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Consolidated Statements of Income - USD ($)
$ in Thousands
 12 Months Ended
Dec. 31, 2020
Dec. 31, 2019
Dec. 31, 2018
Revenues      
Net premiums earned $ 6,991,935 $ 5,786,498 $ 5,231,975
Net investment income 519,608 627,738 563,633
Net realized gains (losses) 823,460 363,198 (408,173)
Other underwriting income 26,784 24,861 15,073
Equity in net income of investments 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      
Losses and loss adjustment expenses 4,689,599 3,133,452 2,890,106
Acquisition expenses 1,004,842 840,945 805,135
Other operating expenses 875,176 800,997 677,809
Corporate expenses 81,988 80,111 78,994
Amortization of intangible assets 69,031 82,104 105,670
Interest expense 143,456 120,872 120,484
Net foreign exchange losses (gains) 83,634 20,609 (69,402)
Total expenses 6,947,726 5,079,090 4,608,796
Income (loss) before income taxes 1,577,549 1,849,110 841,772
Income taxes:      
Current tax expense (benefit) 197,662 144,361 85,863
Deferred tax expense (benefit) (85,824) 11,449 28,088
Income tax expense 111,838 155,810 113,951
Net income 1,465,711 1,693,300 727,821
Net (income) loss attributable to noncontrolling interests (60,190) (56,981) 30,150
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
Net income per common share and common share equivalent      
Basic (per share) $ 3.38 $ 3.97 $ 1.76
Diluted (per share) $ 3.32 $ 3.87 $ 1.73
Weighted average common shares and common share equivalents outstanding      
Basic (shares) 403,062,179 401,802,815 404,347,621
Diluted (shares) 410,259,455 411,609,478 412,906,478