Consolidated Statements of Cash Flows - USD ($) $ in Thousands	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2020	Dec. 31, 2019
Cash flows from operating activities:
Net income (loss)	$ 303,991	$ 207,064	$ 55,870
Adjustments to reconcile net income (loss) to net cash provided by / (used in) operating activities:
Bargain purchase gain, net of tax	(3,855)	0	0
Depreciation and amortization	19,004	22,677	20,460
Goodwill Impairment	0	0	4,100
Amortization of debt issuance costs	2,563	1,512	1,129
Amortization of debt discount (premium)	6,727	4,490	4,598
Noncash lease expense	734	(561)	(2,148)
Asset Impairment Charges	0	2,425	0
(Gain) / loss on extinguishment of debt	3,890	(2,719)	0
Share-based awards	65,718	48,222	33,918
Change in deferred taxes	(14,095)	70,136	13,295
Gain (Loss) on Disposition of Property Plant Equipment	0	0	233
Contingent liability adjustment	(614)	0	0
Payments to Acquire Marketable Securities	(1,136,928)	(1,682,598)	(2,107,956)
Proceeds from sales of securities owned, at fair value	1,007,261	1,793,934	2,042,946
Proceeds from sales of securities sold, not yet purchased, at fair value	257,142	821,829	1,360,075
Payments to cover securities sold, not yet purchased, at fair value	(262,362)	(850,608)	(1,408,043)
Proceeds from other investments	27,477	22,453	23,886
Investment income (loss) principal transactions, net	(66,219)	(161,699)	(74,284)
Consolidated Funds
Purchases of securities owned, at fair value	(4,000)	(1,912,137)	(2,725,439)
Proceeds from sales of securities owned, at fair value	13,748	1,793,528	2,618,200
Purchases of other investments	0	(2,090)	(3,408)
Proceeds from other investments	14,130	6,734	23,954
Investment Income (loss) principal transactions, net	5,990	21,597	(90,900)
(Increase) decrease in operating assets:
Securities owned, at fair value, held at broker-dealer	(496,443)	(335,510)	(990,356)
Receivable on derivative contracts, at fair value	(234,653)	11,394	(37,522)
Securities borrowed	203,584	(1,153,746)	(346,646)
Deposits with clearing organizations, brokers and banks	(6,905)	(13,197)	(2,332)
Receivable from brokers, dealers and clearing organizations	115,397	(1,048,049)	104,418
Receivable from customers, net of allowance	(55,455)	1,684	(67,789)
Fees receivable, net of allowance	16,919	(33,991)	(7,143)
Due from related parties	(10,088)	5,498	7,120
Other assets	(16,738)	63,626	(6,501)
Consolidated Funds
Receivable on derivative contracts, at fair value	(2,917)	(19,710)	(1,417)
Receivable from brokers	0	(961)	(17,636)
Other assets	13	564	(159)
Increase (decrease) in operating liabilities:
Securities sold, not yet purchased, at fair value, held at broker dealer	473,516	286,105	277,119
Securities sold under agreement to repurchase	58,433	(18,208)	23,244
Payable for derivative contracts, at fair value	(15,997)	15,399	44,679
Securities loaned	(889,842)	874,548	1,187,014
Payable to brokers, dealers and clearing organizations	171,410	144,125	42,287
Payable to customers	752,286	1,250,102	(94,929)
Commission management payable	(13,997)	45,367	(23,650)
Compensation payable	29,833	134,522	(38,954)
Fees payable	(27,350)	22,293	(1,025)
Due to related parties	(51)	254	(5,320)
Accounts payable, accrued expenses and other liabilities	15,707	55,879	(3,148)
Consolidated Funds
Contributions received in advance	0	450	50
Payable to brokers	0	8,560	(22,657)
Payable for derivative contracts, at fair value	0	11,967	3,106
Due To Related Parties, Consolidated Funds	16	(386)	581
Accounts payable, accrued expenses and other liabilities	(353)	436	(129)
Net Cash Provided by (Used in) Operating Activities	306,627	513,204	(187,209)
Cash flows from investing activities:
Securities purchased under agreement to resell	191	(191)	0
Purchases of other investments	(98,375)	(48,634)	(19,812)
Purchase of business (see note 3)	(63,246)	(5,647)	(48,581)
Cash Divested from Deconsolidation	(5,620)	(22,382)	55
Proceeds from sales of other investments	99,142	44,371	35,648
Purchase of fixed assets and intangibles	(11,819)	(10,721)	(14,882)
Proceeds from Sale of Property, Plant, and Equipment	4,183	0	0
Net Cash Provided by (Used in) Investing Activities	(75,544)	(43,204)	(47,572)
Cash flows from financing activities:
Repayments of Convertible Debt	(88,119)	(69,842)	(14,065)
Deferred Debt Issuance Costs	(9,312)	(1,700)	(2,077)
Borrowings on notes and other debt	450,286	159,821	87,365
Repayments on notes and other debt	(206,433)	(121,472)	(10,263)
Purchase of treasury stock	(159,822)	(47,314)	(15,217)
Cash dividends paid	(11,373)	(5,710)	0
Preferred dividends paid	6,792	6,792	6,792
Contingent liability payment	(10,698)	(5,653)	(1,234)
Capital contributions by non-controlling interests in operating entities	36,539	9,730	11,108
Capital withdrawals to non-controlling interests in operating entities	(7,601)	(5,605)	(3,788)
Consolidated Funds
Capital contributions by non-controlling interests in Consolidated Funds	19,017	375,716	267,051
Capital withdrawals to non-controlling interests in Consolidated Funds	(21,411)	(255,597)	(111,650)
Net Cash Provided by (Used in) Financing Activities	(15,719)	25,582	200,438
Change in cash and cash equivalents	215,364	495,582	(34,343)
Total cash beginning of period	941,470	445,888	480,231
Cash and cash equivalents	914,343	645,169	301,123
Cash collateral pledged	47,494	110,743	6,563
Segregated Cash	194,701	185,141	107,328
Cash and cash equivalents, Consolidated Funds	296	417	30,874
Total cash at end of period	1,156,834	941,470	445,888
Supplemental information
Cash paid during the year for interest	214,909	153,653	145,877
Cash paid during the year for taxes	119,050	4,783	4,310
Purchase of treasury stock, at cost, through net settlement	40,392	15,147	15,217
Preferred stock dividends declared	6,792	6,792	6,792
Dividends, Preferred Stock, Cash	(6,792)	(6,792)	(6,792)
Dividends, Cash	12,738	6,851	0
Net assets (liabilities) acquired upon acquisition (net of cash)	23,128	9,865	90,727
Initial Recognition Of Right Of Use Asset			103,694
Initial recognition of operating lease liabilities			110,505
Noncash transfer of net assets from Unconsolidated Master Fund to Consolidated Fund			97,655
Increase in noncontrolling interest due to consolidation of entity	0	48,596	0
Decrease in noncontrolling interest due to deconsolidation of entity	74,813	450,600	0
Common stock issuance upon close of acquisition	23,060	926	14,446
Additional Paid-in Capital
Supplemental information
Common stock issuance for purchase of investment	2,500	0	0
Common stock issuance upon close of acquisition	23,060	926	14,436
Common stock issuance for purchase of investment	$ 2,500	$ 0	$ 0