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Reserves for Losses and Loss Adjustment Expenses - Reinsurance Recoverables (Detail) (USD $)
In Millions, unless otherwise specified
3 Months Ended
Mar. 31, 2015
Mar. 31, 2014
Dec. 31, 2014
Liability for Claims and Claims Adjustment Expense [Abstract]      
Net reserves beginning of the year $ 2,137.1us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet $ 2,107.6us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet  
Losses and LAE incurred during current calendar year, net of reinsurance:      
Current accident year 187.4us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense 191.4us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense  
Prior accident years (3.7)us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense (8.9)us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense  
Losses and LAE incurred during calendar year, net of reinsurance 183.7us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredClaims1 182.5us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredClaims1  
Losses and LAE payments made during current calendar year, net of reinsurance:      
Current accident year 19.8us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1 27.9us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1  
Prior accident years 141.0us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidPriorYears1 150.1us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidPriorYears1  
Losses and LAE payments made during current calendar year, net of reinsurance: 160.8us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodIncreaseDecrease 178.0us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodIncreaseDecrease  
Change in participation interest (1.2)agii_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseChangeInParticipationInterest 24.7agii_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseChangeInParticipationInterest  
Foreign exchange adjustments (6.0)us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignExchange 1.7us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignExchange  
Net reserves - end of period 2,152.8us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet 2,138.5us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet  
Reinsurance recoverables on unpaid losses and LAE, end of period 882.3us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims 903.9us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims  
Gross reserves - end of period $ 3,035.1us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense $ 3,042.4us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense $ 3,042.4us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense [1]
[1] Derived from audited consolidated financial statements.