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Segment Information - Summary of underwriting income or loss by segment (Details)
$ in Millions
 3 Months Ended
Mar. 31, 2023
USD ($)
segment
Mar. 31, 2022
USD ($)
Dec. 31, 2022
USD ($)
Segment Reporting Information [Line Items]      
Number of segments | segment 3    
Gross premiums written $ 4,780 $ 3,801  
Premiums ceded (1,356) (1,167)  
Net premiums written 3,424 2,634  
Change in unearned premiums (541) (513)  
Net premiums earned 2,883 2,121  
Other underwriting income 10 6  
Losses and loss adjustment expenses (1,471) (1,001)  
Acquisition expenses (533) (378)  
Other operating expenses (319) (290)  
Underwriting income (loss) 570 458  
Net investment income 199 80  
Net realized gains (losses) 17 (292)  
Equity in net income (loss) of investment funds accounted for using the equity method 48 36  
Other income (loss) 11 (9)  
Corporate expenses [1] (29) (32)  
Transaction costs and other [1] (1) 0  
Amortization of intangible assets (23) (27)  
Interest expense (32) (33)  
Net foreign exchange gains (losses) (18) 4  
Income (loss) before income taxes and income (loss) from operating affiliates 742 185  
Income tax expense (benefit) (64) (12)  
Income (loss) from operating affiliates 39 25  
Net income (loss) 717 198  
Amounts attributable to redeemable noncontrolling interests (2) (2)  
Net income (loss) available to Arch 715 196  
Preferred dividends (10) (10)  
Net income (loss) available to Arch common shareholders $ 705 $ 186  
Underwriting Ratios      
Loss ratio 51.00% 47.20%  
Acquisition expense ratio 18.50% 17.80%  
Other operating expense ratio 11.10% 13.70%  
Combined ratio 80.60% 78.70%  
Goodwill and intangible assets $ 785 $ 926 $ 804
Operating segments | Insurance      
Segment Reporting Information [Line Items]      
Gross premiums written [2] 1,979 1,720  
Premiums ceded (542) (513)  
Net premiums written 1,437 1,207  
Change in unearned premiums (180) (180)  
Net premiums earned 1,257 1,027  
Other underwriting income 0 0  
Losses and loss adjustment expenses (703) (601)  
Acquisition expenses (245) (196)  
Other operating expenses (195) (167)  
Underwriting income (loss) $ 114 $ 63  
Underwriting Ratios      
Loss ratio 55.90% 58.50%  
Acquisition expense ratio 19.50% 19.10%  
Other operating expense ratio 15.50% 16.20%  
Combined ratio 90.90% 93.80%  
Goodwill and intangible assets $ 228 $ 249  
Operating segments | Reinsurance      
Segment Reporting Information [Line Items]      
Gross premiums written [2] 2,460 1,719  
Premiums ceded (734) (580)  
Net premiums written 1,726 1,139  
Change in unearned premiums (396) (335)  
Net premiums earned 1,330 804  
Other underwriting income 4 1  
Losses and loss adjustment expenses (766) (454)  
Acquisition expenses (281) (172)  
Other operating expenses (74) (70)  
Underwriting income (loss) $ 213 $ 109  
Underwriting Ratios      
Loss ratio 57.60% 56.50%  
Acquisition expense ratio 21.10% 21.40%  
Other operating expense ratio 5.60% 8.70%  
Combined ratio 84.30% 86.60%  
Goodwill and intangible assets $ 142 $ 184  
Operating segments | Mortgage      
Segment Reporting Information [Line Items]      
Gross premiums written [2] 343 365  
Premiums ceded (82) (77)  
Net premiums written 261 288  
Change in unearned premiums 35 2  
Net premiums earned 296 290  
Other underwriting income 6 5  
Losses and loss adjustment expenses (2) 54  
Acquisition expenses (7) (10)  
Other operating expenses (50) (53)  
Underwriting income (loss) $ 243 $ 286  
Underwriting Ratios      
Loss ratio 0.60% (18.90%)  
Acquisition expense ratio 2.50% 3.60%  
Other operating expense ratio 16.90% 18.40%  
Combined ratio 20.00% 3.10%  
Goodwill and intangible assets $ 415 $ 493  
[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.