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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
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Dec. 31, 2022 USD ($) segment | Dec. 31, 2021 USD ($) | Dec. 31, 2020 USD ($)
Segment Reporting Information [Line Items] |  |  |  |  |  |
Gross premiums written |  | $ 15,326,447 | $ 12,752,487 |  | $ 10,088,068 |
Premiums ceded |  | (4,249,258) | (3,734,150) |  | (2,650,352) |
Net premiums written |  | 11,077,189 | 9,018,337 |  | 7,437,716 |
Change in unearned premiums |  | (1,399,112) | (936,039) |  | (445,781) |
Net premiums earned |  | 9,678,077 | 8,082,298 |  | 6,991,935 |
Other underwriting income |  | 13,227 | 22,073 |  | 26,784 |
Losses and loss adjustment expenses |  | (5,027,517) | (4,584,803) |  | (4,689,599) |
Acquisition expenses, net |  | (1,739,580) | (1,303,178) |  | (1,004,842) |
Other operating expenses |  | (1,128,175) | (998,595) |  | (875,176) |
Underwriting income (loss) |  | 1,796,032 | 1,217,795 |  | 449,102 |
Net investment income |  | 496,547 | 389,118 |  | 519,608 |
Net realized gains (losses) |  | (662,734) | 379,845 |  | 823,460 |
Equity in net income (loss) of investment funds accounted for using the equity method |  | 115,856 | 366,402 |  | 146,693 |
Other income (loss) |  | (26,165) | 10,244 |  | 29 |
Corporate expenses |  | (94,390) | (77,119) |  | (68,492) |
Transaction costs and other |  | (1,092) | (2,038) |  | (13,496) |
Amortization of intangible assets |  | (106,200) | (82,955) |  | (69,031) |
Interest expense |  | (130,266) | (139,470) |  | (143,456) |
Net foreign exchange gains (losses) |  | 100,905 | 41,529 |  | (83,634) |
Income before income taxes and income (loss) from operating affiliates |  | 1,488,493 | 2,103,351 |  | 1,560,783 |
Income tax (expense) benefit |  | (79,961) | (128,582) |  | (111,838) |
Income (loss) from operating affiliates |  | 73,891 | 264,693 |  | 16,766 |
Net income (loss) |  | 1,482,423 | 2,239,462 |  | 1,465,711 |
Amounts attributable to redeemable noncontrolling interests |  | (5,490) | (4,299) |  | (7,114) |
Amounts attributable to nonredeemable noncontrolling interests |  | 0 | (78,314) |  | (53,076) |
Net income available to Arch |  | 1,476,933 | 2,156,849 |  | 1,405,521 |
Preferred share dividends |  | (40,736) | (48,343) |  | (41,612) |
Loss on redemption of preferred shares |  | 0 | (15,101) |  | 0 |
Net income (loss) available to Arch common shareholders |  | $ 1,436,197 | $ 2,093,405 |  | $ 1,363,909 |
Underwriting Ratios |  |  |  |  |  |
Loss ratio |  | 51.90% | 56.70% |  | 67.10% |
Acquisition expense ratio |  | 18.00% | 16.10% |  | 14.40% |
Other operating expense ratio |  | 11.70% | 12.40% |  | 12.50% |
Combined ratio |  | 81.60% | 85.20% |  | 94.00% |
Goodwill and intangible assets |  | $ 804,289 | $ 944,983 |  | $ 692,863 |
Total investable assets |  | 28,065,497 | 27,442,153 |  | 29,513,907 |
Total assets |  | 47,990,507 | 45,100,945 |  | 43,282,297 |
Total liabilities |  | $ 35,069,605 | 31,545,816 |  | 29,294,856 |
Operating segments | Underwriting Segments |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |
Number of segments | segment |  | 3 |  |  |  |
Gross premiums written | [1] | $ 15,326,447 | 12,463,788 |  | 9,632,691 |
Premiums ceded |  | (4,249,258) | (3,800,153) |  | (2,732,564) |
Net premiums written |  | 11,077,189 | 8,663,635 |  | 6,900,127 |
Change in unearned premiums |  | (1,399,112) | (913,305) |  | (468,543) |
Net premiums earned |  | 9,678,077 | 7,750,330 |  | 6,431,584 |
Other underwriting income |  | 13,227 | 21,334 |  | 24,739 |
Losses and loss adjustment expenses |  | (5,027,517) | (4,325,761) |  | (4,249,117) |
Acquisition expenses, net |  | (1,739,580) | (1,240,437) |  | (906,771) |
Other operating expenses |  | (1,128,175) | (965,726) |  | (819,366) |
Underwriting income (loss) |  | 1,796,032 | 1,239,740 |  | 481,069 |
Net investment income |  | 496,547 | 346,808 |  | 401,908 |
Net realized gains (losses) |  | (662,734) | 299,207 |  | 813,781 |
Equity in net income (loss) of investment funds accounted for using the equity method |  | 115,856 | 366,402 |  | 146,693 |
Other income (loss) |  | (26,165) | 10,244 |  | 29 |
Corporate expenses |  | (94,390) | (77,119) |  | (68,492) |
Transaction costs and other |  | (1,092) | (1,103) |  | (9,456) |
Amortization of intangible assets |  | (106,200) | (82,057) |  | (69,031) |
Interest expense |  | (130,266) | (131,060) |  | (120,214) |
Net foreign exchange gains (losses) |  | 100,905 | 42,854 |  | (80,161) |
Income before income taxes and income (loss) from operating affiliates |  | 1,488,493 | 2,013,916 |  | 1,496,126 |
Income tax (expense) benefit |  | (79,961) | (128,348) |  | (111,812) |
Income (loss) from operating affiliates |  | 73,891 | 264,693 |  | 16,766 |
Net income (loss) |  | 1,482,423 | 2,150,261 |  | 1,401,080 |
Amounts attributable to redeemable noncontrolling interests |  | (5,490) | (2,346) |  | (2,997) |
Amounts attributable to nonredeemable noncontrolling interests |  |  | 0 |  | 0 |
Net income available to Arch |  | 1,476,933 | 2,147,915 |  | 1,398,083 |
Preferred share dividends |  | (40,736) | (48,343) |  | (41,612) |
Loss on redemption of preferred shares |  |  | (15,101) |  |  |
Net income (loss) available to Arch common shareholders |  | $ 1,436,197 | $ 2,084,471 |  | $ 1,356,471 |
Underwriting Ratios |  |  |  |  |  |
Loss ratio |  | 51.90% | 55.80% |  | 66.10% |
Acquisition expense ratio |  | 18.00% | 16.00% |  | 14.10% |
Other operating expense ratio |  | 11.70% | 12.50% |  | 12.70% |
Combined ratio |  | 81.60% | 84.30% |  | 92.90% |
Goodwill and intangible assets |  | $ 804,289 | $ 944,983 |  | $ 685,213 |
Total investable assets |  | 28,065,497 | 27,442,153 |  | 26,856,295 |
Total assets |  | 47,990,507 | 45,100,945 |  | 39,791,983 |
Total liabilities |  | 35,069,605 | 31,545,816 |  | 26,789,149 |
Operating segments | Insurance |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |
Gross premiums written | [1] | 6,930,864 | 5,867,734 |  | 4,688,562 |
Premiums ceded | [2] | (1,910,222) | (1,719,541) |  | (1,525,655) |
Net premiums written |  | 5,020,642 | 4,148,193 |  | 3,162,907 |
Change in unearned premiums |  | (461,307) | (521,725) |  | (291,487) |
Net premiums earned |  | 4,559,335 | 3,626,468 |  | 2,871,420 |
Other underwriting income |  | 0 | 0 |  | (31) |
Losses and loss adjustment expenses |  | (2,782,945) | (2,344,365) |  | (2,092,453) |
Acquisition expenses, net |  | (885,866) | (606,265) |  | (418,483) |
Other operating expenses |  | (665,472) | (558,906) |  | (489,153) |
Underwriting income (loss) |  | $ 225,052 | $ 116,932 |  | $ (128,700) |
Underwriting Ratios |  |  |  |  |  |
Loss ratio |  | 61.00% | 64.60% |  | 72.90% |
Acquisition expense ratio |  | 19.40% | 16.70% |  | 14.60% |
Other operating expense ratio |  | 14.60% | 15.40% |  | 17.00% |
Combined ratio |  | 95.00% | 96.70% |  | 104.50% |
Goodwill and intangible assets |  | $ 228,532 | $ 256,434 |  | $ 280,978 |
Operating segments | Reinsurance |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |
Gross premiums written | [1] | 6,948,438 | 5,093,930 |  | 3,472,086 |
Premiums ceded | [2] | (2,024,462) | (1,839,556) |  | (1,014,716) |
Net premiums written |  | 4,923,976 | 3,254,374 |  | 2,457,370 |
Change in unearned premiums |  | (964,595) | (413,931) |  | (295,141) |
Net premiums earned |  | 3,959,381 | 2,840,443 |  | 2,162,229 |
Other underwriting income |  | 4,871 | 3,669 |  | 4,454 |
Losses and loss adjustment expenses |  | (2,568,843) | (1,924,719) |  | (1,628,320) |
Acquisition expenses, net |  | (813,555) | (536,754) |  | (354,048) |
Other operating expenses |  | (267,531) | (212,810) |  | (168,011) |
Underwriting income (loss) |  | $ 314,323 | $ 169,829 |  | $ 16,304 |
Underwriting Ratios |  |  |  |  |  |
Loss ratio |  | 64.90% | 67.80% |  | 75.30% |
Acquisition expense ratio |  | 20.50% | 18.90% |  | 16.40% |
Other operating expense ratio |  | 6.80% | 7.50% |  | 7.80% |
Combined ratio |  | 92.20% | 94.20% |  | 99.50% |
Goodwill and intangible assets |  | $ 144,846 | $ 183,523 |  | $ 18,963 |
Operating segments | Mortgage |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |
Gross premiums written | [1] | 1,454,971 | 1,507,825 |  | 1,473,999 |
Premiums ceded | [2] | (322,400) | (246,757) |  | (194,149) |
Net premiums written |  | 1,132,571 | 1,261,068 |  | 1,279,850 |
Change in unearned premiums |  | 26,790 | 22,351 |  | 118,085 |
Net premiums earned |  | 1,159,361 | 1,283,419 |  | 1,397,935 |
Other underwriting income |  | 8,356 | 17,665 |  | 20,316 |
Losses and loss adjustment expenses |  | 324,271 | (56,677) |  | (528,344) |
Acquisition expenses, net |  | (40,159) | (97,418) |  | (134,240) |
Other operating expenses |  | (195,172) | (194,010) |  | (162,202) |
Underwriting income (loss) |  | $ 1,256,657 | $ 952,979 |  | $ 593,465 |
Underwriting Ratios |  |  |  |  |  |
Loss ratio |  | (28.00%) | 4.40% |  | 37.80% |
Acquisition expense ratio |  | 3.50% | 7.60% |  | 9.60% |
Other operating expense ratio |  | 16.80% | 15.10% |  | 11.60% |
Combined ratio |  | (7.70%) | 27.10% |  | 59.00% |
Goodwill and intangible assets |  | $ 430,911 | $ 505,026 |  | $ 385,272 |
Operating segments | Other |  |  |  |  |  |
Segment Reporting Information [Line Items] |  |  |  |  |  |
Number of segments | segment |  | 2 |  |  |  |
Gross premiums written | [1] | $ 0 | 457,465 |  | 728,546 |
Premiums ceded |  | 0 | (102,763) | [2] | (190,957) | [2]
Net premiums written |  | 0 | 354,702 |  | 537,589 |
Change in unearned premiums |  | 0 | (22,734) |  | 22,762 |
Net premiums earned |  | 0 | 331,968 |  | 560,351 |
Other underwriting income |  | 0 | 739 |  | 2,045 |
Losses and loss adjustment expenses |  | 0 | (259,042) |  | (440,482) |
Acquisition expenses, net |  | 0 | (62,741) |  | (98,071) |
Other operating expenses |  | 0 | (32,869) |  | (55,810) |
Underwriting income (loss) |  | 0 | (21,945) |  | (31,967) |
Net investment income |  | 0 | 42,310 |  | 117,700 |
Net realized gains (losses) |  | 0 | 80,638 |  | 9,679 |
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 |  | 0 | (935) |  | (4,040) |
Amortization of intangible assets |  | 0 | (898) |  | 0 |
Interest expense |  | 0 | (8,410) |  | (23,242) |
Net foreign exchange gains (losses) |  | 0 | (1,325) |  | (3,473) |
Income before income taxes and income (loss) from operating affiliates |  | 0 | 89,435 |  | 64,657 |
Income tax (expense) benefit |  | 0 | (234) |  | (26) |
Income (loss) from operating affiliates |  | 0 | 0 |  | 0 |
Net income (loss) |  | 0 | 89,201 |  | 64,631 |
Amounts attributable to redeemable noncontrolling interests |  | 0 | (1,953) |  | (4,117) |
Amounts attributable to nonredeemable noncontrolling interests |  | 0 | (78,314) |  | (53,076) |
Net income available to Arch |  | 0 | 8,934 |  | 7,438 |
Preferred share dividends |  | 0 | 0 |  | 0 |
Loss on redemption of preferred shares |  |  | 0 |  |  |
Net income (loss) available to Arch common shareholders |  | $ 0 | $ 8,934 |  | $ 7,438 |
Underwriting Ratios |  |  |  |  |  |
Loss ratio |  | 0.00% | 78.00% |  | 78.60% |
Acquisition expense ratio |  | 0.00% | 18.90% |  | 17.50% |
Other operating expense ratio |  | 0.00% | 9.90% |  | 10.00% |
Combined ratio |  | 0.00% | 106.80% |  | 106.10% |
Goodwill and intangible assets |  | $ 0 | $ 0 |  | $ 7,650 |
Total investable assets |  | 0 | 0 |  | 2,657,612 |
Total assets |  | 0 | 0 |  | 3,490,314 |
Total liabilities |  | $ 0 | $ 0 |  | $ 2,505,707 |
[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.

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- Definition Amount of income (loss) from continuing operations before deduction of income tax expense (benefit) and income (loss) attributable to noncontrolling interest, and addition of income (loss) from affiliates. + References No definition available. + Details
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- Definition Income from those investments in which the Company has classified as ‘investments in operating affiliates’ on the Company’s balance sheets and accounted for using the equity method. + References No definition available. + Details
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