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Reserve for Losses and Loss Adjustment Expenses - Reconciliation of beginning and ending balances of losses and loss adjustment reserves (Details) - USD ($)
$ in Thousands
 12 Months Ended
Dec. 31, 2020
Dec. 31, 2019
Dec. 31, 2018
Liability for Future Policy Benefits and Unpaid Claims and Claims Adjustment Expense [Abstract]      
Reserve for losses and loss adjustment expenses at beginning of year $ 13,891,842 $ 11,853,297 $ 11,383,792
Unpaid losses and loss adjustment expenses recoverable 4,082,650 2,814,291 2,464,910
Net reserve for losses and loss adjustment expenses at beginning of year 9,809,192 9,039,006 8,918,882
Net incurred losses and loss adjustment expenses relating to losses occurring in:      
Current year 4,851,051 3,297,037 3,162,818
Prior years (161,452) (163,585) (272,712)
Total net incurred losses and loss adjustment expenses 4,689,599 3,133,452 2,890,106
Net losses and loss adjustment expense reserves of acquired business [1] 0 209,486 0
Retroactive reinsurance transaction 182,210 (225,500) (420,404)
Foreign exchange (gains) losses and other 179,190 36,003 (143,414)
Net paid losses and loss adjustment expenses relating to losses occurring in:      
Current year (661,529) (621,202) (524,048)
Prior years (1,999,588) (1,762,053) (1,682,116)
Total net paid losses and loss adjustment expenses (2,661,117) (2,383,255) (2,206,164)
Net reserve for losses and loss adjustment expenses at end of year 12,199,074 9,809,192 9,039,006
Unpaid losses and loss adjustment expenses recoverable 4,314,855 4,082,650 2,814,291
Reserve for losses and loss adjustment expenses at end of year $ 16,513,929 $ 13,891,842 $ 11,853,297
[1] Primarily related to the acquisition of Barbican. See Note 2.