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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.

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- Definition The acquisition expense ratio is obtained by dividing acquisition costs, net of certain fee income, by net premiums earned. + References No definition available. + Details
Name: | acgl_AcquisitionExpenseRatioPercentage
Namespace Prefix: | acgl_
Data Type: | num:percentItemType
Balance Type: | na
Period Type: | duration

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- Definition The combined ratio is defined as the sum of the loss ratio, acquisition expense ratio and the other operating expense ratio. + References No definition available. + Details
Name: | acgl_CombinedRatioPercentage
Namespace Prefix: | acgl_
Data Type: | num:percentItemType
Balance Type: | na
Period Type: | duration

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- Definition Investable Assets + References No definition available. + Details
Name: | acgl_InvestableAssets
Namespace Prefix: | acgl_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | instant

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- Definition Other operating expense ratio is obtained by dividing other operating expenses by net premiums earned. + References No definition available. + Details
Name: | acgl_OtherOperatingExpenseRatioPercentage
Namespace Prefix: | acgl_
Data Type: | num:percentItemType
Balance Type: | na
Period Type: | duration

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- Definition Operating cost and expense items that are associated with the entity's normal revenue producing operation, for segment presentation. + References No definition available. + Details
Name: | acgl_SegmentOtherCostAndExpenseOperating
Namespace Prefix: | acgl_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

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- Definition Aggregate revenue less cost of goods and services sold or operating expenses directly attributable to the revenue generation activity. + References No definition available. + Details
Name: | acgl_UnderwritingIncomeLossSegment
Namespace Prefix: | acgl_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
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