months Ended
Mar. 31, 2024
USD ($)
segment
Mar. 31, 2023
USD ($)
Dec. 31, 2023
USD ($)
Segment Reporting Information [Line Items]      
Number of segments | segment 3    
Gross premiums written $ 5,933 $ 4,780  
Premiums ceded (1,848) (1,356)  
Net premiums written 4,085 3,424  
Change in unearned premiums (663) (541)  
Net premiums earned 3,422 2,883  
Other underwriting income 12 10  
Losses and loss adjustment expenses (1,728) (1,471)  
Acquisition expenses (607) (533)  
Other operating expenses (363) (319)  
Underwriting income (loss) 736 570  
Net investment income 327 199  
Net realized gains (losses) 67 17  
Equity in net income (loss) of investment funds accounted for using the equity method 99 48  
Other income (loss) 14 11  
Corporate expenses [1] (46) (29)  
Transaction costs and other [1] (7) (1)  
Amortization of intangible assets (21) (23)  
Interest expense (34) (32)  
Net foreign exchange gains (losses) 31 (18)  
Income (loss) before income taxes and income (loss) from operating affiliates 1,166 742  
Income tax expense (benefit) (101) (64)  
Income (loss) from operating affiliates 55 39  
Net income (loss) 1,120 717  
Net (income) loss attributable to noncontrolling interests 0 (2)  
Net income available to Arch 1,120 715  
Preferred dividends (10) (10)  
Net income (loss) available to Arch common shareholders $ 1,110 $ 705  
Underwriting Ratios      
Loss ratio 50.50% 51.00%  
Acquisition expense ratio 17.70% 18.50%  
Other operating expense ratio 10.60% 11.10%  
Combined ratio 78.80% 80.60%  
Goodwill and intangible assets $ 778 $ 785 $ 731
Operating segments | Insurance      
Segment Reporting Information [Line Items]      
Gross premiums written [2] 2,126 1,979  
Premiums ceded [2] (584) (542)  
Net premiums written 1,542 1,437  
Change in unearned premiums (91) (180)  
Net premiums earned 1,451 1,257  
Other underwriting income 0 0  
Losses and loss adjustment expenses (854) (703)  
Acquisition expenses (276) (245)  
Other operating expenses (235) (195)  
Underwriting income (loss) $ 86 $ 114  
Underwriting Ratios      
Loss ratio 58.90% 55.90%  
Acquisition expense ratio 19.00% 19.50%  
Other operating expense ratio 16.20% 15.50%  
Combined ratio 94.10% 90.90%  
Goodwill and intangible assets $ 293 $ 228  
Operating segments | Reinsurance      
Segment Reporting Information [Line Items]      
Gross premiums written [2] 3,467 2,460  
Premiums ceded [2] (1,201) (734)  
Net premiums written 2,266 1,726  
Change in unearned premiums (600) (396)  
Net premiums earned 1,666 1,330  
Other underwriting income 2 4  
Losses and loss adjustment expenses (883) (766)  
Acquisition expenses (331) (281)  
Other operating expenses (75) (74)  
Underwriting income (loss) $ 379 $ 213  
Underwriting Ratios      
Loss ratio 53.00% 57.60%  
Acquisition expense ratio 19.90% 21.10%  
Other operating expense ratio 4.50% 5.60%  
Combined ratio 77.40% 84.30%  
Goodwill and intangible assets $ 121 $ 142  
Operating segments | Mortgage      
Segment Reporting Information [Line Items]      
Gross premiums written [2] 341 343  
Premiums ceded [2] (64) (82)  
Net premiums written 277 261  
Change in unearned premiums 28 35  
Net premiums earned 305 296  
Other underwriting income 10 6  
Losses and loss adjustment expenses 9 (2)  
Acquisition expenses 0 (7)  
Other operating expenses (53) (50)  
Underwriting income (loss) $ 271 $ 243  
Underwriting Ratios      
Loss ratio (3.00%) 0.60%  
Acquisition expense ratio 0.00% 2.50%  
Other operating expense ratio 17.50% 16.90%  
Combined ratio 14.50% 20.00%  
Goodwill and intangible assets $ 364 $ 415  
[1] Certain expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’
[2] Certain assumed and ceded amounts related to intersegment transactions are included in individual segment results. Accordingly, the sum of such transactions for each segment does not agree to the total due to eliminations.