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Share-Based Compensation and Employee Ownership Plans Narrative (Details) - USD ($)
1 Months Ended 3 Months Ended 12 Months Ended
Jul. 30, 2020
Apr. 30, 2019
Mar. 31, 2016
Dec. 31, 2020
Dec. 31, 2019
Dec. 31, 2020
Dec. 31, 2019
Dec. 31, 2018
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                
Shares granted       2,400,000   2,400,000    
Performance based restricted stock | Minimum                
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                
Percent of RSU's earned           0.00%    
Performance based restricted stock | 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           $ 48,100,000 $ 34,000,000.0 $ 37,000,000.0
Tax benefit of stock-compensation expense recognized in connection with compensation plan           $ 13,800,000 $ 8,800,000 $ 9,700,000
Equity Plans | Restricted Shares and Restricted Stock Units (RSUs)                
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                
Granted, shares           2,709,979 2,435,058  
Vested, shares           2,419,818 2,291,032  
Forfeited, shares           117,108 157,502  
Unrecognized compensation expense       $ 70,800,000   $ 70,800,000    
Period for recognition           2 years 18 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           379,319    
Forfeited, shares           320,681    
Equity Plans | Performance based restricted stock | Share-based Payment Arrangement, Tranche Three [Member]                
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]                
Vested, shares           233,333    
Share-based Compensation Arrangement by Share-based Payment Award, Equity Instruments Other than Options, Aggregate Intrinsic Value, Vested           $ 420,000    
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           $ 50,300,000    
Deferred cash award, interest rate           0.70%    
Deferred cash awards, unrecognized compensation expense       $ 69,800,000   $ 69,800,000