Fair Value - Valuation of Financial Instruments (Details) - USD ($) $ in Thousands	Sep. 30, 2020	Dec. 31, 2019	Sep. 30, 2019
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other	$ 69,145	$ 73,649
Securities sold not yet purchased:
Contingent payment arrangements	4,400		$ 17,384
Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Money markets	131,614	126,401
Securities segregated (U.S. Treasury Bills)	1,868,891	1,094,866
Derivatives	26,670	13,491
Total investments measured at fair value and other measurements	253,692	266,794
Total assets measured at fair value and other measurements	2,280,867	1,501,552
Securities sold not yet purchased:
Short equities – corporate	2,892	17,809
Short exchange-traded options	11,091	12,348
Derivatives	28,230	19,259
Contingent payment arrangements	29,723	22,911
Total liabilities measured at fair value	71,936	72,327
Recurring | Level 1
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Money markets	131,614	126,401
Securities segregated (U.S. Treasury Bills)	0	0
Derivatives	317	939
Total investments	162,159	183,760
Total assets measured at fair value	294,090	311,100
Securities sold not yet purchased:
Short equities – corporate	2,892	17,809
Short exchange-traded options	11,091	12,348
Derivatives	223	871
Contingent payment arrangements	0	0
Total liabilities measured at fair value	14,206	31,028
Recurring | Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Money markets	0	0
Securities segregated (U.S. Treasury Bills)	1,868,891	1,094,866
Derivatives	26,353	12,552
Total investments	22,096	8,952
Total assets measured at fair value	1,917,340	1,116,370
Securities sold not yet purchased:
Short equities – corporate	0	0
Short exchange-traded options	0	0
Derivatives	28,007	18,388
Contingent payment arrangements	0	0
Total liabilities measured at fair value	28,007	18,388
Recurring | Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Money markets	0	0
Securities segregated (U.S. Treasury Bills)	0	0
Derivatives	0	0
Total investments	121	119
Total assets measured at fair value	121	119
Securities sold not yet purchased:
Short equities – corporate	0	0
Short exchange-traded options	0	0
Derivatives	0	0
Contingent payment arrangements	29,723	22,911
Total liabilities measured at fair value	29,723	22,911
Recurring | NAV Expedient
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
NAV Expedient	171	314
Equity securities | Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	166,137	180,331
Equity securities | Recurring | Level 1
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	143,749	170,946
Equity securities | Recurring | Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	22,096	8,952
Equity securities | Recurring | Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	121	119
Equity securities | Recurring | NAV Expedient
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
NAV Expedient	171	314
Other investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other	7,786	8,007
Other investments | Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Total investments measured at fair value and other measurements	14,043	13,890
Other investments | Recurring | Level 1
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Total investments	6,257	5,883
Time deposits
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other	19,900	18,281
Time deposits | Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other	19,900	18,281
Long | Exchange-traded options | Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	12,153	6,931
Long | Exchange-traded options | Recurring | Level 1
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	12,153	6,931
Long | Exchange-traded options | Recurring | Level 2
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	0	0
Long | Exchange-traded options | Recurring | Level 3
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	0	0
Limited partnership hedge funds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other	41,459	47,361
Limited partnership hedge funds | Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other	$ 41,459	$ 47,361