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Net investment income (loss) (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
Net Investment Income [Abstract]                      
Net realized gains (losses) on investments and investment derivatives                 $ 46,369 $ (5,850) $ 446,646
Net change in unrealized gains (losses) on investments and investment derivatives                 14,881 8,381 (412,650)
Net gains (losses) on currencies                 7,998 12,806 (7,305)
Dividend and interest income                 16,035 18,551 53,523
Dividends paid on securities sold, not yet purchased                 0 0 (5,259)
Other expenses                 (1,333) (954) (15,696)
Management and performance fees to related parties (1)                 0 0 (29,845)
Investment income, net, related party investment fund                 194,988 249,626 (280,847)
Net investment income (loss) $ 204,798 $ 121,956 $ 137,211 $ (185,027) $ 61,614 $ (3,138) $ 69,131 $ 154,953 $ 278,938 $ 282,560 $ (251,433)