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Loss And Loss Adjustment Expense Reserves Activity in Loss and loss Adjustment Expense Reserves (Detail) - USD ($)
$ in Millions
 12 Months Ended
Dec. 31, 2017
Dec. 31, 2016
Dec. 31, 2015
Dec. 31, 2014
Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]        
Balance at beginning of period $ 11,368.0 $ 10,039.0 $ 8,857.4  
Less reinsurance recoverables on unpaid losses 1,801.0 1,442.7 1,185.9  
Net balance at beginning of period 9,567.0 8,596.3 7,671.5  
Net loss and loss adjustment reserves acquired 0.0 (2.5) 222.4  
Total beginning reserves   9,567.0 8,593.8 $ 7,893.9
Incurred related to:        
Current year 18,782.1 16,967.1 14,657.1  
Prior years 25.9 (87.5) (315.1)  
Total incurred 18,808.0 16,879.6 14,342.0  
Paid related to:        
Current year 12,201.5 11,149.0 9,577.3  
Prior years 5,256.7 4,757.4 4,062.3  
Total paid 17,458.2 15,906.4 13,639.6  
Net balance at ending of period 10,916.8 9,567.0 8,596.3  
Plus reinsurance recoverables on unpaid losses 2,170.1 1,801.0 1,442.7  
Balance at ending of period $ 13,086.9 $ 11,368.0 $ 10,039.0