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Stockholder's Equity - Activity Relating to Common Shares and Contingently Redeemable Common Shares (Detail)
12 Months Ended
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.