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

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