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Segment Information - Analysis of underwriting income by segment and reconciliation to net income available to common shareholders (Details)
$ in Thousands
 3 Months Ended 12 Months Ended
Dec. 31, 2020
USD ($)
Sep. 30, 2020
USD ($)
Jun. 30, 2020
USD ($)
Mar. 31, 2020
USD ($)
Dec. 31, 2019
USD ($)
Sep. 30, 2019
USD ($)
Jun. 30, 2019
USD ($)
Mar. 31, 2019
USD ($)
Dec. 31, 2020
USD ($)
segment
Dec. 31, 2019
USD ($)
Dec. 31, 2018
USD ($)
Segment Reporting Information [Line Items]                      
Gross premiums written                 $ 10,088,068 $ 8,138,960 $ 6,961,004
Premiums ceded                 (2,650,352) (2,099,893) (1,614,257)
Net premiums written $ 1,758,015 $ 1,874,144 $ 1,668,311 $ 2,137,246 $ 1,455,453 $ 1,613,457 $ 1,444,898 $ 1,525,259 7,437,716 6,039,067 5,346,747
Change in unearned premiums                 (445,781) (252,569) (114,772)
Net premiums earned 1,811,045 1,771,092 1,665,354 1,744,444 1,515,882 1,438,023 1,463,727 1,368,866 6,991,935 5,786,498 5,231,975
Other underwriting income                 26,784 24,861 15,073
Losses and loss adjustment expenses                 (4,689,599) (3,133,452) (2,890,106)
Acquisition expenses, net                 (1,004,842) (840,945) (805,135)
Other operating expenses                 (875,176) (800,997) (677,809)
Underwriting income (loss) 220,987 96,604 (22,539) 154,050 251,421 231,262 293,134 260,148 449,102 1,035,965 873,998
Net investment income 114,458 128,512 131,485 145,153 154,263 161,488 155,038 156,949 519,608 627,738 563,633
Net realized gains (losses) 353,333 280,499 556,588 (366,960) 40,830 61,355 120,757 140,256 823,460 363,198 (408,173)
Equity in net income (loss) of investment funds accounted for using the equity method                 146,693 123,672 45,641
Other income (loss)                 16,795 2,233 2,419
Corporate expenses                 (68,492) (65,667) (58,608)
Transaction costs and other                 (13,496) (14,444) (20,386)
Amortization of intangible assets                 (69,031) (82,104) (105,670)
Interest expense                 (143,456) (120,872) (120,484)
Net foreign exchange gains (losses)                 (83,634) (20,609) 69,402
Income (loss) before income taxes                 1,577,549 1,849,110 841,772
Income tax (expense) benefit                 (111,838) (155,810) (113,951)
Net income                 1,465,711 1,693,300 727,821
Amounts attributable to redeemable noncontrolling interests                 (7,114) (16,909) (18,357)
Amounts attributable to nonredeemable noncontrolling interests                 (53,076) (40,072) 48,507
Net income available to Arch 543,544 419,039 298,821 144,117 326,384 392,453 468,954 448,528 1,405,521 1,636,319 757,971
Preferred share dividends (10,403) (10,403) (10,403) (10,403) (10,403) (10,403) (10,403) (10,403) (41,612) (41,612) (41,645)
Loss on redemption of preferred shares                 0 0 (2,710)
Net income (loss) available to Arch common shareholders 533,141 $ 408,636 $ 288,418 $ 133,714 315,981 $ 382,050 $ 458,551 $ 438,125 $ 1,363,909 $ 1,594,707 $ 713,616
Underwriting Ratios                      
Loss ratio                 67.10% 54.20% 55.20%
Acquisition expense ratio                 14.40% 14.50% 15.40%
Other operating expense ratio                 12.50% 13.80% 13.00%
Combined ratio                 94.00% 82.50% 83.60%
Goodwill and intangible assets 692,863       738,083       $ 692,863 $ 738,083 $ 634,920
Total investable assets 29,513,907       24,990,265       29,513,907 24,990,265 22,324,524
Total assets 43,282,297       37,885,361       43,282,297 37,885,361 32,218,329
Total liabilities 29,294,856       25,569,809       $ 29,294,856 25,569,809 21,780,650
Other                      
Segment Reporting Information [Line Items]                      
Number of segments | segment                 2    
Gross premiums written [1]                 $ 728,546 754,881 735,015
Premiums ceded [2]                 (190,957) (222,019) (130,840)
Net premiums written                 537,589 532,862 604,175
Change in unearned premiums                 22,762 23,827 (25,313)
Net premiums earned                 560,351 556,689 578,862
Other underwriting income                 2,045 2,412 2,722
Losses and loss adjustment expenses                 (440,482) (453,135) (441,255)
Acquisition expenses, net                 (98,071) (105,980) (125,558)
Other operating expenses                 (55,810) (51,651) (37,889)
Underwriting income (loss)                 (31,967) (51,665) (23,118)
Net investment income                 117,700 136,671 125,675
Net realized gains (losses)                 9,679 15,161 (120,915)
Equity in net income (loss) of investment funds accounted for using the equity method                 0 0 0
Other income (loss)                 0 0 0
Corporate expenses                 0 0 0
Transaction costs and other                 (4,040) 0 (9,000)
Amortization of intangible assets                 0 0 0
Interest expense                 (23,242) (27,137) (19,465)
Net foreign exchange gains (losses)                 (3,473) (11,357) 10,691
Income (loss) before income taxes                 64,657 61,673 (36,132)
Income tax (expense) benefit                 (26) (20) (27)
Net income                 64,631 61,653 (36,159)
Amounts attributable to redeemable noncontrolling interests                 (4,117) (16,909) (18,357)
Amounts attributable to nonredeemable noncontrolling interests                 (53,076) (40,072) 48,507
Net income available to Arch                 7,438 4,672 (6,009)
Preferred share dividends                 0 0 0
Loss on redemption of preferred shares                     0
Net income (loss) available to Arch common shareholders                 $ 7,438 $ 4,672 $ (6,009)
Underwriting Ratios                      
Loss ratio                 78.60% 81.40% 76.20%
Acquisition expense ratio                 17.50% 19.00% 21.70%
Other operating expense ratio                 10.00% 9.30% 6.50%
Combined ratio                 106.10% 109.70% 104.40%
Goodwill and intangible assets 7,650       7,650       $ 7,650 $ 7,650 $ 7,650
Total investable assets 2,657,612       2,704,589       2,657,612 2,704,589 2,757,663
Total assets 3,490,314       3,510,893       3,490,314 3,510,893 3,372,856
Total liabilities 2,505,707       2,592,173       $ 2,505,707 2,592,173 2,262,255
Underwriting segments                      
Segment Reporting Information [Line Items]                      
Number of segments | segment                 3    
Gross premiums written [1]                 $ 9,632,691 7,695,645 6,534,423
Premiums ceded                 (2,732,564) (2,189,440) (1,791,851)
Net premiums written                 6,900,127 5,506,205 4,742,572
Change in unearned premiums                 (468,543) (276,396) (89,459)
Net premiums earned                 6,431,584 5,229,809 4,653,113
Other underwriting income                 24,739 22,449 12,351
Losses and loss adjustment expenses                 (4,249,117) (2,680,317) (2,448,851)
Acquisition expenses, net                 (906,771) (734,965) (679,577)
Other operating expenses                 (819,366) (749,346) (639,920)
Underwriting income (loss)                 481,069 1,087,630 897,116
Net investment income                 401,908 491,067 437,958
Net realized gains (losses)                 813,781 348,037 (287,258)
Equity in net income (loss) of investment funds accounted for using the equity method                 146,693 123,672 45,641
Other income (loss)                 16,795 2,233 2,419
Corporate expenses                 (68,492) (65,667) (58,608)
Transaction costs and other                 (9,456) (14,444) (11,386)
Amortization of intangible assets                 (69,031) (82,104) (105,670)
Interest expense                 (120,214) (93,735) (101,019)
Net foreign exchange gains (losses)                 (80,161) (9,252) 58,711
Income (loss) before income taxes                 1,512,892 1,787,437 877,904
Income tax (expense) benefit                 (111,812) (155,790) (113,924)
Net income                 1,401,080 1,631,647 763,980
Amounts attributable to redeemable noncontrolling interests                 (2,997) 0 0
Amounts attributable to nonredeemable noncontrolling interests                 0 0 0
Net income available to Arch                 1,398,083 1,631,647 763,980
Preferred share dividends                 (41,612) (41,612) (41,645)
Loss on redemption of preferred shares                     (2,710)
Net income (loss) available to Arch common shareholders                 $ 1,356,471 $ 1,590,035 $ 719,625
Underwriting Ratios                      
Loss ratio                 66.10% 51.30% 52.60%
Acquisition expense ratio                 14.10% 14.10% 14.60%
Other operating expense ratio                 12.70% 14.30% 13.80%
Combined ratio                 92.90% 79.70% 81.00%
Goodwill and intangible assets 685,213       730,433       $ 685,213 $ 730,433 $ 627,270
Total investable assets 26,856,295       22,285,676       26,856,295 22,285,676 19,566,861
Total assets 39,791,983       34,374,468       39,791,983 34,374,468 28,845,473
Total liabilities 26,789,149       22,977,636       26,789,149 22,977,636 19,518,395
Underwriting segments | Insurance                      
Segment Reporting Information [Line Items]                      
Gross premiums written [1]                 4,688,562 3,907,993 3,262,332
Premiums ceded [2]                 (1,525,655) (1,266,267) (1,050,207)
Net premiums written                 3,162,907 2,641,726 2,212,125
Change in unearned premiums                 (291,487) (244,646) (6,464)
Net premiums earned                 2,871,420 2,397,080 2,205,661
Other underwriting income                 (31) 0 0
Losses and loss adjustment expenses                 (2,092,453) (1,615,475) (1,520,680)
Acquisition expenses, net                 (418,483) (361,614) (349,702)
Other operating expenses                 (489,153) (454,770) (364,138)
Underwriting income (loss)                 $ (128,700) $ (34,779) $ (28,859)
Underwriting Ratios                      
Loss ratio                 72.90% 67.40% 68.90%
Acquisition expense ratio                 14.60% 15.10% 15.90%
Other operating expense ratio                 17.00% 19.00% 16.50%
Combined ratio                 104.50% 101.50% 101.30%
Goodwill and intangible assets 280,978       289,021       $ 280,978 $ 289,021 $ 114,012
Underwriting segments | Reinsurance                      
Segment Reporting Information [Line Items]                      
Gross premiums written [1]                 3,472,086 2,323,223 1,912,522
Premiums ceded [2]                 (1,014,716) (720,500) (539,950)
Net premiums written                 2,457,370 1,602,723 1,372,572
Change in unearned premiums                 (295,141) (136,334) (111,356)
Net premiums earned                 2,162,229 1,466,389 1,261,216
Other underwriting income                 4,454 6,444 (682)
Losses and loss adjustment expenses                 (1,628,320) (1,011,329) (846,882)
Acquisition expenses, net                 (354,048) (239,032) (211,280)
Other operating expenses                 (168,011) (141,484) (133,350)
Underwriting income (loss)                 $ 16,304 $ 80,988 $ 69,022
Underwriting Ratios                      
Loss ratio                 75.30% 69.00% 67.10%
Acquisition expense ratio                 16.40% 16.30% 16.80%
Other operating expense ratio                 7.80% 9.60% 10.60%
Combined ratio                 99.50% 94.90% 94.50%
Goodwill and intangible assets 18,963       2,516       $ 18,963 $ 2,516 $ 0
Underwriting segments | Mortgage                      
Segment Reporting Information [Line Items]                      
Gross premiums written [1]                 1,473,999 1,466,265 1,360,708
Premiums ceded [2]                 (194,149) (204,509) (202,833)
Net premiums written                 1,279,850 1,261,756 1,157,875
Change in unearned premiums                 118,085 104,584 28,361
Net premiums earned                 1,397,935 1,366,340 1,186,236
Other underwriting income                 20,316 16,005 13,033
Losses and loss adjustment expenses                 (528,344) (53,513) (81,289)
Acquisition expenses, net                 (134,240) (134,319) (118,595)
Other operating expenses                 (162,202) (153,092) (142,432)
Underwriting income (loss)                 $ 593,465 $ 1,041,421 $ 856,953
Underwriting Ratios                      
Loss ratio                 37.80% 3.90% 6.90%
Acquisition expense ratio                 9.60% 9.80% 10.00%
Other operating expense ratio                 11.60% 11.20% 12.00%
Combined ratio                 59.00% 24.90% 28.90%
Goodwill and intangible assets $ 385,272       $ 438,896       $ 385,272 $ 438,896 $ 513,258
[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.