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Stockholder's Equity - Activity Relating to Common Shares and Contingently Redeemable Common Shares (Detail) | 12 Months Ended
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Dec. 31, 2014 | Dec. 31, 2013 | Dec. 31, 2012
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Beginning balance, shares | 43,641,000us-gaap_CommonStockSharesIssued |  |  |  |  |
Beginning balance, shares | (8,275,000)us-gaap_TreasuryStockShares |  |  |  |  |
Beginning balance, shares | 35,366,000us-gaap_CommonStockSharesOutstanding |  |  |  |  |
Options exercised | 1,900,000us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised |  |  |  |  |
Shares acquired through cashless exercise | (1,787,000)uve_SharesAcquiredThroughCashlessExercise |  | (1,966,000)uve_SharesAcquiredThroughCashlessExercise |  | (147,000)uve_SharesAcquiredThroughCashlessExercise |
Ending balance, shares | 43,769,000us-gaap_CommonStockSharesIssued |  | 43,641,000us-gaap_CommonStockSharesIssued |  |  |
Ending balance, shares | (9,667,000)us-gaap_TreasuryStockShares |  | (8,275,000)us-gaap_TreasuryStockShares |  |  |
Ending balance, shares | 34,102,000us-gaap_CommonStockSharesOutstanding |  | 35,366,000us-gaap_CommonStockSharesOutstanding |  |  |
Common Stock [Member] |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Beginning balance, shares | 43,641,000us-gaap_CommonStockSharesIssued / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |  | 41,889,000us-gaap_CommonStockSharesIssued / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |  | 41,100,000us-gaap_CommonStockSharesIssued / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |
Conversion of preferred stock | 65,000us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |  | 389,000us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |  |  |
Options exercised | 1,900,000us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |  | 2,330,000us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |  | 285,000us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |
Restricted stock grant | 950,000us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |  | 1,000,000us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |  | 650,000us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |
Shares cancelled | (1,787,000)us-gaap_TreasuryStockSharesRetired / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |  | (1,967,000)us-gaap_TreasuryStockSharesRetired / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |  | (146,000)us-gaap_TreasuryStockSharesRetired / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |
Ending balance, shares | 44,769,000us-gaap_CommonStockSharesIssued / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |  | 43,641,000us-gaap_CommonStockSharesIssued / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |  | 41,889,000us-gaap_CommonStockSharesIssued / us-gaap_StatementEquityComponentsAxis = us-gaap_CommonStockMember |
Treasury Stock [Member] |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Beginning balance, shares | (8,275,000)us-gaap_TreasuryStockShares / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember |  | (1,018,000)us-gaap_TreasuryStockShares / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember |  | (1,018,000)us-gaap_TreasuryStockShares / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember |
Shares repurchased | (2,392,000)us-gaap_TreasuryStockSharesAcquired / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember |  | (7,257,000)us-gaap_TreasuryStockSharesAcquired / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember |  |  |
Shares acquired through cashless exercise | (1,787,000)uve_SharesAcquiredThroughCashlessExercise / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember | [1] | (1,967,000)uve_SharesAcquiredThroughCashlessExercise / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember | [1] | (146,000)uve_SharesAcquiredThroughCashlessExercise / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember | [1]
Shares cancelled | 1,787,000us-gaap_TreasuryStockSharesRetired / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember |  | 1,967,000us-gaap_TreasuryStockSharesRetired / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember |  | 146,000us-gaap_TreasuryStockSharesRetired / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember |
Treasury shares reissued and classified as contingently redeemable common stock | 1,000,000uve_TreasurySharesReissuedAndClassifiedAsTemporaryEquity / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember | [2] |  |  |  |
Ending balance, shares | (9,667,000)us-gaap_TreasuryStockShares / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember |  | (8,275,000)us-gaap_TreasuryStockShares / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember |  | (1,018,000)us-gaap_TreasuryStockShares / us-gaap_StatementEquityComponentsAxis = us-gaap_TreasuryStockMember |
Stock Compensation Plan [Member] |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |
Beginning balance, shares | 35,366,000us-gaap_CommonStockSharesOutstanding / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |  | 40,871,000us-gaap_CommonStockSharesOutstanding / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |  | 40,082,000us-gaap_CommonStockSharesOutstanding / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |
Conversion of preferred stock | 65,000us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |  | 389,000us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |  |  |
Shares repurchased | (2,392,000)us-gaap_TreasuryStockSharesAcquired / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |  | (7,257,000)us-gaap_TreasuryStockSharesAcquired / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |  |  |
Options exercised | 1,900,000us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |  | 2,330,000us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |  | 285,000us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |
Restricted stock grant | 950,000us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |  | 1,000,000us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |  | 650,000us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |
Shares acquired through cashless exercise | (1,787,000)uve_SharesAcquiredThroughCashlessExercise / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember | [1] | (1,967,000)uve_SharesAcquiredThroughCashlessExercise / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember | [1] | (146,000)uve_SharesAcquiredThroughCashlessExercise / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember | [1]
Treasury shares reissued and classified as contingently redeemable common stock | 1,000,000uve_TreasurySharesReissuedAndClassifiedAsTemporaryEquity / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember | [2] |  |  |  |
Ending balance, shares | 35,102,000us-gaap_CommonStockSharesOutstanding / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |  | 35,366,000us-gaap_CommonStockSharesOutstanding / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |  | 40,871,000us-gaap_CommonStockSharesOutstanding / us-gaap_StatementEquityComponentsAxis = us-gaap_StockCompensationPlanMember |
[1] | All shares acquired represent shares tendered to cover the strike price for options and tax withholdings on the intrinsic value of options exercised or Restricted Stock (as defined in “NOTE 9 – SHARE-BASED COMPENSATION “) vested. These shares have been cancelled by the Company.
[2] | Subsequent to December 31, 2014 contingently redeemable common stock was reclassified to common stock.

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