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Share-based Compensation - Summary of Cash-Settled SARs Activity (Detail) (Cash-Settled SARs Activity [Member], USD $)
3 Months Ended
Mar. 31, 2015
Cash-Settled SARs Activity [Member]
 
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Shares, Outstanding at January 1, 2015 2,001,451us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= agii_CashSettledSARsActivityMember
Granted, Shares 866,673us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= agii_CashSettledSARsActivityMember
Exercised, Shares (31,461)us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
/ us-gaap_AwardTypeAxis
= agii_CashSettledSARsActivityMember
Expired or forfeited, Shares (70,547)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod
/ us-gaap_AwardTypeAxis
= agii_CashSettledSARsActivityMember
Shares, Outstanding at March 31, 2015 2,766,116us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= agii_CashSettledSARsActivityMember
Weighted-Average Exercise Price, Outstanding at January 1, 2015 $ 32.76us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= agii_CashSettledSARsActivityMember
Granted, Weighted-Average Exercise Price $ 47.83us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= agii_CashSettledSARsActivityMember
Exercised, Weighted-Average Exercise Price $ 29.77us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= agii_CashSettledSARsActivityMember
Expired or forfeited, Weighted-Average Exercise Price $ 36.28us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= agii_CashSettledSARsActivityMember
Weighted-Average Exercise Price, Outstanding at March 31, 2015 $ 37.42us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= agii_CashSettledSARsActivityMember