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Fair Value of Financial Instruments - Fair Value of Invested Assets (Details) (USD $)
Mar. 31, 2015
Dec. 31, 2014
U.S. treasury securities $ 25,153,905us-gaap_USGovernmentSecuritiesAtCarryingValue $ 20,069,556us-gaap_USGovernmentSecuritiesAtCarryingValue
Certificates of deposit 19,489,000us-gaap_CertificatesOfDepositAtCarryingValue 15,089,000us-gaap_CertificatesOfDepositAtCarryingValue
Total fixed maturities 44,642,905us-gaap_MarketableSecuritiesFixedMaturities 35,158,556us-gaap_MarketableSecuritiesFixedMaturities
Cash and short term investments 62,260,900UNAM_CashAndShortTermInvestments 72,568,570UNAM_CashAndShortTermInvestments
Total financial instruments at fair value 106,903,805UNAM_TotalFinancialInstrumentsAtFairValue 107,727,126UNAM_TotalFinancialInstrumentsAtFairValue
Level 1    
U.S. treasury securities 25,153,905us-gaap_USGovernmentSecuritiesAtCarryingValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel1Member
20,069,556us-gaap_USGovernmentSecuritiesAtCarryingValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel1Member
Certificates of deposit 0us-gaap_CertificatesOfDepositAtCarryingValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel1Member
0us-gaap_CertificatesOfDepositAtCarryingValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel1Member
Total fixed maturities 25,153,905us-gaap_MarketableSecuritiesFixedMaturities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel1Member
20,069,556us-gaap_MarketableSecuritiesFixedMaturities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel1Member
Cash and short term investments 62,260,900UNAM_CashAndShortTermInvestments
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel1Member
72,568,570UNAM_CashAndShortTermInvestments
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel1Member
Total financial instruments at fair value 87,414,805UNAM_TotalFinancialInstrumentsAtFairValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel1Member
92,638,126UNAM_TotalFinancialInstrumentsAtFairValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel1Member
Level 2    
U.S. treasury securities 0us-gaap_USGovernmentSecuritiesAtCarryingValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
0us-gaap_USGovernmentSecuritiesAtCarryingValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
Certificates of deposit 19,489,000us-gaap_CertificatesOfDepositAtCarryingValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
15,089,000us-gaap_CertificatesOfDepositAtCarryingValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
Total fixed maturities 19,489,000us-gaap_MarketableSecuritiesFixedMaturities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
15,089,000us-gaap_MarketableSecuritiesFixedMaturities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
Cash and short term investments 0UNAM_CashAndShortTermInvestments
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
0UNAM_CashAndShortTermInvestments
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
Total financial instruments at fair value 19,489,000UNAM_TotalFinancialInstrumentsAtFairValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
15,089,000UNAM_TotalFinancialInstrumentsAtFairValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel2Member
Level 3    
U.S. treasury securities 0us-gaap_USGovernmentSecuritiesAtCarryingValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
0us-gaap_USGovernmentSecuritiesAtCarryingValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
Certificates of deposit 0us-gaap_CertificatesOfDepositAtCarryingValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
0us-gaap_CertificatesOfDepositAtCarryingValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
Total fixed maturities 0us-gaap_MarketableSecuritiesFixedMaturities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
0us-gaap_MarketableSecuritiesFixedMaturities
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
Cash and short term investments 0UNAM_CashAndShortTermInvestments
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
0UNAM_CashAndShortTermInvestments
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
Total financial instruments at fair value $ 0UNAM_TotalFinancialInstrumentsAtFairValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member
$ 0UNAM_TotalFinancialInstrumentsAtFairValue
/ us-gaap_FairValueByFairValueHierarchyLevelAxis
= us-gaap_FairValueInputsLevel3Member