Share-Based Payments, Deferred Compensation and Employee Ownership Plans - Share-Based Payments and Deferred Compensation Narrative (Details) - USD ($) $ in Millions	3 Months Ended
Mar. 31, 2021	Mar. 31, 2020
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Shares granted	800,000
Equity Plans
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock-compensation expense recognized in connection with compensation plan	$ 28.2	$ 8.3
Tax benefit of stock-compensation expense recognized in connection with compensation plan	$ 10.8	$ 1.8
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 \| 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 \| Equity Plans
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Stock compensation award, vesting period	4 years
Deferred Cash Award \| Cowen Group, Inc. 2010 and 2020 Equity and Incentive Plan
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]
Deferred cash awards granted	$ 34.1
Deferred cash award, interest rate	0.70%
Deferred cash awards, unrecognized compensation expense	$ 90.5

Deferred Compensation Arrangement with Individual, Interest Rate

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- Definition

Deferred Compensation Arrangement with Individual, Total Compensation Cost Not yet Recognized

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- Definition

Deferred cash award granted

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- Definition

Amount of expense for award under share-based payment arrangement. Excludes amount capitalized.

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Amount of tax benefit for recognition of expense of award under share-based payment arrangement.

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- Definition

Period over which grantee's right to exercise award under share-based payment arrangement is no longer contingent on satisfaction of service or performance condition, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. Includes, but is not limited to, combination of market, performance or service condition.

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Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

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- Definition

The difference between the maximum number of shares (or other type of equity) authorized for issuance under the plan (including the effects of amendments and adjustments), and the sum of: 1) the number of shares (or other type of equity) already issued upon exercise of options or other equity-based awards under the plan; and 2) shares (or other type of equity) reserved for issuance on granting of outstanding awards, net of cancellations and forfeitures, if applicable.

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- Definition

Period from grant date that an equity-based award expires, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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