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Segment Information - Summary of underwriting income or loss by segment (Details)
$ in Millions
 3 Months Ended 9 Months Ended
Sep. 30, 2025
USD ($)
Sep. 30, 2024
USD ($)
Sep. 30, 2025
USD ($)
segment
Sep. 30, 2024
USD ($)
Dec. 31, 2024
USD ($)
Segment Reporting Information [Line Items]          
Number of segments | segment     3    
Gross premiums written $ 5,410 $ 5,440 $ 18,069 $ 16,755  
Premiums ceded (1,446) (1,393) (5,242) (4,842)  
Net premiums written 3,964 4,047 12,827 11,913  
Change in unearned premiums 321 (77) (17) (956)  
Net premiums earned 4,285 3,970 12,810 10,957  
Other underwriting income 50 5 165 20  
Losses and loss adjustment expenses (2,200) (2,403) (7,090) (5,958)  
Acquisition expenses (786) (681) (2,374) (1,921)  
Other operating expenses (478) (353) (1,405) (1,062)  
Underwriting income (loss) 871 538 2,106 2,036  
Net investment income 408 399 1,191 1,090  
Net realized gains (losses) 210 169 442 358  
Equity in net income of investments accounted for using the equity method 134 171 349 437  
Other income (loss) 22 8 38 30  
Corporate expenses [1] (28) (19) (107) (88)  
Transaction costs and other [1] (21) (30) (49) (55)  
Amortization of intangible assets (49) (88) (146) (136)  
Interest expense (37) (35) (110) (104)  
Net foreign exchange gains (losses) (7) (63) (122) (31)  
Income (loss) before income taxes and income (loss) from operating affiliates 1,503 1,050 3,592 3,537  
Income tax expense (benefit) (215) (98) (550) (296)  
Income (loss) from operating affiliates 62 36 119 136  
Net income available to Arch 1,350 988 3,161 3,377  
Preferred dividends (10) (10) (30) (30)  
Net income (loss) available to Arch common shareholders $ 1,340 $ 978 $ 3,131 $ 3,347  
Underwriting Ratios          
Loss ratio 51.40% 60.50% 55.40% 54.40%  
Acquisition expense ratio 18.40% 17.20% 18.50% 17.50%  
Other operating expense ratio [2] 10.00%   9.70%    
Other operating expense ratio   8.90%   9.70%  
Combined ratio 79.80% 86.60% 83.60% 81.60%  
Goodwill and intangible assets $ 1,268 $ 1,486 $ 1,268 $ 1,486 $ 1,351
Operating segments | Insurance          
Segment Reporting Information [Line Items]          
Gross premiums written [3] 2,567 2,341 7,893 6,569  
Premiums ceded [3] (614) (521) (1,971) (1,649)  
Net premiums written 1,953 1,820 5,922 4,920  
Change in unearned premiums 16 (55) (124) (226)  
Net premiums earned 1,969 1,765 5,798 4,694  
Other underwriting income 9 [4] 0 25 [4] 0  
Losses and loss adjustment expenses (1,162) (1,087) (3,568) (2,789)  
Acquisition expenses (386) (308) (1,116) (872)  
Other operating expenses [5] (301) (250) (883) (718)  
Underwriting income (loss) $ 129 $ 120 $ 256 $ 315  
Underwriting Ratios          
Loss ratio 59.00% 61.60% 61.50% 59.40%  
Acquisition expense ratio 19.60% 17.40% 19.30% 18.60%  
Other operating expense ratio [2] 14.80%   14.80%    
Other operating expense ratio   14.10%   15.30%  
Combined ratio 93.40% 93.10% 95.60% 93.30%  
Goodwill and intangible assets $ 833 $ 1,025 $ 833 $ 1,025  
Operating segments | Reinsurance          
Segment Reporting Information [Line Items]          
Gross premiums written [3] 2,515 2,763 9,205 9,171  
Premiums ceded [3] (778) (818) (3,093) (3,013)  
Net premiums written 1,737 1,945 6,112 6,158  
Change in unearned premiums 278 (53) 18 (820)  
Net premiums earned 2,015 1,892 6,130 5,338  
Other underwriting income 38 [4] 2 123 [4] 5  
Losses and loss adjustment expenses (1,040) (1,317) (3,524) (3,206)  
Acquisition expenses (398) (374) (1,251) (1,050)  
Other operating expenses [5] (133) (54) (378) (193)  
Underwriting income (loss) $ 482 $ 149 $ 1,100 $ 894  
Underwriting Ratios          
Loss ratio 51.60% 69.60% 57.50% 60.10%  
Acquisition expense ratio 19.80% 19.80% 20.40% 19.70%  
Other operating expense ratio [2] 4.70%   4.20%    
Other operating expense ratio   2.90%   3.60%  
Combined ratio 76.10% 92.30% 82.10% 83.40%  
Goodwill and intangible assets $ 100 $ 113 $ 100 $ 113  
Operating segments | Mortgage          
Segment Reporting Information [Line Items]          
Gross premiums written [3] 330 339 979 1,020  
Premiums ceded [3] (56) (57) (186) (185)  
Net premiums written 274 282 793 835  
Change in unearned premiums 27 31 89 90  
Net premiums earned 301 313 882 925  
Other underwriting income 3 [4] 3 17 [4] 15  
Losses and loss adjustment expenses 2 1 2 37  
Acquisition expenses (2) 1 (7) 1  
Other operating expenses [5] (44) (49) (144) (151)  
Underwriting income (loss) $ 260 $ 269 $ 750 $ 827  
Underwriting Ratios          
Loss ratio (0.50%) (0.40%) (0.20%) (4.00%)  
Acquisition expense ratio 0.70% (0.40%) 0.80% (0.10%)  
Other operating expense ratio [2] 13.30%   14.30%    
Other operating expense ratio   15.60%   16.30%  
Combined ratio 13.50% 14.80% 14.90% 12.20%  
Goodwill and intangible assets $ 335 $ 348 $ 335 $ 348  
[1] Certain expenses have been excluded from ‘Corporate expenses’ and reflected in ‘Transaction costs and other.’
[2] The ‘Other operating expense ratio’ for the 2025 period includes ‘Other underwriting income.’
[3] 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.
[4] ‘Other underwriting income’ includes revenue earned from underwriting-related activities covered under existing service contracts.
[5] ‘Other operating expenses’ primarily include expenses that are related to compensation and employee benefits, information technology and professional fees.