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Investments - Schedule of Reconciliation of Beginning and Ending Balances for Investments Categorized as Level 3 (Detail) (USD $)
In Millions, unless otherwise specified
3 Months Ended 12 Months Ended
Mar. 31, 2015
Dec. 31, 2014
Fair Value Assets Measured On Recurring Basis Unobservable Input Reconciliation [Line Items]    
Beginning balance $ 0.9us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue $ 3.9us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue
Transfers into Level 3 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3
Transfers out of Level 3 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3
Included in net income (loss) 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1
Included in other comprehensive income (loss) 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss 0.1us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss
Purchases 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases
Issuances 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetIssues 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetIssues
Sales (0.1)us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales (0.5)us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales
Settlements 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements (2.6)us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements
Ending balance 0.8us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue 0.9us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue
Amount of total gains or losses for the year included in net income (loss) attributable to the change in unrealized gains or losses relating to assets still held at end of period 0agii_AmountOfGainsOrLossesForPeriodIncludedInNetIncomeAttributableToChangeInUnrealizedGainsOrLossesRelatingToAssetsHeldAtEndOfPeriod 0agii_AmountOfGainsOrLossesForPeriodIncludedInNetIncomeAttributableToChangeInUnrealizedGainsOrLossesRelatingToAssetsHeldAtEndOfPeriod
Other Assets [Member]    
Fair Value Assets Measured On Recurring Basis Unobservable Input Reconciliation [Line Items]    
Beginning balance   2.6us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherAssetsMember
Transfers into Level 3   0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherAssetsMember
Transfers out of Level 3   0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherAssetsMember
Included in net income (loss)   0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherAssetsMember
Included in other comprehensive income (loss)   0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherAssetsMember
Purchases   0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherAssetsMember
Issuances   0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetIssues
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherAssetsMember
Sales   0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherAssetsMember
Settlements   (2.6)us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherAssetsMember
Ending balance   0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherAssetsMember
Amount of total gains or losses for the year included in net income (loss) attributable to the change in unrealized gains or losses relating to assets still held at end of period   0agii_AmountOfGainsOrLossesForPeriodIncludedInNetIncomeAttributableToChangeInUnrealizedGainsOrLossesRelatingToAssetsHeldAtEndOfPeriod
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherAssetsMember
Equity Securities [Member]    
Fair Value Assets Measured On Recurring Basis Unobservable Input Reconciliation [Line Items]    
Beginning balance 0.9us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
1.3us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
Transfers into Level 3 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
Transfers out of Level 3 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersOutOfLevel3
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
Included in net income (loss) 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInEarnings1
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
Included in other comprehensive income (loss) 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
0.1us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
Purchases 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetPurchases
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
Issuances 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetIssues
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetIssues
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
Sales (0.1)us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
(0.5)us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
Settlements 0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
0us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSettlements
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
Ending balance 0.8us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
0.9us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
Amount of total gains or losses for the year included in net income (loss) attributable to the change in unrealized gains or losses relating to assets still held at end of period $ 0agii_AmountOfGainsOrLossesForPeriodIncludedInNetIncomeAttributableToChangeInUnrealizedGainsOrLossesRelatingToAssetsHeldAtEndOfPeriod
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
$ 0agii_AmountOfGainsOrLossesForPeriodIncludedInNetIncomeAttributableToChangeInUnrealizedGainsOrLossesRelatingToAssetsHeldAtEndOfPeriod
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember