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Segment Information - Summary of underwriting income or loss by segment (Details)
$ in Thousands
 3 Months Ended 6 Months Ended
Jun. 30, 2021
USD ($)
Jun. 30, 2020
USD ($)
Jun. 30, 2021
USD ($)
segment
Jun. 30, 2020
USD ($)
Dec. 31, 2020
USD ($)
Segment Reporting Information [Line Items]          
Gross premiums written $ 3,286,291 $ 2,317,692 $ 6,683,497 $ 5,150,522  
Premiums ceded (886,767) (649,381) (1,775,516) (1,344,965)  
Net premiums written 2,399,524 1,668,311 4,907,981 3,805,557  
Change in unearned premiums (278,615) (2,957) (838,650) (395,759)  
Net premiums earned 2,120,909 1,665,354 4,069,331 3,409,798  
Other underwriting income (loss) 5,529 6,667 11,639 13,519  
Losses and loss adjustment expenses (1,159,831) (1,230,522) (2,362,931) (2,345,941)  
Acquisition expenses (335,143) (254,789) (639,624) (502,072)  
Other operating expenses (244,943) (209,249) (505,976) (443,793)  
Underwriting income (loss) 386,521 (22,539) 572,439 131,511  
Net investment income 111,613 131,485 210,469 276,638  
Net realized gains (losses) 202,907 556,588 345,368 189,628  
Equity in net income (loss) of investment funds accounted for using the equity method 122,186 (65,119) 193,872 (69,328)  
Other income (loss) 6,852 33 5,111 65  
Corporate expenses (17,175) (16,943) (40,643) (35,144)  
Transaction costs and other 1,224 (977) (692) (3,572)  
Amortization of intangible assets (15,286) (16,489) (29,688) (33,120)  
Interest expense (35,700) (31,139) (74,046) (63,694)  
Net foreign exchange gains (losses) (17,775) (39,211) 2,288 33,460  
Income (loss) before income taxes and income (loss) from operating affiliates 745,367 495,689 1,184,478 426,444  
Income tax expense (benefit) (51,179) (26,127) (90,039) (54,072)  
Income (loss) from operating affiliates 24,476 (3,173) 99,933 5,343  
Net income (loss) 718,664 466,389 1,194,372 377,715  
Amounts attributable to redeemable noncontrolling interests (1,561) (1,970) (2,416) (3,123)  
Amounts attributable to non-redeemable noncontrolling interests (41,617) (165,598) (78,314) 68,346  
Net income (loss) available to Arch 675,486 298,821 1,113,642 442,938  
Preferred dividends (11,666) (10,403) (22,069) (20,806)  
Net income (loss) available to Arch common shareholders $ 663,820 $ 288,418 $ 1,091,573 $ 422,132  
Underwriting Ratios          
Loss ratio 54.70% 73.90% 58.10% 68.80%  
Acquisition expense ratio 15.80% 15.30% 15.70% 14.70%  
Other operating expense ratio 11.50% 12.60% 12.40% 13.00%  
Combined ratio 82.00% 101.80% 86.20% 96.50%  
Goodwill and intangible assets $ 667,153 $ 688,490 $ 667,153 $ 688,490 $ 692,863
Corporate and Other Segments          
Segment Reporting Information [Line Items]          
Number of segments | segment     2    
Operating segments          
Segment Reporting Information [Line Items]          
Number of segments | segment     3    
Operating segments | Underwriting Segments          
Segment Reporting Information [Line Items]          
Gross premiums written [1] 3,117,505 2,206,410 $ 6,394,798 4,904,947  
Premiums ceded (893,372) (643,955) (1,841,519) (1,391,946)  
Net premiums written 2,224,133 1,562,455 4,553,279 3,513,001  
Change in unearned premiums (287,461) (28,636) (815,916) (374,777)  
Net premiums earned 1,936,672 1,533,819 3,737,363 3,138,224  
Other underwriting income (loss) 5,201 5,799 10,900 12,518  
Losses and loss adjustment expenses (1,019,583) (1,125,736) (2,103,889) (2,130,479)  
Acquisition expenses (300,554) (232,245) (576,883) (457,724)  
Other operating expenses (226,349) (195,047) (473,107) (415,889)  
Underwriting income (loss) $ 395,387 $ (13,410) $ 594,384 $ 146,650  
Underwriting Ratios          
Loss ratio 52.60% 73.40% 56.30% 67.90%  
Acquisition expense ratio 15.50% 15.10% 15.40% 14.60%  
Other operating expense ratio 11.70% 12.70% 12.70% 13.30%  
Combined ratio 79.80% 101.20% 84.40% 95.80%  
Goodwill and intangible assets $ 656,835 $ 680,840 $ 656,835 $ 680,840  
Operating segments | Insurance          
Segment Reporting Information [Line Items]          
Gross premiums written [1] 1,368,867 1,030,362 2,784,753 2,238,007  
Premiums ceded (405,312) (358,101) (826,359) (736,998)  
Net premiums written 963,555 672,261 1,958,394 1,501,009  
Change in unearned premiums (98,128) 15,648 (273,493) (97,181)  
Net premiums earned 865,427 687,909 1,684,901 1,403,828  
Other underwriting income (loss) 0 0 0 0  
Losses and loss adjustment expenses (545,880) (518,203) (1,081,627) (1,025,311)  
Acquisition expenses (136,852) (107,671) (265,074) (215,008)  
Other operating expenses (133,342) (118,757) (270,455) (248,406)  
Underwriting income (loss) $ 49,353 $ (56,722) $ 67,745 $ (84,897)  
Underwriting Ratios          
Loss ratio 63.10% 75.30% 64.20% 73.00%  
Acquisition expense ratio 15.80% 15.70% 15.70% 15.30%  
Other operating expense ratio 15.40% 17.30% 16.10% 17.70%  
Combined ratio 94.30% 108.30% 96.00% 106.00%  
Goodwill and intangible assets $ 270,262 $ 263,086 $ 270,262 $ 263,086  
Operating segments | Reinsurance          
Segment Reporting Information [Line Items]          
Gross premiums written [1] 1,358,020 807,065 2,829,080 1,929,584  
Premiums ceded (433,288) (241,971) (905,236) (567,310)  
Net premiums written 924,732 565,094 1,923,844 1,362,274  
Change in unearned premiums (187,708) (84,897) (541,920) (338,617)  
Net premiums earned 737,024 480,197 1,381,924 1,023,657  
Other underwriting income (loss) 1,053 (651) (145) 1,469  
Losses and loss adjustment expenses (463,823) (383,433) (948,693) (813,502)  
Acquisition expenses (133,585) (90,522) (251,610) (170,128)  
Other operating expenses (44,695) (38,716) (105,209) (84,013)  
Underwriting income (loss) $ 95,974 $ (33,125) $ 76,267 $ (42,517)  
Underwriting Ratios          
Loss ratio 62.90% 79.80% 68.70% 79.50%  
Acquisition expense ratio 18.10% 18.90% 18.20% 16.60%  
Other operating expense ratio 6.10% 8.10% 7.60% 8.20%  
Combined ratio 87.10% 106.80% 94.50% 104.30%  
Goodwill and intangible assets $ 16,168 $ 2,516 $ 16,168 $ 2,516  
Operating segments | Mortgage          
Segment Reporting Information [Line Items]          
Gross premiums written [1] 391,511 369,144 782,757 738,089  
Premiums ceded (55,665) (44,044) (111,716) (88,371)  
Net premiums written 335,846 325,100 671,041 649,718  
Change in unearned premiums (1,625) 40,613 (503) 61,021  
Net premiums earned 334,221 365,713 670,538 710,739  
Other underwriting income (loss) 4,148 6,450 11,045 11,049  
Losses and loss adjustment expenses (9,880) (224,100) (73,569) (291,666)  
Acquisition expenses (30,117) (34,052) (60,199) (72,588)  
Other operating expenses (48,312) (37,574) (97,443) (83,470)  
Underwriting income (loss) $ 250,060 $ 76,437 $ 450,372 $ 274,064  
Underwriting Ratios          
Loss ratio 3.00% 61.30% 11.00% 41.00%  
Acquisition expense ratio 9.00% 9.30% 9.00% 10.20%  
Other operating expense ratio 14.50% 10.30% 14.50% 11.70%  
Combined ratio 26.50% 80.90% 34.50% 62.90%  
Goodwill and intangible assets $ 370,405 $ 415,238 $ 370,405 $ 415,238  
Operating segments | Corporate          
Segment Reporting Information [Line Items]          
Net investment income 89,430 101,031 168,159 214,059  
Net realized gains (losses) 163,394 385,089 264,730 312,980  
Equity in net income (loss) of investment funds accounted for using the equity method 122,186 (65,119) 193,872 (69,328)  
Other income (loss) 6,852 33 5,111 65  
Corporate expenses [2] (17,175) (16,943) (40,643) (35,144)  
Transaction costs and other [2] 1,444 (977) 243 (3,572)  
Amortization of intangible assets (14,388) (16,489) (28,790) (33,120)  
Interest expense (31,439) (25,130) (65,636) (50,375)  
Net foreign exchange gains (losses) (17,892) (42,438) 3,613 20,869  
Income (loss) before income taxes and income (loss) from operating affiliates 697,799 305,647 1,095,043 503,084  
Income tax expense (benefit) (50,953) (26,529) (89,805) (54,474)  
Income (loss) from operating affiliates 24,476 (3,173) 99,933 5,343  
Net income (loss) 671,322 275,945 1,105,171 453,953  
Amounts attributable to redeemable noncontrolling interests (580) (934) (463) (991)  
Amounts attributable to non-redeemable noncontrolling interests 0 0 0 0  
Net income (loss) available to Arch 670,742 275,011 1,104,708 452,962  
Preferred dividends (11,666) (10,403) (22,069) (20,806)  
Net income (loss) available to Arch common shareholders 659,076 264,608 1,082,639 432,156  
Operating segments | Other          
Segment Reporting Information [Line Items]          
Gross premiums written [1] 240,942 157,927 457,465 392,829  
Premiums ceded (65,551) (52,071) (102,763) (100,273)  
Net premiums written 175,391 105,856 354,702 292,556  
Change in unearned premiums 8,846 25,679 (22,734) (20,982)  
Net premiums earned 184,237 131,535 331,968 271,574  
Other underwriting income (loss) 328 868 739 1,001  
Losses and loss adjustment expenses (140,248) (104,786) (259,042) (215,462)  
Acquisition expenses (34,589) (22,544) (62,741) (44,348)  
Other operating expenses (18,594) (14,202) (32,869) (27,904)  
Underwriting income (loss) (8,866) (9,129) (21,945) (15,139)  
Net investment income 22,183 30,454 42,310 62,579  
Net realized gains (losses) 39,513 171,499 80,638 (123,352)  
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] (220) 0 (935) 0  
Amortization of intangible assets (898) 0 (898) 0  
Interest expense (4,261) (6,009) (8,410) (13,319)  
Net foreign exchange gains (losses) 117 3,227 (1,325) 12,591  
Income (loss) before income taxes and income (loss) from operating affiliates 47,568 190,042 89,435 (76,640)  
Income tax expense (benefit) (226) 402 (234) 402  
Income (loss) from operating affiliates 0 0 0 0  
Net income (loss) 47,342 190,444 89,201 (76,238)  
Amounts attributable to redeemable noncontrolling interests (981) (1,036) (1,953) (2,132)  
Amounts attributable to non-redeemable noncontrolling interests (41,617) (165,598) (78,314) 68,346  
Net income (loss) available to Arch 4,744 23,810 8,934 (10,024)  
Preferred dividends 0 0 0 0  
Net income (loss) available to Arch common shareholders $ 4,744 $ 23,810 $ 8,934 $ (10,024)  
Underwriting Ratios          
Loss ratio 76.10% 79.70% 78.00% 79.30%  
Acquisition expense ratio 18.80% 17.10% 18.90% 16.30%  
Other operating expense ratio 10.10% 10.80% 9.90% 10.30%  
Combined ratio 105.00% 107.60% 106.80% 105.90%  
Goodwill and intangible assets $ 10,318 $ 7,650 $ 10,318 $ 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.’