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Share-Based Compensation and Employee Ownership Plans Narrative (Details) - USD ($)
$ in Millions
1 Months Ended 3 Months Ended 9 Months Ended
Jul. 30, 2020
Apr. 30, 2019
Mar. 31, 2016
Sep. 30, 2020
Sep. 30, 2019
Sep. 30, 2020
Sep. 30, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Shares granted       2,500,000   2,500,000  
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       $ 11.6 $ 10.0 $ 35.2 $ 27.2
Tax benefit of stock-compensation expense recognized in connection with compensation plan       3.1 $ 2.6 $ 8.4 $ 6.8
Equity Plans | Restricted Shares and Restricted Stock Units (RSUs)              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Granted, shares           2,638,544 2,322,996
Vested, shares           1,320,318 1,545,850
Forfeited, shares           111,212 156,528
Unrecognized compensation expense       $ 81.8   $ 81.8  
Period for recognition           2 years 2 months 26 days  
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       90,645 0 90,645 0
Delivered, shares       48,021   48,021  
Share-based Compensation Arrangement by Share-based Payment Award, Shares Issued in Period             120,430
Equity Plans | Performance based restricted stock              
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]              
Granted, shares 1,366,666 1,366,666 1,366,666        
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  
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       $ 0.1   $ 50.3  
Deferred cash award, interest rate           0.70%  
Deferred cash awards, unrecognized compensation expense       $ 79.4   $ 79.4