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Share-Based Compensation and Employee Ownership Plans Narrative (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Sep. 30, 2019
Sep. 30, 2018
Sep. 30, 2019
Sep. 30, 2018
Dec. 31, 2018
Dec. 31, 2017
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Granted, shares   88,504   88,504    
Share-based Compensation Arrangement by Share-based Payment Award, Number of Shares Available for Grant 200,000   200,000      
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Number         253,772  
Equity Plans            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
Stock-compensation expense recognized in connection with compensation plan $ 10.0 $ 8.5 $ 27.2 $ 27.6    
Tax benefit of stock-compensation expense recognized in connection with compensation plan 2.6 $ 2.4 $ 6.8 $ 7.2    
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 $ 70.3   $ 70.3      
Vested, shares     1,545,850 1,423,075    
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Number 5,998,580 6,350,015 5,998,580 6,350,015 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   216,912      
Equity Plans | Stock Appreciation Rights (SARs)            
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]            
SAR's, initial term     5 years      
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 award granted $ 0.6   $ 42.7      
Deferred cash award, interest rate     0.70%      
Deferred cash awards, unrecognized compensation expense $ 67.6   $ 67.6