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Financial Instruments and Other Inventory Positions Owned and Financial Instruments and Other Inventory Positions Sold, but Not Yet Purchased - Schedule of Financial Instruments Owned and Financial Instruments Sold, but Not Yet Purchased by Type (Details) - USD ($)
$ in Thousands
Sep. 30, 2022
Dec. 31, 2021
Financial instruments and other inventory positions owned:    
Equity securities $ 2,872 $ 2,831
Convertible securities 146,030 148,057
Fixed income securities 11,055 8,687
Taxable securities 27,042 12,377
Tax-exempt securities 146,530 97,891
Short-term securities 32,480 29,357
Mortgage-backed securities 0 1,277
U.S. government agency securities 57,934 24,361
U.S. government securities 3,384 138
Derivative contracts 13,235 23,998
Total financial instruments and other inventory positions owned 440,562 348,974
Financial instruments and other inventory positions sold, but not yet purchased:    
Equity securities 58,444 77,744
Fixed income securities 5,146 4,950
U.S. government securities 32,412 41,780
Derivative contracts 1,724 4,216
Total financial instruments and other inventory positions sold, but not yet purchased 97,726 128,690
Asset Pledged as Collateral    
Financial instruments and other inventory positions owned:    
Total financial instruments and other inventory positions owned 109,714 118,551
Asset Pledged as Collateral | Short-term Debt    
Financial instruments and other inventory positions owned:    
Total financial instruments and other inventory positions owned $ 109,700 $ 118,600