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Share-Based Compensation and Employee Ownership Plans Narrative (Details) - USD ($)
$ in Millions
1 Months Ended 3 Months Ended 6 Months Ended
Apr. 30, 2019
Mar. 31, 2016
Jun. 30, 2020
Jun. 30, 2019
Jun. 30, 2020
Jun. 30, 2019
Jul. 21, 2020
Dec. 31, 2019
Dec. 31, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                  
Shares granted     0   0        
Subsequent Event                  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                  
Shares granted             3,000,000.0    
Minimum                  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                  
Percent of RSU's earned         0.00%        
Maximum                  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                  
Percent of RSU's earned         200.00%        
Equity Plans                  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                  
Stock-compensation expense recognized in connection with compensation plan     $ 15.3 $ 9.4 $ 23.6 $ 17.2      
Tax benefit of stock-compensation expense recognized in connection with compensation plan     3.5 $ 2.0 $ 5.3 $ 4.2      
Equity Plans | Restricted Shares and Restricted Stock Units (RSUs)                  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                  
Granted, shares         2,268,759 2,194,230      
Vested, shares         1,290,624 1,282,843      
Forfeited, shares         35,441 153,399      
Unrecognized compensation expense     $ 81.7   $ 81.7        
Period for recognition         2 years 5 months 23 days        
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Nonvested, Number     6,219,832 6,486,950 6,219,832 6,486,950   5,364,486 5,962,295
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 0 0 0      
Share-based Compensation Arrangement by Share-based Payment Award, Shares Issued in Period         79,487        
Equity Plans | Performance based restricted stock                  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                  
Granted, shares 1,033,333 1,033,333              
Vested, shares         145,986        
Forfeited, shares         320,681        
Equity Plans | Employee Stock | Minimum                  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                  
Stock compensation award, vesting period         2 years        
Equity Plans | Employee Stock | Maximum                  
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                  
Stock compensation award, vesting period         5 years        
Share-based Compensation Arrangement by Share-based Payment Award, Expiration Period         7 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 awards granted         $ 50.2        
Deferred cash award, interest rate         0.70%        
Deferred cash awards, unrecognized compensation expense     $ 89.5   $ 89.5