Activity in the Liability for Loss and Loss Adjustment Expense (Detail) - USD ($) $ in Thousands		3 Months Ended		9 Months Ended
		Sep. 30, 2020	Sep. 30, 2019	Sep. 30, 2020	Sep. 30, 2019
Activity in liability for loss and loss adjustment expense
Reserves as of January 1				$ 11,928,359	$ 12,250,300
Less: reinsurance recoverables	[1]			1,583,900	1,857,400
Net reserves as of January 1				10,344,500	10,392,900
Other adjustments				(2,300)	(3,200)
Incurred loss and LAE, net of reinsurance, related to:
Current year				3,381,500	2,649,900
Prior years		$ (62,300)	$ (58,900)	(156,000)	(152,900)
Total incurred loss and LAE, net of reinsurance		1,173,655	907,736	3,225,461	2,497,037
Paid loss and LAE, net of reinsurance, related to:
Current year	[2]			504,000	484,400
Prior years	[2]			2,078,000	2,238,900
Total paid loss and LAE, net of reinsurance	[2]			2,582,000	2,723,300
Foreign currency exchange rate effect				74,900	(39,100)
Net reserves as of September 30		11,060,600	10,124,300	11,060,600	10,124,300
Reinsurance recoverables as of September 30	[1]	1,620,900	1,509,700	1,620,900	1,509,700
Reserves as of September 30		$ 12,681,515	$ 11,634,000	$ 12,681,515	$ 11,634,000

[1] Reinsurance recoverables in this table include only ceded loss and LAE reserves.

[2] Includes paid losses, net of reinsurance, related to commutations.