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Segment Information - Analysis of underwriting income by segment and reconciliation to net income available to common shareholders (Details)
$ in Thousands
 12 Months Ended
Dec. 31, 2021
USD ($)
segment
Dec. 31, 2020
USD ($)
Dec. 31, 2019
USD ($)
Segment Reporting Information [Line Items]      
Gross premiums written $ 12,752,487 $ 10,088,068 $ 8,138,960
Premiums ceded (3,734,150) (2,650,352) (2,099,893)
Net premiums written 9,018,337 7,437,716 6,039,067
Change in unearned premiums (936,039) (445,781) (252,569)
Net premiums earned 8,082,298 6,991,935 5,786,498
Other underwriting income 22,073 26,784 24,861
Losses and loss adjustment expenses (4,584,803) (4,689,599) (3,133,452)
Acquisition expenses, net (1,303,178) (1,004,842) (840,945)
Other operating expenses (998,595) (875,176) (800,997)
Underwriting income (loss) 1,217,795 449,102 1,035,965
Net investment income 389,118 519,608 627,738
Net realized gains (losses) 379,845 823,460 363,198
Equity in net income (loss) of investment funds accounted for using the equity method 366,402 146,693 123,672
Other income (loss) 10,244 29 0
Corporate expenses (77,119) (68,492) (65,667)
Transaction costs and other (2,038) (13,496) (14,444)
Amortization of intangible assets (82,955) (69,031) (82,104)
Interest expense (139,470) (143,456) (120,872)
Net foreign exchange gains (losses) 41,529 (83,634) (20,609)
Income (loss) before income taxes and income (loss) from operating affiliates 2,103,351 1,560,783 1,846,877
Income tax (expense) benefit (128,582) (111,838) (155,810)
Income (loss) from operating affiliates 264,693 16,766 2,233
Net income (loss) 2,239,462 1,465,711 1,693,300
Amounts attributable to redeemable noncontrolling interests (4,299) (7,114) (16,909)
Amounts attributable to nonredeemable noncontrolling interests (78,314) (53,076) (40,072)
Net income available to Arch 2,156,849 1,405,521 1,636,319
Preferred share dividends (48,343) (41,612) (41,612)
Loss on redemption of preferred shares (15,101) 0 0
Net income (loss) available to Arch common shareholders $ 2,093,405 $ 1,363,909 $ 1,594,707
Underwriting Ratios      
Loss ratio 56.70% 67.10% 54.20%
Acquisition expense ratio 16.10% 14.40% 14.50%
Other operating expense ratio 12.40% 12.50% 13.80%
Combined ratio 85.20% 94.00% 82.50%
Goodwill and intangible assets $ 944,983 $ 692,863 $ 738,083
Total investable assets 27,442,153 29,513,907 24,990,265
Total assets 45,100,945 43,282,297 37,885,361
Total liabilities $ 31,545,816 29,294,856 25,569,809
Operating segments | Underwriting Segments      
Segment Reporting Information [Line Items]      
Number of segments | segment 3    
Gross premiums written [1] $ 12,463,788 9,632,691 7,695,645
Premiums ceded (3,800,153) (2,732,564) (2,189,440)
Net premiums written 8,663,635 6,900,127 5,506,205
Change in unearned premiums (913,305) (468,543) (276,396)
Net premiums earned 7,750,330 6,431,584 5,229,809
Other underwriting income 21,334 24,739 22,449
Losses and loss adjustment expenses (4,325,761) (4,249,117) (2,680,317)
Acquisition expenses, net (1,240,437) (906,771) (734,965)
Other operating expenses (965,726) (819,366) (749,346)
Underwriting income (loss) 1,239,740 481,069 1,087,630
Net investment income 346,808 401,908 491,067
Net realized gains (losses) 299,207 813,781 348,037
Equity in net income (loss) of investment funds accounted for using the equity method 366,402 146,693 123,672
Other income (loss) 10,244 29  
Corporate expenses (77,119) (68,492) (65,667)
Transaction costs and other (1,103) (9,456) (14,444)
Amortization of intangible assets (82,057) (69,031) (82,104)
Interest expense (131,060) (120,214) (93,735)
Net foreign exchange gains (losses) 42,854 (80,161) (9,252)
Income (loss) before income taxes and income (loss) from operating affiliates 2,013,916 1,496,126 1,785,204
Income tax (expense) benefit (128,348) (111,812) (155,790)
Income (loss) from operating affiliates 264,693 16,766 2,233
Net income (loss) 2,150,261 1,401,080 1,631,647
Amounts attributable to redeemable noncontrolling interests (2,346) (2,997) 0
Amounts attributable to nonredeemable noncontrolling interests 0 0 0
Net income available to Arch 2,147,915 1,398,083 1,631,647
Preferred share dividends (48,343) (41,612) (41,612)
Loss on redemption of preferred shares (15,101)    
Net income (loss) available to Arch common shareholders $ 2,084,471 $ 1,356,471 $ 1,590,035
Underwriting Ratios      
Loss ratio 55.80% 66.10% 51.30%
Acquisition expense ratio 16.00% 14.10% 14.10%
Other operating expense ratio 12.50% 12.70% 14.30%
Combined ratio 84.30% 92.90% 79.70%
Goodwill and intangible assets $ 944,983 $ 685,213 $ 730,433
Total investable assets 27,442,153 26,856,295 22,285,676
Total assets 45,100,945 39,791,983 34,374,468
Total liabilities 31,545,816 26,789,149 22,977,636
Operating segments | Insurance      
Segment Reporting Information [Line Items]      
Gross premiums written [1] 5,867,734 4,688,562 3,907,993
Premiums ceded [2] (1,719,541) (1,525,655) (1,266,267)
Net premiums written 4,148,193 3,162,907 2,641,726
Change in unearned premiums (521,725) (291,487) (244,646)
Net premiums earned 3,626,468 2,871,420 2,397,080
Other underwriting income 0 (31) 0
Losses and loss adjustment expenses (2,344,365) (2,092,453) (1,615,475)
Acquisition expenses, net (606,265) (418,483) (361,614)
Other operating expenses (558,906) (489,153) (454,770)
Underwriting income (loss) $ 116,932 $ (128,700) $ (34,779)
Underwriting Ratios      
Loss ratio 64.60% 72.90% 67.40%
Acquisition expense ratio 16.70% 14.60% 15.10%
Other operating expense ratio 15.40% 17.00% 19.00%
Combined ratio 96.70% 104.50% 101.50%
Goodwill and intangible assets $ 256,434 $ 280,978 $ 289,021
Operating segments | Reinsurance      
Segment Reporting Information [Line Items]      
Gross premiums written [1] 5,093,930 3,472,086 2,323,223
Premiums ceded [2] (1,839,556) (1,014,716) (720,500)
Net premiums written 3,254,374 2,457,370 1,602,723
Change in unearned premiums (413,931) (295,141) (136,334)
Net premiums earned 2,840,443 2,162,229 1,466,389
Other underwriting income 3,669 4,454 6,444
Losses and loss adjustment expenses (1,924,719) (1,628,320) (1,011,329)
Acquisition expenses, net (536,754) (354,048) (239,032)
Other operating expenses (212,810) (168,011) (141,484)
Underwriting income (loss) $ 169,829 $ 16,304 $ 80,988
Underwriting Ratios      
Loss ratio 67.80% 75.30% 69.00%
Acquisition expense ratio 18.90% 16.40% 16.30%
Other operating expense ratio 7.50% 7.80% 9.60%
Combined ratio 94.20% 99.50% 94.90%
Goodwill and intangible assets $ 183,523 $ 18,963 $ 2,516
Operating segments | Mortgage      
Segment Reporting Information [Line Items]      
Gross premiums written [1] 1,507,825 1,473,999 1,466,265
Premiums ceded [2] (246,757) (194,149) (204,509)
Net premiums written 1,261,068 1,279,850 1,261,756
Change in unearned premiums 22,351 118,085 104,584
Net premiums earned 1,283,419 1,397,935 1,366,340
Other underwriting income 17,665 20,316 16,005
Losses and loss adjustment expenses (56,677) (528,344) (53,513)
Acquisition expenses, net (97,418) (134,240) (134,319)
Other operating expenses (194,010) (162,202) (153,092)
Underwriting income (loss) $ 952,979 $ 593,465 $ 1,041,421
Underwriting Ratios      
Loss ratio 4.40% 37.80% 3.90%
Acquisition expense ratio 7.60% 9.60% 9.80%
Other operating expense ratio 15.10% 11.60% 11.20%
Combined ratio 27.10% 59.00% 24.90%
Goodwill and intangible assets $ 505,026 $ 385,272 $ 438,896
Operating segments | Other      
Segment Reporting Information [Line Items]      
Number of segments | segment 2    
Gross premiums written [1] $ 457,465 728,546 754,881
Premiums ceded [2] (102,763) (190,957) (222,019)
Net premiums written 354,702 537,589 532,862
Change in unearned premiums (22,734) 22,762 23,827
Net premiums earned 331,968 560,351 556,689
Other underwriting income 739 2,045 2,412
Losses and loss adjustment expenses (259,042) (440,482) (453,135)
Acquisition expenses, net (62,741) (98,071) (105,980)
Other operating expenses (32,869) (55,810) (51,651)
Underwriting income (loss) (21,945) (31,967) (51,665)
Net investment income 42,310 117,700 136,671
Net realized gains (losses) 80,638 9,679 15,161
Equity in net income (loss) of investment funds accounted for using the equity method 0 0 0
Other income (loss) 0 0  
Corporate expenses 0 0 0
Transaction costs and other (935) (4,040) 0
Amortization of intangible assets (898) 0 0
Interest expense (8,410) (23,242) (27,137)
Net foreign exchange gains (losses) (1,325) (3,473) (11,357)
Income (loss) before income taxes and income (loss) from operating affiliates 89,435 64,657 61,673
Income tax (expense) benefit (234) (26) (20)
Income (loss) from operating affiliates 0 0 0
Net income (loss) 89,201 64,631 61,653
Amounts attributable to redeemable noncontrolling interests (1,953) (4,117) (16,909)
Amounts attributable to nonredeemable noncontrolling interests (78,314) (53,076) (40,072)
Net income available to Arch 8,934 7,438 4,672
Preferred share dividends 0 0 0
Loss on redemption of preferred shares 0    
Net income (loss) available to Arch common shareholders $ 8,934 $ 7,438 $ 4,672
Underwriting Ratios      
Loss ratio 78.00% 78.60% 81.40%
Acquisition expense ratio 18.90% 17.50% 19.00%
Other operating expense ratio 9.90% 10.00% 9.30%
Combined ratio 106.80% 106.10% 109.70%
Goodwill and intangible assets $ 0 $ 7,650 $ 7,650
Total investable assets 0 2,657,612 2,704,589
Total assets 0 3,490,314 3,510,893
Total liabilities $ 0 $ 2,505,707 $ 2,592,173
[1] 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.
[2] Certain amounts included in the gross premiums written of each segment are related to intersegment transactions and are included in the gross premiums written of each segment. 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.