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Schedule II - Condensed Financial Information of Registrant - Statement of Income (Details) - USD ($)
$ in Thousands
 3 Months Ended 12 Months Ended
Dec. 31, 2020
Sep. 30, 2020
Jun. 30, 2020
Mar. 31, 2020
Dec. 31, 2019
Sep. 30, 2019
Jun. 30, 2019
Mar. 31, 2019
Dec. 31, 2020
Dec. 31, 2019
Dec. 31, 2018
Revenues                      
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
Total revenues                 8,525,275 6,928,200 5,450,568
Expenses                      
Corporate expenses                 81,988 80,111 78,994
Interest expense                 143,456 120,872 120,484
Net foreign exchange gains (losses)                 (83,634) (20,609) 69,402
Total expenses                 6,947,726 5,079,090 4,608,796
Income tax expense (benefit)                 111,838 155,810 113,951
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 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
Parent                      
Revenues                      
Net investment income                 53 212 49
Net realized gains (losses)                 (2,110) 0 29
Other income (loss)                 (437) (762) 1,918
Total revenues                 (2,494) (550) 1,996
Expenses                      
Corporate expenses                 65,566 62,701 64,279
Interest expense                 40,445 22,154 22,147
Net foreign exchange gains (losses)                 3 1 30
Total expenses                 106,014 84,856 86,456
Income (loss) before income taxes                 (108,508) (85,406) (84,460)
Income tax expense (benefit)                 0 0 0
Income (loss) before equity in net income of subsidiaries                 (108,508) (85,406) (84,460)
Equity in net income of subsidiaries                 1,514,029 1,721,725 842,431
Net income available to Arch                 1,405,521 1,636,319 757,971
Preferred share dividends                 (41,612) (41,612) (41,645)
Loss on redemption of preferred shares                 0 0 (2,710)
Net income available to Arch common shareholders                 $ 1,363,909 $ 1,594,707 $ 713,616