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Borrowings - Credit Agreement (Details)					1 Months Ended			9 Months Ended
	Feb. 19, 2025 USD ($)	Jun. 21, 2024 USD ($)	Dec. 12, 2023 USD ($)	Jan. 13, 2023 USD ($)	Dec. 31, 2023 USD ($) swap	Jan. 31, 2020 USD ($) swap	Oct. 31, 2019 USD ($)	Sep. 30, 2025 USD ($)	Sep. 23, 2025 USD ($)	Jan. 31, 2025	Dec. 31, 2024 USD ($)	Sep. 30, 2024	Jun. 30, 2024 USD ($)	Jan. 31, 2022	Jan. 13, 2022 USD ($)	Apr. 30, 2021
Debt Instrument [Line Items]
Commitment fee (as a percent)								0.50%
Fixed interest rate percentage (as a percent)												4.30%
Receivables from broker-dealers and clearing organizations								$ 2,633,329,000			$ 1,100,850,000
Total principal of long-term borrowings								2,068,665,000			1,767,265,000
Interest Rate Swap
Debt Instrument [Line Items]
Derivative contract term					2 years		5 years
Derivative, notional amount					$ 1,525,000,000		$ 525,000,000						$ 1,075,000,000
Fixed interest rate percentage (as a percent)														4.50%		4.50%
January 2020 Interest Rate Swap
Debt Instrument [Line Items]
Derivative contract term						5 years
Derivative, notional amount						$ 1,000,000,000
Number of interest rate swaps | swap						2
Fixed interest rate percentage (as a percent)										4.40%				4.60%		4.60%
December 2023 Interest Rate Swap
Debt Instrument [Line Items]
Derivative contract term					2 years
Derivative, notional amount					$ 1,525,000,000
Number of interest rate swaps | swap					2
Fixed interest rate percentage (as a percent)					7.50%
Receivables from broker-dealers and clearing organizations					$ 55,800,000
June 2024 Interest Rate Swap
Debt Instrument [Line Items]
Derivative, notional amount					1,525,000,000			1,075,000,000
Receivables from broker-dealers and clearing organizations					2,000,000
Reclassification from AOCI to other income		$ 5,700,000
Committed facility
Debt Instrument [Line Items]
Total principal of long-term borrowings								$ 50,000,000			$ 0
Committed facility | Scenario 1
Debt Instrument [Line Items]
Interest rate margin (as a percent)								1.00%
Committed facility | Scenario 2
Debt Instrument [Line Items]
Interest rate margin (as a percent)								1.50%
Committed facility | SOFR
Debt Instrument [Line Items]
Interest rate margin (as a percent)								2.50%
Committed facility | SOFR | Scenario 2
Debt Instrument [Line Items]
Interest rate margin (as a percent)								0.00%
Committed facility | VFH
Debt Instrument [Line Items]
Maximum borrowing capacity															$ 250,000,000
Letter of credit | VFH
Debt Instrument [Line Items]
Maximum borrowing capacity															20,000,000
Swingline subfacility | VFH
Debt Instrument [Line Items]
Maximum borrowing capacity															20,000,000
Amended Credit Agreement | Overnight Bank Funding Rate
Debt Instrument [Line Items]
Interest rate margin (as a percent)								0.50%
Amended Credit Agreement | SOFR
Debt Instrument [Line Items]
Interest rate margin (as a percent)								1.00%
Senior Secured Second Lien Notes | Scenario 1
Debt Instrument [Line Items]
Commitment fee stepdown (as a percent)								0.375%
Senior Secured Second Lien Notes | Scenario 2
Debt Instrument [Line Items]
Commitment fee stepdown (as a percent)								0.25%
First Lien Term Loan
Debt Instrument [Line Items]
Debt amortization, percentage of original aggregate principal amount								1.00%
Repayments of term loan			$ 55,000,000	$ 18,000,000
First Lien Term Loan Facility
Debt Instrument [Line Items]
Short-term debt								$ 0
First Lien Term Loan
Debt Instrument [Line Items]
Face amount															$ 1,800,000,000
First Lien Term Loan | First Lien Notes Due 2031
Debt Instrument [Line Items]
Face amount		500,000,000.0
Term Loan | Interest Rate Swap
Debt Instrument [Line Items]
Total principal of long-term borrowings								$ 1,545,000,000
Term Loan | June 2024 Interest Rate Swap
Debt Instrument [Line Items]
Fixed interest rate percentage (as a percent)								7.17%
Term Loan | Scenario 1
Debt Instrument [Line Items]
Interest rate margin (as a percent)								1.50%
Term Loan | Scenario 2
Debt Instrument [Line Items]
Interest rate margin (as a percent)								2.00%
Term Loan | SOFR
Debt Instrument [Line Items]
Interest rate margin (as a percent)								3.00%
Term Loan | SOFR | Scenario 1
Debt Instrument [Line Items]
Interest rate margin (as a percent)								0.50%
Term Loan | VFH | Interest Rate Swap
Debt Instrument [Line Items]
Face amount					$ 1,525,000,000		$ 525,000,000	$ 1,075,000,000
Fixed interest rate percentage (as a percent)								6.92%
Term Loan | VFH | January 2020 Interest Rate Swap | Interest Rate Swap
Debt Instrument [Line Items]
Face amount						$ 1,000,000,000
Line of credit | First Lien Notes Due 2031
Debt Instrument [Line Items]
Face amount		$ 1,245,000,000
Debt instrument, term		3 years
Line of credit | First Lien Notes Due 2031 | Minimum
Debt Instrument [Line Items]
Total principal of long-term borrowings		$ 250,000,000.0
Line of credit | First Lien Notes Due 2031 | Maximum
Debt Instrument [Line Items]
Total principal of long-term borrowings		$ 300,000,000.0
Line of credit | New Term Loans
Debt Instrument [Line Items]
Face amount	$ 1,245,000,000								$ 1,545,000,000
Total principal of long-term borrowings									$ 300,000,000.0
Line of credit | Component one | New Term Loans
Debt Instrument [Line Items]
Interest rate margin (as a percent)	1.50%
Line of credit | Component two | New Term Loans
Debt Instrument [Line Items]
Interest rate margin (as a percent)	2.50%
Line of credit | First Lien Term Loan | Component one | First Lien Notes Due 2031
Debt Instrument [Line Items]
Debt instrument, additional basis spread on variable rate (as a percent)		1.75%
Line of credit | First Lien Term Loan | Component one | New Term Loans
Debt Instrument [Line Items]
Interest rate margin (as a percent)		1.00%
Line of credit | Line of credit | New Term Loans
Debt Instrument [Line Items]
Interest rate margin (as a percent)	0.50%	0.50%
Percentage of periodic payment (as a percent)	1.00%	1.00%
Line of credit | Senior Secured Credit Facility | New Term Loans
Debt Instrument [Line Items]
Interest rate margin (as a percent)	1.00%	1.00%
Line of credit | Senior Secured Credit Facility | Component one | New Term Loans
Debt Instrument [Line Items]
Interest rate margin (as a percent)	1.00%
Line of credit | Secured debt | Component two | New Term Loans
Debt Instrument [Line Items]
Interest rate margin (as a percent)	0.00%	0.00%
Line of credit | Secured debt | SOFR | Component two | First Lien Notes Due 2031
Debt Instrument [Line Items]
Debt instrument, additional basis spread on variable rate (as a percent)		2.75%

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