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Investments (Tables) | 12 Months Ended
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Dec. 31, 2018
Investments [Abstract] |
Schedule of Fair Value of Fixed Maturity Investments Trading | The following table summarizes the fair value of fixed maturity investments trading:
|  | December 31, 2018 |  | December 31, 2017 |
| U.S. treasuries | $ | 3,331,411 |  |  | $ | 3,168,763 |  |
| Agencies | 174,883 |  |  | 47,646 |  |
| Municipal | 6,854 |  |  | 509,802 |  |
| Non-U.S. government | 279,818 |  |  | 287,660 |  |
| Non-U.S. government-backed corporate | 160,063 |  |  | 163,651 |  |
| Corporate | 2,450,244 |  |  | 2,063,459 |  |
| Agency mortgage-backed | 817,880 |  |  | 500,456 |  |
| Non-agency mortgage-backed | 278,680 |  |  | 300,331 |  |
| Commercial mortgage-backed | 282,294 |  |  | 202,062 |  |
| Asset-backed | 306,743 |  |  | 182,725 |  |
| Total fixed maturity investments trading | $ | 8,088,870 |  |  | $ | 7,426,555 |  |
The following table summarizes the fair value of equity investments trading:
|  | December 31, 2018 |  | December 31, 2017 |
| Financials | $ | 200,357 |  |  | $ | 253,543 |  |
| Communications and technology | 42,333 |  |  | 49,526 |  |
| Industrial, utilities and energy | 24,520 |  |  | 34,325 |  |
| Consumer | 20,639 |  |  | 24,779 |  |
| Healthcare | 18,925 |  |  | 21,364 |  |
| Basic materials | 3,478 |  |  | 4,717 |  |
| Total | $ | 310,252 |  |  | $ | 388,254 |  |
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.
| At December 31, 2018 | Amortized Cost |  | Fair Value |
| Due in less than one year | $ | 511,932 |  |  | $ | 507,728 |  |
| Due after one through five years | 4,799,196 |  |  | 4,762,712 |  |
| Due after five through ten years | 1,086,697 |  |  | 1,056,087 |  |
| Due after ten years | 79,084 |  |  | 76,746 |  |
| Mortgage-backed | 1,376,565 |  |  | 1,378,854 |  |
| Asset-backed | 310,488 |  |  | 306,743 |  |
| Total | $ | 8,163,962 |  |  | $ | 8,088,870 |  |
Schedule of Net Investment Income | The components of net investment income are as follows:
| Year ended December 31, | 2018 |  | 2017 |  | 2016 |
| Fixed maturity investments | $ | 211,973 |  |  | $ | 179,624 |  |  | $ | 160,661 |  |
| Short term investments | 33,571 |  |  | 11,082 |  |  | 5,127 |  |
| Equity investments | 4,474 |  |  | 3,628 |  |  | 4,235 |  |
| Other investments |  |  |  |  |  |
| Private equity investments | 477 |  |  | 33,999 |  |  | 6,155 |  |
| Other | 22,475 |  |  | 8,067 |  |  | 20,181 |  |
| Cash and cash equivalents | 3,810 |  |  | 1,196 |  |  | 788 |  |
|  | 276,780 |  |  | 237,596 |  |  | 197,147 |  |
| Investment expenses | (14,914 | ) |  | (15,387 | ) |  | (15,421 | ) |
| Net investment income | $ | 261,866 |  |  | $ | 222,209 |  |  | $ | 181,726 |  |
Schedule of Net Realized and Unrealized Gains (Losses) On Investments and Net Other-Than-Temporary Impairments | Net realized and unrealized (losses) gains on investments are as follows:
| Year ended December 31, | 2018 |  | 2017 |  | 2016 |
| Gross realized gains | $ | 21,284 |  |  | $ | 49,121 |  |  | $ | 72,739 |  |
| Gross realized losses | (91,098 | ) |  | (38,832 | ) |  | (38,315 | ) |
| Net realized (losses) gains on fixed maturity investments | (69,814 | ) |  | 10,289 |  |  | 34,424 |  |
| Net unrealized (losses) gains on fixed maturity investments trading | (57,310 | ) |  | 8,479 |  |  | 26,954 |  |
| Net realized and unrealized losses on investments-related derivatives | (8,784 | ) |  | (2,490 | ) |  | (15,414 | ) |
| Net realized gains on equity investments trading sold during the period | 27,739 |  |  | 80,027 |  |  | 14,190 |  |
| Net unrealized (losses) gains on equity investments trading still held at reporting date | (66,900 | ) |  | 39,517 |  |  | 81,174 |  |
| Net realized and unrealized (losses) gains on equity investments trading | (39,161 | ) |  | 119,544 |  |  | 95,364 |  |
| Net realized and unrealized (losses) gains on investments | $ | (175,069 | ) |  | $ | 135,822 |  |  | $ | 141,328 |  |
Schedule of Other Investments | The table below shows the fair value of the Company’s portfolio of other investments:
| At December 31, | 2018 |  | 2017 |
| Catastrophe bonds | $ | 516,571 |  |  | $ | 380,475 |  |
| Private equity investments | 242,647 |  |  | 196,220 |  |
| Senior secured bank loan funds | 14,482 |  |  | 17,574 |  |
| Hedge funds | 11,233 |  |  | 524 |  |
| Total other investments | $ | 784,933 |  |  | $ | 594,793 |  |
Schedule of Equity Method Investments | The table below shows the Company’s portfolio of investments in other ventures, under equity method:
|  | 2018 |  | 2017 |
| At December 31, | Investment |  | Ownership % |  | Carrying Value |  | Investment |  | Ownership % |  | Carrying Value |
| Tower Hill Companies | 64,750 |  |  | 24.9 | % |  | 38,241 |  |  | 64,750 |  |  | 26.3 | % |  | 42,167 |  |
| Top Layer Re | 65,375 |  |  | 50.0 | % |  | 46,562 |  |  | 65,375 |  |  | 50.0 | % |  | 50,211 |  |
| Other | 35,862 |  |  | 30.6 | % |  | 30,369 |  |  | 13,650 |  |  | 40.4 | % |  | 9,596 |  |
| Total investments in other ventures, under equity method | $ | 165,987 |  |  |  |  | $ | 115,172 |  |  | $ | 143,775 |  |  |  |  | $ | 101,974 |  |
Schedule of Equity In Earnings of Equity Method Investments | The table below shows the Company’s equity in earnings of other ventures, under equity method:
| Year ended December 31, | 2018 |  | 2017 |  | 2016 |
| Tower Hill Companies | $ | 9,605 |  |  | $ | (1,647 | ) |  | $ | 10,379 |  |
| Top Layer Re | 8,852 |  |  | 9,851 |  |  | (8,576 | ) |
| Other | 17 |  |  | (174 | ) |  | (840 | ) |
| Total equity in earnings of other ventures | $ | 18,474 |  |  | $ | 8,030 |  |  | $ | 963 |  |

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