Fair Value - Valuation of Financial Instruments (Details) - USD ($) $ in Thousands	Sep. 30, 2022	Dec. 31, 2021
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other	$ 62,503	$ 77,959
Securities sold not yet purchased:
Contingent payment arrangements	273,145	38,260
Time deposits
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other	17,298	21,024
Limited partnership hedge funds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other	42,227	50,920
Other investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other	2,978	6,015
Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Money markets	162,391	151,156
Securities segregated (U.S. Treasury Bills)	1,335,107	1,503,828
Derivatives	37,348	15,422
Total investments measured at fair value and other measurements	211,550	273,418
Total assets measured at fair value and other measurements	1,746,396	1,943,824
Securities sold not yet purchased:
Short equities – corporate	51	1,054
Short exchange-traded options	192	2,774
Derivatives	11,758	16,923
Contingent payment arrangements	273,145	38,260
Total liabilities measured at fair value	285,146	59,011
Recurring | Time deposits
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other	17,298	21,024
Recurring | Limited partnership hedge funds
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Other	42,227	50,920
Recurring | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	138,103	184,472
Recurring | Long exchange-traded options | Long
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	4,837	1,893
Recurring | Other investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Total investments measured at fair value and other measurements	9,085	15,109
Level 1 | Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Money markets	162,391	151,156
Securities segregated (U.S. Treasury Bills)	0	0
Derivatives	8,053	392
Total investments	124,124	155,904
Total assets measured at fair value	294,568	307,452
Securities sold not yet purchased:
Short equities – corporate	51	1,054
Short exchange-traded options	192	2,774
Derivatives	0	1,186
Contingent payment arrangements	0	0
Total liabilities measured at fair value	243	5,014
Level 1 | Recurring | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	113,180	144,917
Level 1 | Recurring | Long exchange-traded options | Long
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	4,837	1,893
Level 1 | Recurring | Other investments
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Total investments	6,107	9,094
Level 2 | Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Money markets	0	0
Securities segregated (U.S. Treasury Bills)	1,335,107	1,503,828
Derivatives	29,295	15,030
Total investments	24,680	39,284
Total assets measured at fair value	1,389,082	1,558,142
Securities sold not yet purchased:
Short equities – corporate	0	0
Short exchange-traded options	0	0
Derivatives	11,758	15,737
Contingent payment arrangements	0	0
Total liabilities measured at fair value	11,758	15,737
Level 2 | Recurring | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	24,680	39,284
Level 2 | Recurring | Long exchange-traded options | Long
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	0	0
Level 3 | Recurring
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	120	126
Total assets measured at fair value	120	126
Securities sold not yet purchased:
Short equities – corporate	0	0
Short exchange-traded options	0	0
Derivatives	0	0
Contingent payment arrangements	273,145	38,260
Total liabilities measured at fair value	273,145	38,260
Level 3 | Recurring | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	120	126
Level 3 | Recurring | Long exchange-traded options | Long
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	0	0
NAV Expedient | Recurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Total investments	123	145
Total assets measured at fair value	123	145
NAV Expedient | Recurring | Equity securities
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Trading securities	$ 123	$ 145