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Unaudited Condensed Quarterly Financial Information (Details) - USD ($)
$ / shares in Units, $ 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
Quarterly Financial Information Disclosure [Abstract]                      
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
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
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)
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 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
Net income (loss) attributable to Arch                 1,465,711 1,693,300 727,821
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)
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
Basic (per share) $ 1.32 $ 1.01 $ 0.72 $ 0.33 $ 0.78 $ 0.95 $ 1.14 $ 1.09 $ 3.38 $ 3.97 $ 1.76
Diluted (per share) $ 1.30 $ 1.00 $ 0.71 $ 0.32 $ 0.76 $ 0.92 $ 1.12 $ 1.07 $ 3.32 $ 3.87 $ 1.73