Fair Value Disclosures - Quantitative Information about Significant Unobservable Inputs Used in Level 3 Fair Value Measurements (Details)	3 Months Ended	9 Months Ended
	May 31, 2024 USD ($)	Aug. 31, 2023	May 31, 2024 $ / shares	May 31, 2024	May 31, 2024 $ / Bond	May 31, 2024 € / shares	May 31, 2024 poundSterlingPerShare	May 31, 2024 € / Bond	Nov. 30, 2023 USD ($)	Nov. 30, 2023 $ / shares	Nov. 30, 2023	Nov. 30, 2023 $ / Bond	Nov. 30, 2023 € / Bond
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	$ 21,499,675,000								$ 20,538,090,000
Financial instruments sold, not yet purchased	11,926,366,000								11,251,154,000
Other secured financings	3,965,000								3,898,000
Long-term debt	1,875,817,000								1,708,443,000
Corporate debt securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	5,335,965,000								4,947,334,000
Financial instruments sold, not yet purchased	2,938,413,000								2,842,900,000
CDOs and CLOs
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	525,327,000								934,108,000
Financial instruments sold, not yet purchased	3,125,000								36,000
Commercial mortgage-backed securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	412,978,000								345,410,000
Financial instruments sold, not yet purchased	1,049,000								840,000
Other ABS
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	245,633,000								372,709,000
Loans and other receivables
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	1,558,315,000								1,450,318,000
Investments at fair value
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	138,066,000								130,835,000
Loans
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments sold, not yet purchased	74,685,000								175,349,000
Level 3
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	691,332,000								680,580,000
Financial instruments sold, not yet purchased	43,498,000								62,452,000
Long-term debt	784,212,000								744,597,000
Level 3 | Scenario analysis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Other secured financings	3,965,000								3,898,000
Level 3 | Volatility benchmarking and market approach
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Derivative liability	37,154,000								56,779,000
Level 3 | Non-exchange-traded securities | Market approach
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	178,755,000								181,294,000
Level 3 | Non-exchange-traded securities | Market approach | Price | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / shares			0							0
Level 3 | Non-exchange-traded securities | Market approach | Price | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / shares			325							325
Level 3 | Non-exchange-traded securities | Market approach | Price | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / shares			56							59
Level 3 | Corporate debt securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	38,717,000								26,112,000
Financial instruments sold, not yet purchased	506,000								124,000
Level 3 | Corporate debt securities | Market approach
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	38,717,000
Level 3 | Corporate debt securities | Market approach | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / shares										40
Level 3 | Corporate debt securities | Market approach | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / shares										94
Level 3 | Corporate debt securities | Market approach | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / shares										50
Level 3 | Corporate debt securities | Market approach | Price
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0
Level 3 | Corporate debt securities | Market approach | Price | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / Bond					95
Level 3 | Corporate debt securities | Market approach | Price | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / shares			57
Level 3 | Corporate debt securities | Scenario analysis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Derivative liability									124,000
Level 3 | Corporate debt securities | Scenario analysis | Estimated recovery percentage
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input											0.04
Financial instruments sold, not yet purchased, measurement input											0.04
Level 3 | Corporate debt securities | Discounted cash flows | Discount rate/yield
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input											0.11
Level 3 | Corporate debt securities | Discounted cash flows, market approach, scenario analysis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned									26,112,000
Level 3 | CDOs and CLOs
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	68,626,000								64,862,000
Financial instruments sold, not yet purchased	0								0
Level 3 | CDOs and CLOs | Market approach | Price | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / Bond					54							48
Level 3 | CDOs and CLOs | Market approach | Price | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / Bond					109							100
Level 3 | CDOs and CLOs | Market approach | Price | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / Bond					95							88
Level 3 | CDOs and CLOs | Discounted cash flows | Constant prepayment rate
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0.20
Level 3 | CDOs and CLOs | Discounted cash flows | Constant prepayment rate | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input											0.15
Level 3 | CDOs and CLOs | Discounted cash flows | Constant prepayment rate | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input											0.20
Level 3 | CDOs and CLOs | Discounted cash flows | Constant prepayment rate | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input											0.19
Level 3 | CDOs and CLOs | Discounted cash flows | Constant default rate
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0.02
Level 3 | CDOs and CLOs | Discounted cash flows | Constant default rate | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input											0.02
Level 3 | CDOs and CLOs | Discounted cash flows | Discount rate/yield | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0.15							0.21
Level 3 | CDOs and CLOs | Discounted cash flows | Discount rate/yield | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0.24							0.26
Level 3 | CDOs and CLOs | Discounted cash flows | Discount rate/yield | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0.21							0.24
Level 3 | CDOs and CLOs | Discounted cash flows | Loss severity
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0.30
Level 3 | CDOs and CLOs | Discounted cash flows | Loss severity | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input											0.35
Level 3 | CDOs and CLOs | Discounted cash flows | Loss severity | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input											0.40
Level 3 | CDOs and CLOs | Discounted cash flows | Loss severity | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input											0.36
Level 3 | CDOs and CLOs | Discounted cash flows and market approach
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	55,917,000								64,862,000
Level 3 | Commercial mortgage-backed securities
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	477,000								508,000
Financial instruments sold, not yet purchased	1,049,000								840,000
Level 3 | Commercial mortgage-backed securities | Scenario analysis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned									508,000
Level 3 | Commercial mortgage-backed securities | Scenario analysis | Estimated recovery percentage
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input											0.28
Level 3 | Other ABS
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	$ 168,736,000								$ 117,661,000
Level 3 | Other ABS | Market approach | Price
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input	100								100
Level 3 | Other ABS | Scenario analysis | Estimated recovery percentage
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input	1
Level 3 | Other ABS | Discounted cash flows | Discount rate/yield | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0.19							0.10
Level 3 | Other ABS | Discounted cash flows | Discount rate/yield | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0.20							0.21
Level 3 | Other ABS | Discounted cash flows | Discount rate/yield | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0.20							0.18
Level 3 | Other ABS | Discounted cash flows | Cumulative loss rate
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0.28
Level 3 | Other ABS | Discounted cash flows | Cumulative loss rate | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input											0.09
Level 3 | Other ABS | Discounted cash flows | Cumulative loss rate | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0.33							0.32
Level 3 | Other ABS | Discounted cash flows | Cumulative loss rate | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0.29							0.25
Level 3 | Other ABS | Discounted cash flows | Duration (years) | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input, term	1 year 4 months 24 days	1 year 1 month 6 days
Level 3 | Other ABS | Discounted cash flows | Duration (years) | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input, term	1 year 10 months 24 days	2 years 2 months 12 days
Level 3 | Other ABS | Discounted cash flows | Duration (years) | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input, term	1 year 9 months 18 days	1 year 8 months 12 days
Level 3 | Other ABS | Discounted cash flows and market approach
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	$ 151,839,000								$ 102,423,000
Level 3 | Loans and other receivables
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	92,546,000								130,101,000
Level 3 | Loans and other receivables | Market approach and scenario analysis
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned									130,101,000
Level 3 | Loans and other receivables | Market approach
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	92,546,000
Level 3 | Loans and other receivables | Market approach | Price | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / Bond					49							82
Level 3 | Loans and other receivables | Market approach | Price | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / Bond					200							157
Level 3 | Loans and other receivables | Market approach | Price | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / Bond					92							127
Level 3 | Loans and other receivables | Scenario analysis | Estimated recovery percentage | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0.07							0.07
Level 3 | Loans and other receivables | Scenario analysis | Estimated recovery percentage | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				1							0.73
Level 3 | Loans and other receivables | Scenario analysis | Estimated recovery percentage | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input				0.68							0.40
Level 3 | Embedded options | Market approach | Basis points upfront | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Derivative liability, measurement input				0.00002							0.00004
Level 3 | Embedded options | Market approach | Basis points upfront | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Derivative liability, measurement input				0.00254							0.00255
Level 3 | Embedded options | Market approach | Basis points upfront | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Derivative liability, measurement input				0.00137							0.00179
Level 3 | Embedded options | Volatility benchmarking | Volatility | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Derivative asset, measurement input											0.60
Level 3 | Embedded options | Volatility benchmarking | Volatility | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Derivative asset, measurement input											0
Level 3 | Investments at fair value
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	138,057,000								130,835,000
Level 3 | Investments at fair value | Market approach
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned	$ 133,912,000								$ 127,237,000
Level 3 | Private equity securities | Market approach | Price
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input						7,760	0.5
Level 3 | Private equity securities | Market approach | Price | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / shares			1							1
Level 3 | Private equity securities | Market approach | Price | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / shares			5,000							6,819
Level 3 | Private equity securities | Market approach | Price | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / shares			360							484
Level 3 | Private equity securities | Market approach | Discount rate/yield
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input | $ / shares			0.28
Level 3 | Private equity securities | Market approach | Discount rate/yield | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input											0.28
Level 3 | Private equity securities | Market approach | Revenue
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input	30,253,269
Level 3 | Private equity securities | Market approach | Revenue | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments owned, measurement input									30,538,979
Level 3 | Loans
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments sold, not yet purchased	$ 1,584,000								$ 1,521,000
Level 3 | Loans | Market approach
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Debt instrument, fair value	1,584,000
Derivative liability									$ 1,521,000
Level 3 | Loans | Market approach | Price
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Financial instruments sold, not yet purchased, measurement input									101
Level 3 | Loans | Market approach | Price | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Debt instrument, measurement input | $ / Bond					115
Level 3 | Loans | Market approach | Price | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Debt instrument, measurement input | $ / Bond					0
Level 3 | Equity options | Volatility benchmarking
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Derivative liability									$ 2,395,000
Level 3 | Equity options | Volatility benchmarking | Volatility | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Derivative liability, measurement input				24.6							0.31
Level 3 | Equity options | Volatility benchmarking | Volatility | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Derivative liability, measurement input				47.9							0.87
Level 3 | Equity options | Volatility benchmarking | Volatility | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Derivative liability, measurement input				34.6							0.42
Level 3 | Other secured financings | Scenario analysis | Estimated recovery percentage | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Other secured financings, measurement input				0.60							0.18
Level 3 | Other secured financings | Scenario analysis | Estimated recovery percentage | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Other secured financings, measurement input				1							0.73
Level 3 | Other secured financings | Scenario analysis | Estimated recovery percentage | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Other secured financings, measurement input				0.93							0.53
Level 3 | Long-term debt | Market approach
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Long-term debt	$ 784,212,000								$ 744,597,000
Level 3 | Long-term debt | Market approach | Price | Minimum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Long-term debt, measurement input					57			64				57	60
Level 3 | Long-term debt | Market approach | Price | Maximum
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Long-term debt, measurement input					103			104				114	103
Level 3 | Long-term debt | Market approach | Price | Weighted Average
Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Line Items]
Long-term debt, measurement input					78			86				78	84