Consolidated Statements of Cash Flows - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Dec. 31, 2020	Sep. 30, 2020	Jun. 30, 2020	Mar. 31, 2020	Dec. 31, 2019	Sep. 30, 2019	Jun. 30, 2019	Mar. 31, 2019	Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Cash flows from operating activities [Abstract]
Net income	$ 148,013	$ 135,103	$ (29,951)	$ 140,461	$ 161,184	$ 173,438	$ 166,730	$ 170,957	$ 393,626	$ 672,309	$ 606,011
Adjustments to reconcile net income to net cash provided by (used in) operating activities:
Net (gains) losses on investments and other financial instruments	(17,376)	$ (17,652)	$ (47,276)	22,027	(4,257)	(13,009)	(12,540)	(21,913)	(60,277)	(51,719)	42,476
Loss on extinguishment of debt					0	5,940	16,798	0	0	22,738	0
Deferred income tax provision									102,079	157,162	120,573
Impairment of goodwill					4,828	$ 0	$ 0	0	0	4,828	0
Amortization and impairment of other acquired intangible assets									5,144	22,288	12,429
Depreciation, other amortization, and other impairments, net									66,585	50,439	56,661
Change in:
Accrued investment income									(1,714)	2,545	(3,485)
Accounts and notes receivable									(29,280)	(25,504)	(4,599)
Reinsurance recoverables									(56,226)	(2,574)	(2,497)
Deferred policy acquisition costs									2,454	(3,448)	(324)
Prepaid reinsurance premiums									96,218	53,772	(31,119)
Unearned premiums									(178,031)	(112,535)	15,419
Reserve for losses and LAE									443,648	3,404	(109,642)
Reinsurance funds withheld									(13,274)	(29,383)	32,814
Other assets									(57,538)	(130,953)	49,868
Other liabilities									(54,980)	61,062	(106,799)
Net cash provided by (used in) operating activities									658,434	694,431	677,786
Cash flows from investing activities:
Proceeds from sales of Fixed-maturity investments available for sale									963,589	986,647	728,584
Proceeds from sales of Trading securities									11,602	130,537	58,317
Proceeds from sales of Equity securities									90,450	69,779	95,697
Proceeds from redemptions of Fixed-maturity investments available for sale									645,068	464,777	457,595
Proceeds from redemptions of Trading securities									22,913	37,684	54,329
Purchases of Fixed-maturity investments available for sale									(2,449,762)	(1,913,703)	(1,875,069)
Purchases of Equity securities									(85,014)	(57,422)	(69,160)
Sales, redemptions and (purchases) of Short-term investments, net									(82,925)	8,017	(108,325)
Sales, redemptions and (purchases) of Other assets and other invested assets, net									1,434	(739)	2,590
Proceeds from sale of subsidiary, net of cash sold									16,481	0	0
Purchases of property and equipment									(17,016)	(27,626)	(26,008)
Acquisitions, net of cash acquired									0	0	(7,964)
Net cash provided by (used in) investing activities									(883,180)	(302,049)	(689,414)
Cash flows from financing activities:
Dividends and dividend equivalents paid									(97,458)	(2,061)	(2,140)
Issuance of senior notes, net									515,567	442,439	0
Repayments and repurchases of senior notes									0	(610,763)	0
Issuance of common stock									1,553	2,416	1,385
Repurchases of common shares									(226,305)	(300,201)	(50,053)
Proceeds from (Payments for) Other Financing Activities									(2,292)	(989)	(1,510)
Change in secured borrowings, net (with terms three months or less)									(37,475)	13,862	39,342
Proceeds from secured borrowings (with terms greater than three months)									207,034	115,275	56,449
Repayments of secured borrowings (with terms greater than three months)									(137,927)	(62,932)	(20,917)
Repayment of other borrowings									(79)	(152)	(170)
Net cash provided by (used in) financing activities									222,618	(403,106)	22,386
Effect of exchange rate changes on cash and restricted cash									0	(4)	0
Increase (decrease) in cash and restricted cash									(2,128)	(10,728)	10,758
Cash and restricted cash, beginning of period				96,274				107,002	96,274	107,002	96,244
Cash and restricted cash, end of period	94,146				96,274				94,146	96,274	107,002
Supplemental disclosures of cash flow information:
Income taxes paid (Note 10)									81,404	71,469	8,364
Interest paid									60,564	45,762	56,688
Parent Company
Cash flows from operating activities [Abstract]
Net income									393,626	672,309	606,011
Adjustments to reconcile net income to net cash provided by (used in) operating activities:
Net (gains) losses on investments and other financial instruments									(5,682)	(12,863)	470
Loss on extinguishment of debt									0	(22,738)	0
Change in:
Net cash provided by (used in) operating activities									(13,741)	143,664	254,698
Cash flows from investing activities:
Proceeds from sales of Fixed-maturity investments available for sale									304,737	296,171	6,779
Proceeds from sales of Trading securities									0	56,787	0
Proceeds from sales of Equity securities									13,401	16,916	0
Proceeds from redemptions of Fixed-maturity investments available for sale									238,161	149,767	12,391
Proceeds from redemptions of Trading securities									0	114	0
Purchases of Fixed-maturity investments available for sale									(691,874)	(293,284)	(37,552)
Sales, redemptions and (purchases) of Short-term investments, net									(53,024)	157,045	(131,164)
Sales, redemptions and (purchases) of Other assets and other invested assets, net									6,068	6,958	3,317
Net cash provided by (used in) investing activities									(180,717)	316,679	(183,201)
Cash flows from financing activities:
Dividends and dividend equivalents paid									(97,458)	(2,061)	(2,140)
Issuance of senior notes, net									515,567	442,439	0
Repayments and repurchases of senior notes									0	(610,763)	0
Issuance of common stock									1,553	2,416	1,385
Repurchases of common shares									(226,305)	(300,201)	(50,053)
Proceeds from (Payments for) Other Financing Activities									(2,292)	(989)	(1,510)
Net cash provided by (used in) financing activities									191,065	(469,159)	(52,318)
Effect of exchange rate changes on cash and restricted cash									0	(2)	0
Increase (decrease) in cash and restricted cash									(3,393)	(8,818)	19,179
Cash and restricted cash, beginning of period				$ 23,534				$ 32,352	23,534	32,352	13,173
Cash and restricted cash, end of period	$ 20,141				$ 23,534				$ 20,141	$ 23,534	$ 32,352