Consolidated Statements of Cash Flows - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2019	Dec. 31, 2018	Dec. 31, 2017
Cash flows from operating activities [Abstract]
Net income	$ 672,309	$ 606,011	$ 121,088
Adjustments to reconcile net income to net cash provided by (used in) operating activities:
Net (gains) losses on investments and other financial instruments	(51,719)	42,476	(3,621)
Loss on extinguishment of debt	22,738	0	51,469
Deferred income tax provision	157,162	120,573	166,527
Impairment of goodwill	4,828	0	184,374
Amortization and impairment of other acquired intangible assets	22,288	12,429	27,797
Depreciation, other amortization, and other impairments, net	50,439	56,661	58,038
Change in:
Accounts and notes receivable	(25,504)	(4,599)	3,628
Prepaid reinsurance premiums	53,772	(31,119)	(157,071)
Unearned premiums	(112,535)	15,419	42,716
Reserve for losses and LAE	3,404	(109,642)	(252,681)
Reinsurance funds withheld	(29,383)	32,814	130,397
Other assets	(134,430)	43,562	(16,491)
Other liabilities	61,062	(106,799)	4,405
Net cash provided by (used in) operating activities	694,431	677,786	360,575
Cash flows from investing activities:
Proceeds from sales of Fixed-maturity investments available for sale	986,647	728,584	888,219
Proceeds from sales of Trading securities	130,537	58,317	194,784
Proceeds from sales of Equity securities	69,779	95,697	38,318
Proceeds from redemptions of Fixed-maturity investments available for sale	464,777	457,595	463,548
Proceeds from redemptions of Trading securities	37,684	54,329	79,296
Purchases of Fixed-maturity investments available for sale	(1,913,703)	(1,875,069)	(1,947,916)
Purchases of Equity securities	(57,422)	(69,160)	(213,469)
Sales, redemptions and (purchases) of Short-term investments, net	8,017	(108,325)	324,258
Sales, redemptions and (purchases) of Other assets and other invested assets, net	(739)	2,590	882
Net cash received (transferred) in sale of subsidiaries	0	0	(650)
Purchases of property and equipment, net	(27,626)	(26,008)	(28,676)
Acquisitions, net of cash acquired	0	(7,964)	(86)
Net cash provided by (used in) investing activities	(302,049)	(689,414)	(201,492)
Cash flows from financing activities:
Dividends paid	(2,061)	(2,140)	(2,154)
Issuance of senior notes, net	442,439	0	442,163
Repayments and repurchases of senior notes	(610,763)	0	(593,527)
Proceeds from termination of capped calls	0	0	4,208
Issuance of common stock	2,416	1,385	7,132
Repurchases of common shares	(300,201)	(50,053)	(6)
Proceeds from (Payments for) Other Financing Activities	(989)	(1,510)	(1,993)
Change in secured borrowings, net (with terms less than 3 months)	13,862	39,342	19,357
Proceeds from secured borrowings (with terms greater than 3 months)	115,275	56,449	0
Repayments of secured borrowings (with terms greater than 3 months)	(62,932)	(20,917)	0
Repayment of other borrowings	(152)	(170)	(264)
Net cash provided by (used in) financing activities	(403,106)	22,386	(125,084)
Effect of exchange rate changes on cash and restricted cash	(4)	0	431
Increase (decrease) in cash and restricted cash	(10,728)	10,758	34,430
Cash and restricted cash, beginning of period	107,002	96,244	61,814
Cash and restricted cash, end of period	96,274	107,002	96,244
Supplemental disclosures of cash flow information:
Income taxes paid (received) (Note 10)	71,469	8,364	94,328
Interest paid	$ 45,762	$ 56,688	$ 57,453