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Share-based Compensation - Summary of Stock-Settled SARs Activity (Detail) (Stock-Settled SARs Activity [Member], USD $)
3 Months Ended
Mar. 31, 2015
Stock-Settled SARs Activity [Member]
 
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]  
Shares, Outstanding at January 1, 2015 1,313,901us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= agii_StockSettledSARsActivityMember
Granted, Shares 243,306us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriod
/ us-gaap_AwardTypeAxis
= agii_StockSettledSARsActivityMember
Exercised, Shares (24,622)us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised
/ us-gaap_AwardTypeAxis
= agii_StockSettledSARsActivityMember
Expired or forfeited, Shares (9,210)us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriod
/ us-gaap_AwardTypeAxis
= agii_StockSettledSARsActivityMember
Shares, Outstanding at March 31, 2015 1,523,375us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber
/ us-gaap_AwardTypeAxis
= agii_StockSettledSARsActivityMember
Weighted-Average Exercise Price, Outstanding at January 1, 2015 $ 28.65us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= agii_StockSettledSARsActivityMember
Granted, Weighted-Average Exercise Price $ 37.33us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= agii_StockSettledSARsActivityMember
Exercised, Weighted-Average Exercise Price $ 28.11us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= agii_StockSettledSARsActivityMember
Expired or forfeited, Weighted-Average Exercise Price $ 30.68us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresAndExpirationsInPeriodWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= agii_StockSettledSARsActivityMember
Weighted-Average Exercise Price, Outstanding at March 31, 2015 $ 29.26us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice
/ us-gaap_AwardTypeAxis
= agii_StockSettledSARsActivityMember