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Investments - Schedule of Company's Gross Realized Investment Gains (Losses) (Detail) (USD $)
In Millions, unless otherwise specified
3 Months Ended
Mar. 31, 2015
Mar. 31, 2014
Schedule Of Investments [Line Items]    
Gross realized investment gains and other $ 29.1agii_GrossRealizedInvestmentAndOtherGains $ 23.8agii_GrossRealizedInvestmentAndOtherGains
Gross realized investment and other losses (13.1)agii_GrossRealizedInvestmentAndOtherLosses (12.7)agii_GrossRealizedInvestmentAndOtherLosses
Net realized investment and other gains 16.0us-gaap_RealizedInvestmentGainsLosses 11.1us-gaap_RealizedInvestmentGainsLosses
Other Investments [Member]    
Schedule Of Investments [Line Items]    
Gross realized investment gains and other 20.9agii_GrossRealizedInvestmentAndOtherGains
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherInvestmentsMember
12.7agii_GrossRealizedInvestmentAndOtherGains
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherInvestmentsMember
Gross realized investment and other losses (7.1)agii_GrossRealizedInvestmentAndOtherLosses
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherInvestmentsMember
(4.9)agii_GrossRealizedInvestmentAndOtherLosses
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherInvestmentsMember
Other Assets [Member]    
Schedule Of Investments [Line Items]    
Gross realized investment and other losses 0agii_GrossRealizedInvestmentAndOtherLosses
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherAssetsMember
(4.0)agii_GrossRealizedInvestmentAndOtherLosses
/ us-gaap_BalanceSheetLocationAxis
= us-gaap_OtherAssetsMember
Fixed Maturities [Member]    
Schedule Of Investments [Line Items]    
Gross realized investment gains and other 4.1agii_GrossRealizedInvestmentAndOtherGains
/ us-gaap_InvestmentTypeAxis
= us-gaap_FixedMaturitiesMember
4.6agii_GrossRealizedInvestmentAndOtherGains
/ us-gaap_InvestmentTypeAxis
= us-gaap_FixedMaturitiesMember
Gross realized investment and other losses (3.7)agii_GrossRealizedInvestmentAndOtherLosses
/ us-gaap_InvestmentTypeAxis
= us-gaap_FixedMaturitiesMember
(3.5)agii_GrossRealizedInvestmentAndOtherLosses
/ us-gaap_InvestmentTypeAxis
= us-gaap_FixedMaturitiesMember
Equity Securities [Member]    
Schedule Of Investments [Line Items]    
Gross realized investment gains and other 3.8agii_GrossRealizedInvestmentAndOtherGains
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
6.5agii_GrossRealizedInvestmentAndOtherGains
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
Gross realized investment and other losses (0.7)agii_GrossRealizedInvestmentAndOtherLosses
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
(0.1)agii_GrossRealizedInvestmentAndOtherLosses
/ us-gaap_InvestmentTypeAxis
= us-gaap_EquitySecuritiesMember
Real Estate Holdings [Member]    
Schedule Of Investments [Line Items]    
Gross realized investment gains and other 0.3agii_GrossRealizedInvestmentAndOtherGains
/ us-gaap_InvestmentTypeAxis
= us-gaap_RealEstateMember
0agii_GrossRealizedInvestmentAndOtherGains
/ us-gaap_InvestmentTypeAxis
= us-gaap_RealEstateMember
Short-Term Investments [Member]    
Schedule Of Investments [Line Items]    
Gross realized investment and other losses (1.1)agii_GrossRealizedInvestmentAndOtherLosses
/ us-gaap_InvestmentTypeAxis
= us-gaap_ShortTermInvestmentsMember
(0.2)agii_GrossRealizedInvestmentAndOtherLosses
/ us-gaap_InvestmentTypeAxis
= us-gaap_ShortTermInvestmentsMember
Other-Than-Temporary Impairment Losses on Fixed Maturities [Member]    
Schedule Of Investments [Line Items]    
Gross realized investment and other losses (0.4)agii_GrossRealizedInvestmentAndOtherLosses
/ us-gaap_InvestmentTypeAxis
= agii_OtherThanTemporaryImpairmentLossesOnFixedMaturitiesMember
0agii_GrossRealizedInvestmentAndOtherLosses
/ us-gaap_InvestmentTypeAxis
= agii_OtherThanTemporaryImpairmentLossesOnFixedMaturitiesMember
Other-Than-Temporary Impairment Losses on Equity Securities [Member]    
Schedule Of Investments [Line Items]    
Gross realized investment and other losses $ (0.1)agii_GrossRealizedInvestmentAndOtherLosses
/ us-gaap_InvestmentTypeAxis
= agii_OtherThanTemporaryImpairmentLossesOnEquitySecuritiesMember
$ 0agii_GrossRealizedInvestmentAndOtherLosses
/ us-gaap_InvestmentTypeAxis
= agii_OtherThanTemporaryImpairmentLossesOnEquitySecuritiesMember