Consolidated Statements of Cash Flows - USD ($)	12 Months Ended
	Dec. 31, 2022	Dec. 31, 2021	Dec. 31, 2020
Cash flows from operating activities:
Net income (loss)	$ 65,855,000	$ 303,991,000	$ 207,064,000
Adjustments to reconcile net income (loss) to net cash provided by / (used in) operating activities:
Bargain purchase gain, net of tax	0	(3,855,000)	0
Depreciation and amortization	27,725,000	19,004,000	22,677,000
Amortization of debt issuance costs	2,473,000	2,563,000	1,512,000
Amortization of debt discount (premium)	309,000	6,727,000	4,490,000
Noncash lease expense	1,429,000	734,000	(561,000)
Asset Impairment Charges	0	0	2,425,000
(Gain) / loss on extinguishment of debt	0	3,890,000	(2,719,000)
Share-based awards	60,272,000	65,718,000	48,222,000
Change in deferred taxes	(29,045,000)	(14,095,000)	70,136,000
Net loss (gain) on disposal of fixed assets	216,000	0	0
Contingent liability adjustment	0	(614,000)	0
Purchases of securities owned, at fair value	(1,202,243,000)	(1,136,928,000)	(1,682,598,000)
Proceeds from sales of securities owned, at fair value	999,934,000	1,007,261,000	1,793,934,000
Proceeds from sales of securities sold, not yet purchased, at fair value	6,621,546,000	257,142,000	821,829,000
Payments to cover securities sold, not yet purchased, at fair value	(6,240,064,000)	(262,362,000)	(850,608,000)
Proceeds from sales of other investments	28,894,000	27,477,000	22,453,000
Investment income (loss) principal transactions, net	(157,798,000)	(66,219,000)	(161,699,000)
Consolidated Funds
Purchases of securities owned, at fair value	0	(4,000,000)	(1,912,137,000)
Proceeds from sales of securities owned, at fair value	0	13,748,000	1,793,528,000
Payments to Acquire Other Investments Operating Activities, Consolidated Funds	0	0	(2,090,000)
Proceeds from other investments	0	14,130,000	6,734,000
Investment income (loss) principal transactions, net	49,235,000	5,990,000	21,597,000
(Increase) decrease in operating assets:
Securities owned, at fair value, held at broker-dealer	450,760,000	(496,443,000)	(335,510,000)
Receivable on derivative contracts, at fair value	(208,556,000)	(234,653,000)	11,394,000
Securities borrowed	406,547,000	203,584,000	(1,153,746,000)
Deposits with clearing organizations, brokers and banks	23,925,000	(6,905,000)	(13,197,000)
Receivable from brokers, dealers and clearing organizations	(250,478,000)	115,397,000	(1,048,049,000)
Receivable from customers, net of allowance	117,747,000	(55,455,000)	1,684,000
Fees receivable, net of allowance	32,592,000	16,919,000	(33,991,000)
Insurance and reinsurance assets	7,717,000	(9,465,000)	(18,498,000)
Due from related parties	9,156,000	(10,088,000)	5,498,000
Other assets	(30,125,000)	(7,273,000)	82,124,000
Consolidated Funds
Receivable on derivative contracts, at fair value	0	(2,917,000)	(19,710,000)
Increase (Decrease) in Receivable from Broker-Dealers and Clearing Organizations, Consolidated Funds	0	0	(961,000)
Other assets	0	13,000	564,000
Increase (decrease) in operating liabilities:
Securities sold, not yet purchased, at fair value, held at broker dealer	(503,565,000)	473,516,000	286,105,000
Securities sold under agreement to repurchase	69,661,000	58,433,000	(18,208,000)
Payable for derivative contracts, at fair value	9,502,000	(15,997,000)	15,399,000
Securities loaned	(386,734,000)	(889,842,000)	874,548,000
Payable to brokers, dealers and clearing organizations	197,356,000	171,410,000	144,125,000
Payable to customers	230,802,000	752,286,000	1,250,102,000
Commission management payable	12,863,000	(13,997,000)	45,367,000
Insurance and reinsurance liabilities	(51,147,000)	4,041,000	63,856,000
Compensation payable	(81,185,000)	29,833,000	134,522,000
Fees payable	9,579,000	(27,350,000)	22,293,000
Due to related parties	(43,000)	(51,000)	254,000
Accounts payable, accrued expenses and other liabilities	(1,714,000)	11,666,000	(7,977,000)
Consolidated Funds
Contributions received in advance	0	0	450,000
Payable to brokers	0	0	8,560,000
Payable for derivative contracts, at fair value	0	0	11,967,000
Due To Related Parties, Consolidated Funds	(23,000)	16,000	(386,000)
Accounts payable, accrued expenses and other liabilities	(63,000)	(353,000)	436,000
Net Cash Provided by (Used in) Operating Activities	171,594,000	306,818,000	513,013,000
Cash flows from investing activities:
Securities purchased under agreements to resell	(121,718,000)	191,000	(191,000)
Purchases of other investments	(63,875,000)	(98,375,000)	(48,634,000)
Purchase of business and/or asset acquisition	187,613,000	(63,246,000)	(5,647,000)
Cash at deconsolidated entity	0	(5,620,000)	(22,382,000)
Proceeds from sales of other investments	64,017,000	99,142,000	44,371,000
Purchase of fixed assets and intangibles	(12,537,000)	(11,819,000)	(10,721,000)
Proceeds from Sale of Property, Plant, and Equipment	0	4,183,000	0
Net Cash Provided by (Used in) Investing Activities	175,218,000	(75,735,000)	(43,013,000)
Cash flows from financing activities:
Repayments on convertible debt	0	(88,119,000)	(69,842,000)
Deferred debt issuance cost	(72,000)	(9,312,000)	(1,700,000)
Borrowings on notes and other debt	4,175,000	450,286,000	159,821,000
Repayments on notes and other debt	(10,095,000)	(206,433,000)	(121,472,000)
Purchase of treasury stock	(31,078,000)	(159,822,000)	(47,314,000)
Cash dividends paid	(15,152,000)	(11,373,000)	(5,710,000)
Preferred stock dividends paid	(6,792,000)	(6,792,000)	(6,792,000)
Contingent liability payment	(10,076,000)	(10,698,000)	(5,653,000)
Capital contributions by non-controlling interests in operating entities	24,311,000	36,539,000	9,730,000
Capital distributions to non-controlling interests in operating entities	(10,626,000)	(7,601,000)	(5,605,000)
Consolidated Funds
Capital contributions by non-controlling interests in Consolidated Funds	0	19,017,000	375,716,000
Capital distributions to non-controlling interests in Consolidated Funds	0	(21,411,000)	(255,597,000)
Net cash provided by / (used in) financing activities	(55,405,000)	(15,719,000)	25,582,000
Change in cash and cash equivalents	291,407,000	215,364,000	495,582,000
Total cash beginning of period	1,156,834,000	941,470,000	445,888,000
Cash and cash equivalents	1,139,652,000	914,343,000	645,169,000
Cash collateral pledged	122,687,000	47,494,000	110,743,000
Segregated Cash	185,872,000	194,701,000	185,141,000
Cash and cash equivalents, Consolidated Funds	30,000	296,000	417,000
Total cash at end of period	1,448,241,000	1,156,834,000	941,470,000
Supplemental information
Cash paid during the year for interest	187,628,000	214,909,000	153,653,000
Cash paid during the year for taxes	50,988,000	119,050,000	4,783,000
Purchase of treasury stock, at cost, through net settlement	36,082,000	40,392,000	15,147,000
Preferred stock dividends declared	6,792,000	6,792,000	6,792,000
Cash dividends declared	16,253,000	12,738,000	6,851
Net assets (liabilities) acquired upon acquisition (net of cash)	(187,613,000)	23,128,000	9,865,000
Increase in noncontrolling interest due to consolidation of entity	0	0	48,596,000
Net decrease in non-controlling interests in Consolidated Fund due to deconsolidation of Consolidated Fund	0	74,813,000	450,600,000
Common stock issuance for purchase of investment	0	2,500,000	0
Common stock issuance upon close of acquisition	$ 1,881,000	$ 23,060,000	$ 926,000