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Share-Based Compensation and Employee Ownership Plans Narrative (Details) - USD ($)
$ in Millions
12 Months Ended
Dec. 31, 2019
Dec. 31, 2018
Dec. 31, 2017
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Granted, shares 0 88,504  
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Available for Grant 0    
Equity Plans      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock-compensation expense recognized in connection with compensation plan $ 34.0 $ 37.0 $ 28.4
Tax benefit of stock-compensation expense recognized in connection with compensation plan $ 8.8 $ 9.7 $ 7.7
Equity Plans | Employee Stock Option      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock options, initial term 7 years    
Equity Plans | Employee Stock Option | Minimum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock compensation award, vesting period 2 years    
Equity Plans | Employee Stock Option | Maximum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock compensation award, vesting period 5 years    
Equity Plans | Restricted Shares and Restricted Stock Units (RSUs)      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Unrecognized compensation expense $ 62.6    
Vested, shares 2,291,032 1,961,824  
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Number 5,364,486 5,962,295 5,579,293
Equity Plans | Restricted Stock | Minimum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock compensation award, vesting period 2 years    
Equity Plans | Restricted Stock | Maximum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock compensation award, vesting period 5 years    
Equity Plans | Restricted Stock Units (RSUs) | Non-employee Director      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Granted, shares 0    
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Number 216,912 253,772  
Equity Plans | Stock Appreciation Rights (SARs)      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
SAR's, initial term 5 years    
Vested, shares   75,000  
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Number 0 0 75,000
Deferred Cash Award | Cowen Group, Inc. 2010 Equity and Incentive Plan      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Stock compensation award, vesting period 4 years    
Deferred cash awards granted $ 42.5    
Deferred cash award, interest rate 0.70%    
Deferred cash awards, unrecognized compensation expense $ 60.3