Activity in the Liability for Loss and Loss Adjustment Expense (Detail) - USD ($) $ in Thousands		12 Months Ended
		Dec. 31, 2020		Dec. 31, 2019	Dec. 31, 2018
Activity in liability for loss and loss adjustment expense
Reserves as of January 1		$ 11,928,359		$ 12,250,300	$ 11,871,300
Less: reinsurance recoverables	[1]	1,583,900		1,857,400	1,650,100
Net reserves as of January 1		10,344,500		10,392,900	10,221,200
Other adjustments		(4,000)		(2,300)	900
Incurred loss and LAE, net of reinsurance, related to:
Current year		4,559,900		3,871,100	3,849,400
Prior years		(220,800)		(184,700)	(329,000)
Total incurred loss and LAE, net of reinsurance		4,339,046		3,686,435	3,520,431
Paid loss and LAE, net of reinsurance, related to:
Current year	[2]	931,700		884,600	838,900
Prior years	[2]	2,571,800		2,839,900	2,419,000
Total paid loss and LAE, net of reinsurance	[2]	3,503,500		3,724,500	3,257,900
Foreign currency exchange rate effect		90,800		(8,000)	(91,700)
Net reserves as of December 31		11,266,900	[3]	10,344,500	10,392,900
Reinsurance recoverables as of December 31	[1]	1,703,700	[3]	1,583,900	1,857,400
Reserves as of December 31		$ 12,970,626	[3]	$ 11,928,359	$ 12,250,300

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

[2] Includes paid loss and LAE, net of reinsurance, related to commutations.

[3] Includes unallocated LAE, which aggregate to 1.0 percent of gross loss and LAE reserves as of December 31, 2020. Net loss and LAE reserves by component are shown in the preceding tables, and consolidated gross loss and LAE reserves is presented in the consolidated balance sheets.