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Investments (Tables) | 6 Months Ended
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Jun. 30, 2016
Investments [Abstract] |
Schedule of Fair Value of Fixed Maturity Investments Trading | The following table summarizes the fair value of fixed maturity investments trading:
|  | June 30, 2016 |  | December 31, 2015 |
| U.S. treasuries | $ | 2,660,051 |  |  | $ | 2,064,944 |  |
| Agencies | 126,549 |  |  | 137,976 |  |
| Municipal | 561,456 |  |  | 583,282 |  |
| Non-U.S. government (Sovereign debt) | 313,699 |  |  | 334,981 |  |
| Non-U.S. government-backed corporate | 157,606 |  |  | 138,994 |  |
| Corporate | 1,840,407 |  |  | 2,055,323 |  |
| Agency mortgage-backed | 513,517 |  |  | 504,368 |  |
| Non-agency mortgage-backed | 251,015 |  |  | 262,235 |  |
| Commercial mortgage-backed | 498,682 |  |  | 554,625 |  |
| Asset-backed | 150,147 |  |  | 128,277 |  |
| Total fixed maturity investments trading | $ | 7,073,129 |  |  | $ | 6,765,005 |  |
Schedule of Fair Value of Fixed Maturity Investments Available For Sale | The following table summarizes the amortized cost, fair value and related unrealized gains and losses and non-credit other-than-temporary impairments of fixed maturity investments available for sale:
|  |  |  | Included in Accumulated Other Comprehensive Income |  |  |  |  |
| June 30, 2016 | Amortized Cost |  | Gross Unrealized Gains |  | Gross Unrealized Losses |  | Fair Value |  | Non-Credit Other-Than- Temporary Impairments (1) |
| Agency mortgage-backed | $ | 139 |  |  | $ | 10 |  |  | $ | — |  |  | $ | 149 |  |  | $ | — |  |
| Non-agency mortgage-backed | 6,214 |  |  | 1,278 |  |  | — |  |  | 7,492 |  |  | 503 |  |
| Commercial mortgage-backed | 4,570 |  |  | 223 |  |  | — |  |  | 4,793 |  |  | — |  |
| Total fixed maturity investments available for sale | $ | 10,923 |  |  | $ | 1,511 |  |  | $ | — |  |  | $ | 12,434 |  |  | $ | 503 |  |
|  |  |  | Included in Accumulated Other Comprehensive Income |  |  |  |  |
| December 31, 2015 | Amortized Cost |  | Gross Unrealized Gains |  | Gross Unrealized Losses |  | Fair Value |  | Non-Credit Other-Than- Temporary Impairments (1) |
| Agency mortgage-backed | $ | 143 |  |  | $ | 7 |  |  | $ | — |  |  | $ | 150 |  |  | $ | — |  |
| Non-agency mortgage-backed | 7,005 |  |  | 1,523 |  |  | — |  |  | 8,528 |  |  | 550 |  |
| Commercial mortgage-backed | 6,578 |  |  | 293 |  |  | — |  |  | 6,871 |  |  | — |  |
| Asset-backed | 2,217 |  |  | 47 |  |  | — |  |  | 2,264 |  |  | — |  |
| Total fixed maturity investments available for sale | $ | 15,943 |  |  | $ | 1,870 |  |  | $ | — |  |  | $ | 17,813 |  |  | $ | 550 |  |
(1) | Represents the non-credit component of other-than-temporary impairments recognized in accumulated other comprehensive income adjusted for subsequent sales of securities. It does not include the change in fair value subsequent to the impairment measurement date.
Schedule of Contractual Maturities of Fixed Maturity Investments | Contractual maturities of fixed maturity investments 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.
|  | Trading |  | Available for Sale |  | Total Fixed Maturity Investments |
| June 30, 2016 | Amortized Cost |  | Fair Value |  | Amortized Cost |  | Fair Value |  | Amortized Cost |  | Fair Value |
| Due in less than one year | $ | 273,579 |  |  | $ | 266,356 |  |  | $ | — |  |  | $ | — |  |  | $ | 273,579 |  |  | $ | 266,356 |  |
| Due after one through five years | 4,136,965 |  |  | 4,163,134 |  |  | — |  |  | — |  |  | 4,136,965 |  |  | 4,163,134 |  |
| Due after five through ten years | 1,026,303 |  |  | 1,049,939 |  |  | — |  |  | — |  |  | 1,026,303 |  |  | 1,049,939 |  |
| Due after ten years | 171,187 |  |  | 180,339 |  |  | — |  |  | — |  |  | 171,187 |  |  | 180,339 |  |
| Mortgage-backed | 1,244,139 |  |  | 1,263,214 |  |  | 10,923 |  |  | 12,434 |  |  | 1,255,062 |  |  | 1,275,648 |  |
| Asset-backed | 155,028 |  |  | 150,147 |  |  | — |  |  | — |  |  | 155,028 |  |  | 150,147 |  |
| Total | $ | 7,007,201 |  |  | $ | 7,073,129 |  |  | $ | 10,923 |  |  | $ | 12,434 |  |  | $ | 7,018,124 |  |  | $ | 7,085,563 |  |
Schedule of Fair Value of Equity Investments Trading | The following table summarizes the fair value of equity investments trading:
|  | June 30, 2016 |  | December 31, 2015 |
| Financials | $ | 196,662 |  |  | $ | 193,716 |  |
| Communications and technology | 33,704 |  |  | 65,833 |  |
| Industrial, utilities and energy | 28,585 |  |  | 51,168 |  |
| Consumer | 21,047 |  |  | 40,918 |  |
| Healthcare | 17,949 |  |  | 36,148 |  |
| Basic materials | 3,351 |  |  | 6,094 |  |
| Total | $ | 301,298 |  |  | $ | 393,877 |  |
Schedule of Net Investment Income | The components of net investment income are as follows:
|  | Three months ended |  | Six months ended |
|  | June 30, 2016 |  | June 30, 2015 |  | June 30, 2016 |  | June 30, 2015 |
| Fixed maturity investments | $ | 46,091 |  |  | $ | 33,791 |  |  | $ | 82,097 |  |  | $ | 59,730 |  |
| Short term investments | 1,227 |  |  | 297 |  |  | 2,227 |  |  | 494 |  |
| Equity investments | 865 |  |  | 1,913 |  |  | 2,528 |  |  | 4,517 |  |
| Other investments |  |  |  |  |  |  |  |
| Private equity investments | 4,356 |  |  | 5,425 |  |  | (5,002 | ) |  | 15,838 |  |
| Other | 5,035 |  |  | 674 |  |  | 8,344 |  |  | 4,182 |  |
| Cash and cash equivalents | 209 |  |  | 127 |  |  | 338 |  |  | 275 |  |
|  | 57,783 |  |  | 42,227 |  |  | 90,532 |  |  | 85,036 |  |
| Investment expenses | (3,659 | ) |  | (3,623 | ) |  | (7,545 | ) |  | (6,725 | ) |
| Net investment income | $ | 54,124 |  |  | $ | 38,604 |  |  | $ | 82,987 |  |  | $ | 78,311 |  |
Schedule of Net Realized and Unrealized Gains On Investments and Net Other-Than-Temporary Impairments | Net realized and unrealized gains on investments are as follows:
|  | Three months ended |  | Six months ended |
|  | June 30, 2016 |  | June 30, 2015 |  | June 30, 2016 |  | June 30, 2015 |
| Gross realized gains | $ | 22,661 |  |  | $ | 8,672 |  |  | $ | 40,411 |  |  | $ | 30,204 |  |
| Gross realized losses | (7,804 | ) |  | (21,552 | ) |  | (22,469 | ) |  | (26,423 | ) |
| Net realized gains (losses) on fixed maturity investments | 14,857 |  |  | (12,880 | ) |  | 17,942 |  |  | 3,781 |  |
| Net unrealized gains (losses) on fixed maturity investments trading | 44,271 |  |  | (48,104 | ) |  | 129,736 |  |  | (22,132 | ) |
| Net realized and unrealized (losses) gains on investments-related derivatives | (9,151 | ) |  | 19,816 |  |  | (28,600 | ) |  | 15,608 |  |
| Net realized gains on equity investments trading | 14,729 |  |  | 8,832 |  |  | 13,911 |  |  | 16,313 |  |
| Net unrealized gains (losses) on equity investments trading | 5,066 |  |  | 5,624 |  |  | (1,564 | ) |  | 1,467 |  |
| Net realized and unrealized gains (losses) on investments | $ | 69,772 |  |  | $ | (26,712 | ) |  | $ | 131,425 |  |  | $ | 15,037 |  |

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