Fair Value Measurements for Operating Entities and Consolidated Funds - Carrying Value Disclosures (Details) - USD ($)		Dec. 31, 2020	Dec. 31, 2019	Dec. 31, 2018
Cash and cash equivalents		$ 645,169,000	$ 301,123,000	$ 259,148,000
Cash collateral pledged		110,743,000	6,563,000	6,318,000
Segregated cash		185,141,000	107,328,000	$ 176,647,000
Securities Purchased under Agreements to Resell		191,000	0
Securities borrowed		1,908,187,000	754,441,000
Loans Receivable, Net		7,682,000	42,830,000
Cash and cash equivalents, Consolidated Funds		417,000	30,874,000
Securities Sold under Agreements to Repurchase		5,036,000	23,244,000
Securities sold under agreements to repurchase, Fair value		5,544,000	27,384,000
Securities Loaned		2,476,414,000	1,601,866,000
Convertible debt	[1]	80,808,000	118,688,000
Long-term Debt	[2]	383,067,000	345,451,000
Convertible Debt
Convertible debt		80,808,000
Convertible debt, unamortized discount		6,700,000	14,900,000
Notes Payable, Other Payables [Member]
Debt Instrument, Unamortized Premium		400,000	500,000
Level 1
Cash and cash equivalents, Fair Value		645,169,000	301,123,000
Segregated cash fair value disclosures		185,141,000	107,328,000
Cash and cash equivalents, Consolidated Funds, Fair Value		417,000	30,874,000
Level 2
Cash collateral pledged, Fair Value		110,743,000	6,563,000
Federal Funds Sold and Securities Borrowed or Purchased under Agreements to Resell, Fair Value Disclosure		204,000	0
Securities Borrowed, Fair Value Disclosure		1,908,187,000	754,441,000
Securities sold under agreements to repurchase, Fair value		5,544,000	27,384,000
Securities loaned, fair value disclosure		2,476,414,000	1,601,866,000
Convertible debt, Fair Value	[3]	135,444,000	148,786,000
Notes payable and other debt, Fair Value	[4]	405,840,000	372,591,000
Level 3
Loans Receivable, Fair Value Disclosure	[5]	$ 7,682,000	$ 42,830,000

[1] The carrying amount of the convertible debt includes an unamortized discount of $6.7 million and $14.9 million as of December 31, 2020 and 2019, respectively.

[2] The carrying amount of the notes payable and other debt includes an unamortized premium of $0.4 million and $0.5 million as of December 31, 2020 and 2019, respectively.

[3] The convertible debt includes the conversion option and is based on the last broker quote available.

[4] Notes payable and other debt are based on the last broker quote available.

[5] The fair market value of level 3 loans is calculated using discounted cash flows where applicable.