Consolidated Statements of Cash Flows - USD ($) $ / shares in Thousands, $ in Thousands	9 Months Ended
	Sep. 30, 2021	Sep. 30, 2020
Cash flows from operating activities:
Net income (loss)	$ 244,009	$ 104,353
Adjustments to reconcile net income (loss) to net cash provided by / (used in) operating activities:
Bargain purchase gain, net of tax	(3,855)	0
Depreciation and amortization	13,715	17,324
Amortization of debt issuance costs	2,042	1,023
Amortization of debt discount (premium)	6,695	3,393
Noncash lease expense	(989)	(1,490)
(Gain) / loss on extinguishment of debt	3,890	0
Share-based awards	44,327	35,287
Change in deferred taxes	3,367	48,056
Contingent liability adjustment	(614)	0
Purchases of securities owned, at fair value	(799,398)	(1,275,400)
Proceeds from sales of securities owned, at fair value	677,573	1,318,623
Proceeds from sales of securities sold, not yet purchased, at fair value	183,724	729,526
Payments to cover securities sold, not yet purchased, at fair value	(179,576)	(745,683)
Proceeds from other investments	23,252	21,964
Investment income (loss) principal transactions, net	(67,855)	(80,533)
Consolidated Funds
Purchases of securities owned, at fair value	(4,000)	(1,912,137)
Proceeds from sales of securities owned, at fair value	11,956	1,793,399
Purchases of other investments	0	(2,090)
Proceeds from other investments	14,130	6,734
Investment Income (loss) principal transactions, net	3,645	27,216
(Increase) decrease in operating assets:
Securities owned, at fair value, held at broker-dealer	(1,781,200)	603,885
Receivable on derivative contracts, at fair value	(160,939)	4,783
Securities borrowed	(260,869)	(517,987)
Deposits with clearing organizations, brokers and banks	28,154	1,680
Receivable from brokers, dealers and clearing organizations	(345,529)	(709,126)
Receivable from customers, net of allowance	(120,492)	22,439
Fees receivable, net of allowance	5,122	(11,876)
Due from related parties	(9,093)	3,086
Other assets	(27,656)	69,185
Consolidated Funds
Receivable on derivative contracts, at fair value	(2,917)	(19,710)
Receivable from brokers	0	(961)
Other assets	13	273
Increase (decrease) in operating liabilities:
Securities sold, not yet purchased, at fair value, held at broker dealer	620,715	2,302
Securities sold under agreement to repurchase	48,803	(17,026)
Payable for derivative contracts, at fair value	(29,288)	1,293
Securities loaned	876,042	(274,949)
Payable to brokers, dealers and clearing organizations	252,666	41,832
Payable to customers	1,052,102	720,915
Commission management payable	765	46,158
Compensation payable	159,071	116,035
Fees payable	(13,964)	60,311
Due to related parties	57	24
Accounts payable, accrued expenses and other liabilities	5,064	37,729
Consolidated Funds
Contributions received in advance	0	450
Payable to brokers	0	8,560
Payable for derivative contracts, at fair value	0	11,967
Due To Related Parties, Consolidated Funds	(2)	(257)
Accounts payable, accrued expenses and other liabilities	(397)	75
Net Cash Provided by (Used in) Operating Activities	472,266	290,655
Cash flows from investing activities:
Securities purchased under agreement to resell	191	0
Purchases of other investments	(85,271)	(38,658)
Purchase of business (see note 3)	2,109	0
Cash Divested from Deconsolidation	(5,620)	(20,939)
Proceeds from sales of other investments	87,525	29,784
Purchase of fixed assets and intangibles	(7,357)	(11,558)
Net Cash Provided by (Used in) Investing Activities	(8,423)	(41,371)
Cash flows from financing activities:
Repayments of Convertible Debt	(88,119)	0
Deferred Debt Issuance Costs	(6,642)	(1,700)
Borrowings on notes and other debt	301,786	134,810
Repayments on notes and other debt	(203,919)	(95,458)
Purchase of treasury stock	$ (122,945)	$ (43,442)
Common Stock, Dividends, Per Share, Cash Paid	$ (8,205)	$ (3,433)
Preferred Dividends Paid	$ 5,094	$ 5,094
Payment for Contingent Consideration Liability, Financing Activities	(10,698)	(5,653)
Capital contributions by non-controlling interests in operating entities	30,361	7,276
Capital withdrawals to non-controlling interests in operating entities	(6,456)	(4,330)
Consolidated Funds
Capital contributions by non-controlling interests in Consolidated Funds	19,017	339,966
Capital withdrawals to non-controlling interests in Consolidated Funds	(20,161)	(227,617)
Net Cash Provided by (Used in) Financing Activities	(121,075)	95,325
Change in cash and cash equivalents	342,768	344,609
Total cash beginning of period	941,470	445,888
Cash and cash equivalents	1,057,123	539,733
Cash collateral pledged	48,996	110,666
Segregated Cash	177,693	139,152
Cash and cash equivalents, Consolidated Funds	426	946
Total cash at end of period	1,284,238	790,497
Supplemental information
Cash paid during the year for interest	162,468	116,457
Cash paid during the year for taxes	88,094	1,984
Purchase of treasury stock, at cost, through net settlement	26,078	6,296
Dividends, Preferred Stock, Cash	(5,094)	(5,094)
Dividends, Cash	9,388	4,144
Net assets (liabilities) acquired upon acquisition (net of cash)	3,107	0
Increase in noncontrolling interest due to consolidation of entity	0	48,596
Decrease in noncontrolling interest due to deconsolidation of entity	74,813	360,711
Common stock issuance upon close of acquisition	$ 2,202	$ 926