Collateralized transactions - Narrative (Details)	9 Months Ended
	Sep. 30, 2023 USD ($) dealer	Dec. 31, 2022 USD ($)
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Bank call loans	$ 56,200,000	$ 0
Market value of securities	57,900,000	9,300,000
Customer securities under customer margin loans that are available to be pledged	1,500,000,000
Re-pledged amounts under securities loans agreements	218,400,000
Customer securities directly with the Options Clearing Corporation to secure obligations and margin requirements under option contracts written by customers	311,300,000
Outstanding letters of credit	0
Amounts pledged	$ 680,891,000	175,724,000
Number of broker-dealers | dealer	4
Receivable from brokers and clearing organizations	$ 100,400,000
Minimum
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Number of business days for related transactions (in days)	1 day
Maximum
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Number of business days for related transactions (in days)	2 days
Corporate equities
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Fair value of securities received as collateral	$ 137,900,000	124,100,000
Corporate equities | Reverse Repurchase Agreements
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Fair value of collateral	5,100,000	28,000,000
Corporate equities | Securities Borrowed Transactions
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Fair value of securities received as collateral, sold and re-pledged under securities loaned	$ 63,500,000	39,400,000
Corporate equities | Repurchase Agreements
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]
Fair value of collateral		$ 28,000,000