Fair Value - Valuation of Financial Instruments by Pricing Observability Levels (Details) - USD ($) $ in Thousands	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Investments:
Investments, other measurements	$ 77,959	$ 73,281
Securities sold not yet purchased:
Contingent payment arrangements	7,800	4,400	$ 17,384
Other investments
Investments:
Investments, other measurements	6,015	12,271
Time deposits
Investments:
Investments, other measurements	21,024	18,602
Hedge funds
Investments:
Investments, other measurements	50,920	42,408
Recurring
Assets, Fair Value Disclosure [Abstract]
Money markets	151,156	130,675
Securities segregated (U.S. Treasury Bills)	1,503,828	1,752,906
Derivatives	15,422	21,741
Investments:
Total investments measured at fair value and other measurements	273,418	253,375
Total assets measured at fair value and other measurements	1,943,824	2,158,697
Securities sold not yet purchased:
Short equities – corporate	1,054	5,305
Short exchange-traded options	2,774	12,486
Derivatives	16,923	30,537
Contingent payment arrangements	38,260	27,750
Total liabilities measured at fair value	59,011	76,078
Recurring | Level 1
Assets, Fair Value Disclosure [Abstract]
Money markets	151,156	130,675
Securities segregated (U.S. Treasury Bills)	0	0
Derivatives	392	118
Investments:
Total investments	155,904	162,243
Total assets measured at fair value	307,452	293,036
Securities sold not yet purchased:
Short equities – corporate	1,054	5,305
Short exchange-traded options	2,774	12,486
Derivatives	1,186	1,834
Contingent payment arrangements	0	0
Total liabilities measured at fair value	5,014	19,625
Recurring | Level 2
Assets, Fair Value Disclosure [Abstract]
Money markets	0	0
Securities segregated (U.S. Treasury Bills)	1,503,828	1,752,906
Derivatives	15,030	21,623
Investments:
Total investments	39,284	17,565
Total assets measured at fair value	1,558,142	1,792,094
Securities sold not yet purchased:
Short equities – corporate	0	0
Short exchange-traded options	0	0
Derivatives	15,737	28,703
Contingent payment arrangements	0	0
Total liabilities measured at fair value	15,737	28,703
Recurring | Level 3
Assets, Fair Value Disclosure [Abstract]
Money markets	0	0
Securities segregated (U.S. Treasury Bills)	0	0
Derivatives	0	0
Investments:
Total investments	126	125
Total assets measured at fair value	126	125
Securities sold not yet purchased:
Short equities – corporate	0	0
Short exchange-traded options	0	0
Derivatives	0	0
Contingent payment arrangements	38,260	27,750
Total liabilities measured at fair value	38,260	27,750
Recurring | NAV Expedient
Investments:
Total investments	145	161
Total assets measured at fair value	145	161
Recurring | Equity securities
Investments:
Investments	184,472	165,556
Recurring | Equity securities | Level 1
Investments:
Investments	144,917	147,705
Recurring | Equity securities | Level 2
Investments:
Investments	39,284	17,565
Recurring | Equity securities | Level 3
Investments:
Investments	126	125
Recurring | Equity securities | NAV Expedient
Investments:
Investments	145	161
Recurring | Other investments
Investments:
Investments, other measurements		19,282
Total investments measured at fair value and other measurements	15,109
Recurring | Other investments | Level 1
Investments:
Total investments	9,094	7,011
Recurring | Other investments | Level 2
Investments:
Total investments	0	0
Recurring | Other investments | Level 3
Investments:
Total investments	0	0
Recurring | Time deposits
Investments:
Investments, other measurements	21,024	18,602
Recurring | Hedge funds
Investments:
Investments, other measurements	50,920	42,408
Recurring | Long exchange-traded options | Exchange-traded options
Investments:
Investments	1,893	7,527
Recurring | Long exchange-traded options | Exchange-traded options | Level 1
Investments:
Investments	1,893	7,527
Recurring | Long exchange-traded options | Exchange-traded options | Level 2
Investments:
Investments	0	0
Recurring | Long exchange-traded options | Exchange-traded options | Level 3
Investments:
Investments	$ 0	$ 0