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Quarterly Financial Data (Unaudited) - Unaudited Quarterly Financial Data (Detail) (USD $)
In Thousands, except Per Share data, unless otherwise specified
3 Months Ended 12 Months Ended
Dec. 31, 2014
Sep. 30, 2014
Jun. 30, 2014
Mar. 31, 2014
Dec. 31, 2013
Sep. 30, 2013
Jun. 30, 2013
Mar. 31, 2013
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Quarterly Financial Information Disclosure [Abstract]                      
Premiums earned $ 97,070us-gaap_PremiumsEarnedNet $ 95,928us-gaap_PremiumsEarnedNet $ 93,516us-gaap_PremiumsEarnedNet $ 89,233us-gaap_PremiumsEarnedNet $ 86,695us-gaap_PremiumsEarnedNet $ 81,596us-gaap_PremiumsEarnedNet $ 81,983us-gaap_PremiumsEarnedNet $ 79,709us-gaap_PremiumsEarnedNet $ 375,747us-gaap_PremiumsEarnedNet $ 329,983us-gaap_PremiumsEarnedNet $ 290,689us-gaap_PremiumsEarnedNet
Net investment income 7,166us-gaap_NetInvestmentIncome 6,495us-gaap_NetInvestmentIncome 6,845us-gaap_NetInvestmentIncome 6,708us-gaap_NetInvestmentIncome 6,763us-gaap_NetInvestmentIncome 6,947us-gaap_NetInvestmentIncome 6,649us-gaap_NetInvestmentIncome 6,670us-gaap_NetInvestmentIncome 27,214us-gaap_NetInvestmentIncome 27,029us-gaap_NetInvestmentIncome 27,018us-gaap_NetInvestmentIncome
Net realized gains (losses) on investments 516us-gaap_MarketableSecuritiesRealizedGainLoss (152)us-gaap_MarketableSecuritiesRealizedGainLoss 232us-gaap_MarketableSecuritiesRealizedGainLoss 101us-gaap_MarketableSecuritiesRealizedGainLoss 710us-gaap_MarketableSecuritiesRealizedGainLoss (654)us-gaap_MarketableSecuritiesRealizedGainLoss (1,291)us-gaap_MarketableSecuritiesRealizedGainLoss 24us-gaap_MarketableSecuritiesRealizedGainLoss 697us-gaap_MarketableSecuritiesRealizedGainLoss (1,211)us-gaap_MarketableSecuritiesRealizedGainLoss 2,979us-gaap_MarketableSecuritiesRealizedGainLoss
Total revenues 104,886us-gaap_Revenues 102,336us-gaap_Revenues 100,624us-gaap_Revenues 96,173us-gaap_Revenues 94,309us-gaap_Revenues 88,003us-gaap_Revenues 87,511us-gaap_Revenues 86,512us-gaap_Revenues 404,019us-gaap_Revenues 356,335us-gaap_Revenues 321,248us-gaap_Revenues
Income before income taxes 23,936us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest 19,348us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest 17,061us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest 13,404us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest 25,030us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest 12,447us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest 10,647us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest 11,080us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest 73,749us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest 59,204us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest 37,143us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest
Net income 16,865us-gaap_NetIncomeLoss 13,479us-gaap_NetIncomeLoss 12,773us-gaap_NetIncomeLoss 10,549us-gaap_NetIncomeLoss 17,443us-gaap_NetIncomeLoss 9,699us-gaap_NetIncomeLoss 7,644us-gaap_NetIncomeLoss 8,851us-gaap_NetIncomeLoss 53,666us-gaap_NetIncomeLoss 43,637us-gaap_NetIncomeLoss 29,353us-gaap_NetIncomeLoss
Net income available to common shareholders 16,865us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted 13,479us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted 12,773us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted 10,549us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted 17,364us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted 9,673us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted 7,618us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted 8,836us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted 53,666us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted 43,495us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted 29,331us-gaap_NetIncomeLossAvailableToCommonStockholdersDiluted
Earnings per share:                      
Basic $ 0.90us-gaap_EarningsPerShareBasic $ 0.72us-gaap_EarningsPerShareBasic $ 0.69us-gaap_EarningsPerShareBasic $ 0.57us-gaap_EarningsPerShareBasic $ 0.94us-gaap_EarningsPerShareBasic $ 0.53us-gaap_EarningsPerShareBasic $ 0.42us-gaap_EarningsPerShareBasic $ 0.48us-gaap_EarningsPerShareBasic $ 2.88us-gaap_EarningsPerShareBasic $ 2.37us-gaap_EarningsPerShareBasic $ 1.62us-gaap_EarningsPerShareBasic
Diluted $ 0.89us-gaap_EarningsPerShareDiluted $ 0.71us-gaap_EarningsPerShareDiluted $ 0.68us-gaap_EarningsPerShareDiluted $ 0.56us-gaap_EarningsPerShareDiluted $ 0.92us-gaap_EarningsPerShareDiluted $ 0.52us-gaap_EarningsPerShareDiluted $ 0.41us-gaap_EarningsPerShareDiluted $ 0.47us-gaap_EarningsPerShareDiluted $ 2.84us-gaap_EarningsPerShareDiluted $ 2.32us-gaap_EarningsPerShareDiluted $ 1.58us-gaap_EarningsPerShareDiluted
Comprehensive income $ 17,597us-gaap_ComprehensiveIncomeNetOfTax $ 13,596us-gaap_ComprehensiveIncomeNetOfTax $ 15,789us-gaap_ComprehensiveIncomeNetOfTax $ 13,789us-gaap_ComprehensiveIncomeNetOfTax $ 15,819us-gaap_ComprehensiveIncomeNetOfTax $ 8,654us-gaap_ComprehensiveIncomeNetOfTax $ 3,584us-gaap_ComprehensiveIncomeNetOfTax $ 8,306us-gaap_ComprehensiveIncomeNetOfTax $ 60,771us-gaap_ComprehensiveIncomeNetOfTax $ 36,363us-gaap_ComprehensiveIncomeNetOfTax $ 30,117us-gaap_ComprehensiveIncomeNetOfTax
Extraordinary cash dividends declared per common share $ 1.000amsf_SpecialCashDividendDeclaredPerShare     $ 0.500amsf_SpecialCashDividendDeclaredPerShare         $ 1.50amsf_SpecialCashDividendDeclaredPerShare $ 0.00amsf_SpecialCashDividendDeclaredPerShare  
Cash dividends declared per common share $ 0.12us-gaap_CommonStockDividendsPerShareDeclared $ 0.12us-gaap_CommonStockDividendsPerShareDeclared $ 0.12us-gaap_CommonStockDividendsPerShareDeclared $ 0.12us-gaap_CommonStockDividendsPerShareDeclared $ 0.08us-gaap_CommonStockDividendsPerShareDeclared $ 0.08us-gaap_CommonStockDividendsPerShareDeclared $ 0.08us-gaap_CommonStockDividendsPerShareDeclared $ 0.08us-gaap_CommonStockDividendsPerShareDeclared $ 0.48us-gaap_CommonStockDividendsPerShareDeclared $ 0.32us-gaap_CommonStockDividendsPerShareDeclared