Investments (Amortized cost or cost and fair value of investments) (Details) - USD ($) $ in Thousands		Mar. 31, 2018	Dec. 31, 2017	Mar. 31, 2017	Dec. 31, 2016
Amortized cost (or cost) and estimated fair value of investments
Fixed maturities, at amortized cost or cost		$ 5,874,140	$ 5,876,261
Short-term investments, at amortized cost or cost		3,638,995	3,381,714
Other investments, at amortized cost or cost		331,950	330,416
Investments in investment affiliates, at cost		75,302	61,944
Total investments		9,920,387	9,650,335
Fixed maturities, at fair value		5,803,022	5,858,348
Short-term investments, at fair value		3,638,940	3,381,757
Other investments, at fair value		357,246	355,218
Investments in investment affiliates, at fair value		113,471	100,137
Total investments		9,912,679	9,695,460
Managed investments
Amortized cost (or cost) and estimated fair value of investments
Fixed maturities, at amortized cost or cost		5,653,620	5,644,929
Short-term investments, at amortized cost or cost		188,306	229,968
Other investments, at amortized cost or cost		331,950	330,416
Total investments		6,249,178	6,267,257
Fixed maturities, at fair value		5,583,095	5,628,654
Short-term investments, at fair value		188,251	230,011
Other investments, at fair value		357,246	355,218
Total investments		6,242,063	6,314,020
Managed investments | U.S. government and government agency
Amortized cost (or cost) and estimated fair value of investments
Fixed maturities, at amortized cost or cost		598,080	733,510
Fixed maturities, at fair value		589,161	727,397
Managed investments | Non-U.S. government and government agency
Amortized cost (or cost) and estimated fair value of investments
Fixed maturities, at amortized cost or cost		318,542	310,845
Fixed maturities, at fair value		318,345	312,239
Managed investments | U.S. states, municipalities and political subdivisions
Amortized cost (or cost) and estimated fair value of investments
Fixed maturities, at amortized cost or cost		186,551	201,347
Fixed maturities, at fair value		184,964	201,303
Managed investments | Agency residential mortgage-backed securities
Amortized cost (or cost) and estimated fair value of investments
Fixed maturities, at amortized cost or cost		992,087	984,387
Fixed maturities, at fair value		968,258	978,049
Managed investments | Non-agency residential mortgage-backed securities
Amortized cost (or cost) and estimated fair value of investments
Fixed maturities, at amortized cost or cost		43,522	40,264
Fixed maturities, at fair value		43,487	40,373
Managed investments | U.S. corporate
Amortized cost (or cost) and estimated fair value of investments
Fixed maturities, at amortized cost or cost		1,553,311	1,531,498
Fixed maturities, at fair value		1,534,805	1,533,395
Managed investments | Non-U.S. corporate
Amortized cost (or cost) and estimated fair value of investments
Fixed maturities, at amortized cost or cost		417,264	420,522
Fixed maturities, at fair value		415,156	422,249
Managed investments | Bank loans
Amortized cost (or cost) and estimated fair value of investments
Fixed maturities, at amortized cost or cost		475,154	450,320
Fixed maturities, at fair value		468,815	442,951
Managed investments | Asset-backed securities
Amortized cost (or cost) and estimated fair value of investments
Fixed maturities, at amortized cost or cost		744,051	657,234
Fixed maturities, at fair value		741,712	658,303
Managed investments | Commercial mortgage-backed securities
Amortized cost (or cost) and estimated fair value of investments
Fixed maturities, at amortized cost or cost		325,058	315,002
Fixed maturities, at fair value		318,392	312,395
Managed investments | Hedge funds
Amortized cost (or cost) and estimated fair value of investments
Other investments, at amortized cost or cost		6,954	6,954
Other investments, at fair value		15,758	15,774
Managed investments | Private equity investments
Amortized cost (or cost) and estimated fair value of investments
Other investments, at amortized cost or cost		64,424	63,684
Other investments, at fair value		79,774	78,407
Managed investments | Fixed income investment funds
Amortized cost (or cost) and estimated fair value of investments
Other investments, at amortized cost or cost		199,802	203,167
Other investments, at fair value		200,944	204,426
Managed investments | Overseas deposits
Amortized cost (or cost) and estimated fair value of investments
Other investments, at amortized cost or cost		60,770	56,611
Other investments, at fair value		60,770	56,611
Non-managed investments
Amortized cost (or cost) and estimated fair value of investments
Fixed maturities, at amortized cost or cost		220,520	231,332
Short-term investments, at amortized cost or cost		3,450,689	3,151,746
Total investments		3,671,209	3,383,078
Fixed maturities, at fair value		219,927	229,694
Short-term investments, at fair value		3,450,689	3,151,746
Total investments		3,670,616	3,381,440
Non-managed investments | Catastrophe bonds
Amortized cost (or cost) and estimated fair value of investments
Fixed maturities, at amortized cost or cost		220,520	231,332
Fixed maturities, at fair value		219,927	229,694
Investment affiliate
Amortized cost (or cost) and estimated fair value of investments
Investments in investment affiliates, at cost	[1]	75,302	61,944
Investments in investment affiliates, at fair value		$ 113,471	$ 100,137	$ 94,697	$ 100,431

[1] The Company’s investments in investment affiliates have been treated as equity method investments with the corresponding gains and losses recorded in income as “Income from investment affiliates.”