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Investments - Narrative (Details) - USD ($) $ in Thousands |  | 3 Months Ended | 6 Months Ended | 9 Months Ended |  |
--- | --- | --- | --- | --- | --- | ---
Jul. 01, 2023 | Sep. 30, 2023 | Sep. 30, 2022 | Jun. 30, 2023 | Sep. 30, 2023 | Sep. 30, 2022 | Dec. 31, 2022 | Dec. 31, 2021
Net Investment Income [Line Items] |  |  |  |  |  |  |  |
Management fees |  | $ 10,958 | $ 14,420 |  | $ 35,806 | $ 40,601 |  |
Restricted cash and cash equivalents |  | 98,979 |  |  | 98,979 |  | $ 130,783 |
Cash, cash equivalents and restricted cash |  | 903,527 | 1,352,256 |  | 903,527 | 1,352,256 | 1,207,203 | $ 964,126
Cash and cash equivalents |  | 804,548 |  |  | 804,548 |  | 1,076,420 |
Capital Requirements | Asset Pledged as Collateral |  |  |  |  |  |  |  |
Net Investment Income [Line Items] |  |  |  |  |  |  |  |
Investments, fair value |  | 226,900 |  |  | 226,900 |  | 274,000 |
Restricted cash and cash equivalents |  | 1,800 |  |  | 1,800 |  | 2,100 |
Trust Accounts | Asset Pledged as Collateral |  |  |  |  |  |  |  |
Net Investment Income [Line Items] |  |  |  |  |  |  |  |
Investments, fair value |  | 54,100 |  |  | 54,100 |  | 39,000 |
Restricted cash and cash equivalents |  | 1,400 |  |  | 1,400 |  | 1,300 |
Underwriting Obligations | Asset Pledged as Collateral |  |  |  |  |  |  |  |
Net Investment Income [Line Items] |  |  |  |  |  |  |  |
Investments, fair value |  | 34,900 |  |  | 34,900 |  | 0 |
Restricted cash and cash equivalents |  | 95,500 |  |  | 95,500 |  | 126,800 |
Escrow Funds | Asset Pledged as Collateral |  |  |  |  |  |  |  |
Net Investment Income [Line Items] |  |  |  |  |  |  |  |
Restricted cash and cash equivalents |  | 300 |  |  | 300 |  | 600 |
TS Hamilton Fund |  |  |  |  |  |  |  |
Net Investment Income [Line Items] |  |  |  |  |  |  |  |
Management fee percentage | 2.50% |  |  | 3.00% |  |  |  |
Management fees |  | 10,400 | 14,000 |  | 34,400 | 39,500 |  |
Incentive allocation | 30.00% |  |  |  |  |  |  |
Incentive allocation, reduction (as a percent) | 50.00% |  |  |  |  |  |  |
Incentive allocation, cumulative net profits (as a percent) | 200.00% |  |  |  |  |  |  |
Incentive allocation, excess profits (as a percent) | 25.00% |  |  | 20.00% |  |  |  |
Incentive allocation, net profits (as a percent) | 10.00% |  |  | 15.00% |  |  |  |
Incentive allocation |  | 9,100 | $ (15,300) |  | 15,100 | $ 68,000 |  |
Cash and cash equivalents |  | $ 450,759 |  |  | $ 450,759 |  | $ 800,239 |
TS Hamilton Fund | Hamilton Re |  |  |  |  |  |  |  |
Net Investment Income [Line Items] |  |  |  |  |  |  |  |
Initial term |  | 3 years |  |  | 3 years |  |  |
Capital account withdrawal, monthly liquidity, number of calendar days prior to month end |  | 15 days |  |  | 15 days |  |  |
Capital account withdrawal, daily liquidity, number of business day's written notice |  | 1 day |  |  | 1 day |  |  |
Two Sigma Futures Portfolio, LLC (FTV) |  |  |  |  |  |  |  |
Net Investment Income [Line Items] |  |  |  |  |  |  |  |
Percentage of ownership in funds |  | 20.10% |  |  | 20.10% |  |  |
Two Sigma Spectrum Portfolio, LLC (STV) |  |  |  |  |  |  |  |
Net Investment Income [Line Items] |  |  |  |  |  |  |  |
Percentage of ownership in funds |  | 16.10% |  |  | 16.10% |  |  |
Two Sigma Equity Spectrum Portfolio, LLC (ESTV) |  |  |  |  |  |  |  |
Net Investment Income [Line Items] |  |  |  |  |  |  |  |
Percentage of ownership in funds |  | 8.60% |  |  | 8.60% |  |  |
Two Sigma Hamilton Fund, LLC | Hamilton Re |  |  |  |  |  |  |  |
Net Investment Income [Line Items] |  |  |  |  |  |  |  |
Commitment for investment in Two Sigma Funds | $ 1,800,000 |  |  |  |  |  |  |
Investment in Two Sigma Funds, as a percentage of net tangible assets | 60.00% |  |  | 95.00% |  |  |  |

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