Fair Value Measurements for Operating Entities and Consolidated Funds - Carrying Value Disclosures (Details) - USD ($)		Mar. 31, 2021	Dec. 31, 2020	Mar. 31, 2020
Cash and cash equivalents		$ 1,147,531,000	$ 645,169,000	$ 270,079,000
Cash collateral pledged		110,303,000	110,743,000	7,538,000
Segregated cash		168,942,000	185,141,000	$ 131,266,000
Securities Purchased under Agreements to Resell		0	191,000
Securities borrowed		1,996,757,000	1,908,187,000
Loans Receivable, Net		4,467,000	7,682,000
Cash and cash equivalents, Consolidated Funds		935,000	417,000
Securities Sold under Agreements to Repurchase		2,546,000	5,036,000
Securities sold under agreements to repurchase, Fair value		2,759,000	5,544,000
Securities Loaned		3,083,945,000	2,476,414,000
Convertible debt	[1]	81,682,000	80,808,000
Long-term Debt	[2]	542,519,000	383,067,000
Convertible Debt
Convertible debt		81,682,000
Unamortized discount		5,800,000	6,700,000
Notes Payable, Other Payables
Unamortized discount		1,500,000
Debt Instrument, Unamortized Premium		300,000	400,000
Level 1
Cash and cash equivalents, Fair Value		1,147,531,000	645,169,000
Segregated cash fair value disclosures		168,942,000	185,141,000
Cash and cash equivalents, Consolidated Funds, Fair Value		935,000	417,000
Level 2
Cash collateral pledged, Fair Value		110,303,000	110,743,000
Federal Funds Sold and Securities Borrowed or Purchased under Agreements to Resell, Fair Value Disclosure		0	204,000
Securities Borrowed, Fair Value Disclosure		1,996,757,000	1,908,187,000
Securities sold under agreements to repurchase, Fair value		2,759,000	5,544,000
Securities loaned, fair value disclosure		3,083,945,000	2,476,414,000
Convertible debt, Fair Value	[3]	181,597,000	135,444,000
Notes payable and other debt, Fair Value	[4]	568,212,000	405,840,000
Level 3
Loans Receivable, Fair Value Disclosure	[5]	$ 4,467,000	$ 7,682,000

[1] The carrying amount of the convertible debt includes an unamortized discount of $5.8 million and $6.7 million as of March 31, 2021 and December 31, 2020, respectively.

[2] The carrying amount of the notes payable and other debt includes an unamortized discount and unamortized premium of $1.5 million and $0.3 million as of March 31, 2021, respectively and unamortized premium of $0.4 million as of December 31, 2020

[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.