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Segment Information - Summary of underwriting income or loss by segment (Details)
$ in Thousands
 3 Months Ended 9 Months Ended
Sep. 30, 2021
USD ($)
Sep. 30, 2020
USD ($)
Sep. 30, 2021
USD ($)
segment
Sep. 30, 2020
USD ($)
Dec. 31, 2020
USD ($)
Segment Reporting Information [Line Items]          
Gross premiums written $ 3,207,415 $ 2,681,032 $ 9,890,912 $ 7,831,554  
Premiums ceded (1,131,486) (806,888) (2,907,002) (2,151,853)  
Net premiums written 2,075,929 1,874,144 6,983,910 5,679,701  
Change in unearned premiums (146,592) (103,052) (985,242) (498,811)  
Net premiums earned 1,929,337 1,771,092 5,998,668 5,180,890  
Other underwriting income (loss) 7,274 5,413 18,913 18,932  
Losses and loss adjustment expenses (1,226,019) (1,216,273) (3,588,950) (3,562,214)  
Acquisition expenses (306,015) (247,942) (945,639) (750,014)  
Other operating expenses (230,832) (215,686) (736,808) (659,479)  
Underwriting income (loss) 173,745 96,604 746,184 228,115  
Net investment income 88,195 128,512 298,664 405,150  
Net realized gains (losses) (25,040) 280,499 320,328 470,127  
Equity in net income (loss) of investment funds accounted for using the equity method 105,398 126,735 299,270 57,407  
Other income (loss) (3,960) 0 1,151 65  
Corporate expenses (18,636) (16,263) (59,279) (51,407)  
Transaction costs and other (1,036) (1,674) (1,728) (5,246)  
Amortization of intangible assets (20,135) (16,715) (49,823) (49,835)  
Interest expense (33,176) (41,343) (107,222) (105,037)  
Net foreign exchange gains (losses) 36,078 (44,885) 38,366 (11,425)  
Income (loss) before income taxes and income (loss) from operating affiliates 301,433 511,470 1,485,911 937,914  
Income tax expense (benefit) (4,137) (23,707) (94,176) (77,779)  
Income (loss) from operating affiliates 124,119 919 224,052 6,262  
Net income (loss) 421,415 488,682 1,615,787 866,397  
Amounts attributable to redeemable noncontrolling interests (1,473) (1,875) (3,889) (4,998)  
Amounts attributable to non-redeemable noncontrolling interests 0 (67,768) (78,314) 578  
Net income (loss) available to Arch 419,942 419,039 1,533,584 861,977  
Preferred dividends (16,090) (10,403) (38,159) (31,209)  
Loss on redemption of preferred shares (15,101) 0 (15,101) 0  
Net income (loss) available to Arch common shareholders $ 388,751 $ 408,636 $ 1,480,324 $ 830,768  
Underwriting Ratios          
Loss ratio 63.50% 68.70% 59.80% 68.80%  
Acquisition expense ratio 15.90% 14.00% 15.80% 14.50%  
Other operating expense ratio 12.00% 12.20% 12.30% 12.70%  
Combined ratio 91.40% 94.90% 87.90% 96.00%  
Goodwill and intangible assets $ 963,322 $ 713,777 $ 963,322 $ 713,777 $ 692,863
Operating segments | Underwriting Segments          
Segment Reporting Information [Line Items]          
Number of segments | segment     3    
Gross premiums written [1] 3,207,415 2,556,914 $ 9,602,213 7,461,860  
Premiums ceded (1,131,486) (830,086) (2,973,005) (2,222,031)  
Net premiums written 2,075,929 1,726,828 6,629,208 5,239,829  
Change in unearned premiums (146,592) (101,767) (962,508) (476,544)  
Net premiums earned 1,929,337 1,625,061 5,666,700 4,763,285  
Other underwriting income (loss) 7,274 4,867 18,174 17,385  
Losses and loss adjustment expenses (1,226,019) (1,100,460) (3,329,908) (3,230,939)  
Acquisition expenses (306,015) (223,524) (882,898) (681,248)  
Other operating expenses (230,832) (201,067) (703,939) (616,956)  
Underwriting income (loss) $ 173,745 $ 104,877 $ 768,129 $ 251,527  
Underwriting Ratios          
Loss ratio 63.50% 67.70% 58.80% 67.80%  
Acquisition expense ratio 15.90% 13.80% 15.60% 14.30%  
Other operating expense ratio 12.00% 12.40% 12.40% 13.00%  
Combined ratio 91.40% 93.90% 86.80% 95.10%  
Goodwill and intangible assets $ 963,322 $ 706,127 $ 963,322 $ 706,127  
Operating segments | Insurance          
Segment Reporting Information [Line Items]          
Gross premiums written [1] 1,596,619 1,206,328 4,381,372 3,444,335  
Premiums ceded (442,806) (382,167) (1,269,165) (1,119,165)  
Net premiums written 1,153,813 824,161 3,112,207 2,325,170  
Change in unearned premiums (215,143) (105,007) (488,636) (202,188)  
Net premiums earned 938,670 719,154 2,623,571 2,122,982  
Other underwriting income (loss) 0 (31) 0 (31)  
Losses and loss adjustment expenses (668,630) (525,321) (1,750,257) (1,550,632)  
Acquisition expenses (152,467) (102,420) (417,541) (317,428)  
Other operating expenses (138,931) (122,541) (409,386) (370,947)  
Underwriting income (loss) $ (21,358) $ (31,159) $ 46,387 $ (116,056)  
Underwriting Ratios          
Loss ratio 71.20% 73.00% 66.70% 73.00%  
Acquisition expense ratio 16.20% 14.20% 15.90% 15.00%  
Other operating expense ratio 14.80% 17.00% 15.60% 17.50%  
Combined ratio 102.20% 104.20% 98.20% 105.50%  
Goodwill and intangible assets $ 261,103 $ 282,146 $ 261,103 $ 282,146  
Operating segments | Reinsurance          
Segment Reporting Information [Line Items]          
Gross premiums written [1] 1,251,760 1,004,590 4,080,840 2,934,174  
Premiums ceded (630,371) (400,388) (1,535,607) (967,698)  
Net premiums written 621,389 604,202 2,545,233 1,966,476  
Change in unearned premiums 57,313 (49,704) (484,607) (388,321)  
Net premiums earned 678,702 554,498 2,060,626 1,578,155  
Other underwriting income (loss) 3,293 298 3,148 1,767  
Losses and loss adjustment expenses (545,846) (422,084) (1,494,539) (1,235,586)  
Acquisition expenses (129,450) (85,388) (381,060) (255,516)  
Other operating expenses (45,647) (41,818) (150,856) (125,831)  
Underwriting income (loss) $ (38,948) $ 5,506 $ 37,319 $ (37,011)  
Underwriting Ratios          
Loss ratio 80.40% 76.10% 72.50% 78.30%  
Acquisition expense ratio 19.10% 15.40% 18.50% 16.20%  
Other operating expense ratio 6.70% 7.50% 7.30% 8.00%  
Combined ratio 106.20% 99.00% 98.30% 102.50%  
Goodwill and intangible assets $ 176,128 $ 20,319 $ 176,128 $ 20,319  
Operating segments | Mortgage          
Segment Reporting Information [Line Items]          
Gross premiums written [1] 360,934 346,248 1,143,691 1,084,337  
Premiums ceded (60,207) (47,783) (171,923) (136,154)  
Net premiums written 300,727 298,465 971,768 948,183  
Change in unearned premiums 11,238 52,944 10,735 113,965  
Net premiums earned 311,965 351,409 982,503 1,062,148  
Other underwriting income (loss) 3,981 4,600 15,026 15,649  
Losses and loss adjustment expenses (11,543) (153,055) (85,112) (444,721)  
Acquisition expenses (24,098) (35,716) (84,297) (108,304)  
Other operating expenses (46,254) (36,708) (143,697) (120,178)  
Underwriting income (loss) $ 234,051 $ 130,530 $ 684,423 $ 404,594  
Underwriting Ratios          
Loss ratio 3.70% 43.60% 8.70% 41.90%  
Acquisition expense ratio 7.70% 10.20% 8.60% 10.20%  
Other operating expense ratio 14.80% 10.40% 14.60% 11.30%  
Combined ratio 26.20% 64.20% 31.90% 63.40%  
Goodwill and intangible assets $ 526,091 $ 403,662 $ 526,091 $ 403,662  
Operating segments | Corporate and Other Segments          
Segment Reporting Information [Line Items]          
Number of segments | segment     2    
Operating segments | Corporate          
Segment Reporting Information [Line Items]          
Net investment income 88,195 99,857 $ 256,354 313,916  
Net realized gains (losses) (25,040) 210,984 239,690 523,964  
Equity in net income (loss) of investment funds accounted for using the equity method 105,398 126,735 299,270 57,407  
Other income (loss) (3,960) 0 1,151 65  
Corporate expenses [2] (18,636) (16,263) (59,279) (51,407)  
Transaction costs and other [2] (1,036) (1,674) (793) (5,246)  
Amortization of intangible assets (20,135) (16,715) (48,925) (49,835)  
Interest expense (33,176) (36,224) (98,812) (86,599)  
Net foreign exchange gains (losses) 36,078 (38,681) 39,691 (17,812)  
Income (loss) before income taxes and income (loss) from operating affiliates 301,433 432,896 1,396,476 935,980  
Income tax expense (benefit) (4,137) (23,638) (93,942) (78,112)  
Income (loss) from operating affiliates 124,119 919 224,052 6,262  
Net income (loss) 421,415 410,177 1,526,586 864,130  
Amounts attributable to redeemable noncontrolling interests (1,473) (882) (1,936) (1,873)  
Amounts attributable to non-redeemable noncontrolling interests 0 0 0 0  
Net income (loss) available to Arch 419,942 409,295 1,524,650 862,257  
Preferred dividends (16,090) (10,403) (38,159) (31,209)  
Loss on redemption of preferred shares (15,101)   (15,101)    
Net income (loss) available to Arch common shareholders 388,751 398,892 1,471,390 831,048  
Operating segments | Other          
Segment Reporting Information [Line Items]          
Gross premiums written [1] 0 197,480 457,465 590,309  
Premiums ceded 0 (50,164) (102,763) (150,437)  
Net premiums written 0 147,316 354,702 439,872  
Change in unearned premiums 0 (1,285) (22,734) (22,267)  
Net premiums earned 0 146,031 331,968 417,605  
Other underwriting income (loss) 0 546 739 1,547  
Losses and loss adjustment expenses 0 (115,813) (259,042) (331,275)  
Acquisition expenses 0 (24,418) (62,741) (68,766)  
Other operating expenses 0 (14,619) (32,869) (42,523)  
Underwriting income (loss) 0 (8,273) (21,945) (23,412)  
Net investment income 0 28,655 42,310 91,234  
Net realized gains (losses) 0 69,515 80,638 (53,837)  
Equity in net income (loss) of investment funds accounted for using the equity method 0 0 0 0  
Other income (loss) 0 0 0 0  
Corporate expenses [2] 0 0 0 0  
Transaction costs and other [2] 0 0 (935) 0  
Amortization of intangible assets 0 0 (898) 0  
Interest expense 0 (5,119) (8,410) (18,438)  
Net foreign exchange gains (losses) 0 (6,204) (1,325) 6,387  
Income (loss) before income taxes and income (loss) from operating affiliates 0 78,574 89,435 1,934  
Income tax expense (benefit) 0 (69) (234) 333  
Income (loss) from operating affiliates 0 0 0 0  
Net income (loss) 0 78,505 89,201 2,267  
Amounts attributable to redeemable noncontrolling interests 0 (993) (1,953) (3,125)  
Amounts attributable to non-redeemable noncontrolling interests 0 (67,768) (78,314) 578  
Net income (loss) available to Arch 0 9,744 8,934 (280)  
Preferred dividends 0 0 0 0  
Loss on redemption of preferred shares 0   0    
Net income (loss) available to Arch common shareholders $ 0 $ 9,744 $ 8,934 $ (280)  
Underwriting Ratios          
Loss ratio 0.00% 79.30% 78.00% 79.30%  
Acquisition expense ratio 0.00% 16.70% 18.90% 16.50%  
Other operating expense ratio 0.00% 10.00% 9.90% 10.20%  
Combined ratio 0.00% 106.00% 106.80% 106.00%  
Goodwill and intangible assets $ 0 $ 7,650 $ 0 $ 7,650  
[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 expenses have been excluded from ‘corporate expenses’ and reflected in ‘transaction costs and other.’