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Investments (Tables) | 9 Months Ended
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Sep. 30, 2018
Investments [Abstract] |
Schedule of Fair Value of Fixed Maturity Investments Trading | The following table summarizes the fair value of fixed maturity investments trading:
|  | September 30, 2018 |  | December 31, 2017 |
| U.S. treasuries | $ | 3,117,911 |  |  | $ | 3,168,763 |  |
| Agencies | 143,980 |  |  | 47,646 |  |
| Municipal | 7,061 |  |  | 509,802 |  |
| Non-U.S. government (Sovereign debt) | 254,169 |  |  | 287,660 |  |
| Non-U.S. government-backed corporate | 137,512 |  |  | 163,651 |  |
| Corporate | 2,448,795 |  |  | 2,063,459 |  |
| Agency mortgage-backed | 836,376 |  |  | 500,456 |  |
| Non-agency mortgage-backed | 289,649 |  |  | 300,331 |  |
| Commercial mortgage-backed | 257,434 |  |  | 202,062 |  |
| Asset-backed | 321,892 |  |  | 182,725 |  |
| Total fixed maturity investments trading | $ | 7,814,779 |  |  | $ | 7,426,555 |  |
Schedule of Contractual Maturities of Fixed Maturity Investments | Contractual maturities of fixed maturity investments trading are described in the following table. Expected maturities will differ from contractual maturities because borrowers may have the right to call or prepay obligations with or without call or prepayment penalties.
| September 30, 2018 | Amortized Cost |  | Fair Value |
| Due in less than one year | $ | 303,364 |  |  | $ | 301,817 |  |
| Due after one through five years | 4,759,113 |  |  | 4,694,059 |  |
| Due after five through ten years | 1,029,502 |  |  | 1,020,157 |  |
| Due after ten years | 96,311 |  |  | 93,395 |  |
| Mortgage-backed | 1,390,933 |  |  | 1,383,459 |  |
| Asset-backed | 322,661 |  |  | 321,892 |  |
| Total | $ | 7,901,884 |  |  | $ | 7,814,779 |  |
Schedule of Fair Value of Equity Investments Trading | The following table summarizes the fair value of equity investments trading:
|  | September 30, 2018 |  | December 31, 2017 |
| Financials | $ | 262,173 |  |  | $ | 253,543 |  |
| Communications and technology | 60,235 |  |  | 49,526 |  |
| Industrial, utilities and energy | 34,755 |  |  | 34,325 |  |
| Consumer | 26,649 |  |  | 24,779 |  |
| Healthcare | 25,250 |  |  | 21,364 |  |
| Basic materials | 4,209 |  |  | 4,717 |  |
| Total | $ | 413,271 |  |  | $ | 388,254 |  |
Schedule of Net Investment Income | The components of net investment income are as follows:
|  | Three months ended |  | Nine months ended |
|  | September 30, 2018 |  | September 30, 2017 |  | September 30, 2018 |  | September 30, 2017 |
| Fixed maturity investments | $ | 55,725 |  |  | $ | 45,305 |  |  | $ | 151,784 |  |  | $ | 133,080 |  |
| Short term investments | 9,403 |  |  | 2,771 |  |  | 22,340 |  |  | 7,476 |  |
| Equity investments | 903 |  |  | 930 |  |  | 3,091 |  |  | 2,630 |  |
| Other investments |  |  |  |  |  |  |  |
| Private equity investments | 8,723 |  |  | 6,371 |  |  | 12,149 |  |  | 20,784 |  |
| Other | 8,665 |  |  | (11,491 | ) |  | 27,346 |  |  | (4,520 | ) |
| Cash and cash equivalents | 1,104 |  |  | 352 |  |  | 2,708 |  |  | 836 |  |
|  | 84,523 |  |  | 44,238 |  |  | 219,418 |  |  | 160,286 |  |
| Investment expenses | (3,827 | ) |  | (3,981 | ) |  | (10,890 | ) |  | (11,541 | ) |
| Net investment income | $ | 80,696 |  |  | $ | 40,257 |  |  | $ | 208,528 |  |  | $ | 148,745 |  |
Schedule of Net Realized and Unrealized Gains (Losses) | Net realized and unrealized gains (losses) on investments are as follows:
|  | Three months ended |  | Nine months ended |
|  | September 30, 2018 |  | September 30, 2017 |  | September 30, 2018 |  | September 30, 2017 |
| Gross realized gains | $ | 5,229 |  |  | $ | 16,343 |  |  | $ | 14,945 |  |  | $ | 43,053 |  |
| Gross realized losses | (15,327 | ) |  | (6,126 | ) |  | (67,699 | ) |  | (29,902 | ) |
| Net realized (losses) gains on fixed maturity investments | (10,098 | ) |  | 10,217 |  |  | (52,754 | ) |  | 13,151 |  |
| Net unrealized (losses) gains on fixed maturity investments trading | (8,730 | ) |  | 5,545 |  |  | (73,522 | ) |  | 48,940 |  |
| Net realized and unrealized gains (losses) on investments-related derivatives | 2,563 |  |  | (4,020 | ) |  | (763 | ) |  | (4,344 | ) |
| Net realized gains on equity investments trading sold during the period | 21,259 |  |  | 13,675 |  |  | 21,841 |  |  | 49,736 |  |
| Net unrealized gains on equity investments trading still held at reporting date | 8,636 |  |  | 16,635 |  |  | 18,783 |  |  | 36,055 |  |
| Net realized and unrealized gains on equity investments trading | 29,895 |  |  | 30,310 |  |  | 40,624 |  |  | 85,791 |  |
| Net realized and unrealized gains (losses) on investments | $ | 13,630 |  |  | $ | 42,052 |  |  | $ | (86,415 | ) |  | $ | 143,538 |  |

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