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Invested Assets - Change in Unrealized Appreciation or Depreciation of Investments Carried at Fair Value (Detail) (USD $)
In Millions, unless otherwise specified
3 Months Ended
Mar. 31, 2015
Mar. 31, 2014
Investments, Debt and Equity Securities [Abstract]    
Change in unrealized appreciation of fixed maturities $ 152cb_FixedMaturitiesChangeInUnrealizedAppreciationOrDepreciation $ 362cb_FixedMaturitiesChangeInUnrealizedAppreciationOrDepreciation
Change in unrealized appreciation of equity securities 15cb_EquitySecuritiesChangeInUnrealizedAppreciationOrDepreciation (1)cb_EquitySecuritiesChangeInUnrealizedAppreciationOrDepreciation
Change in unrealized appreciation of fixed maturities and equity securities 167us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax 361us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentBeforeTax
Deferred income tax 58us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesTax 126us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesTax
Total change in unrealized appreciation (depreciation) of fixed maturities and equity securities, Net of tax $ 109us-gaap_AvailableForSaleSecuritiesChangeInNetUnrealizedHoldingGainLossNetOfTax $ 235us-gaap_AvailableForSaleSecuritiesChangeInNetUnrealizedHoldingGainLossNetOfTax