Fair value measurements - Schedule of Assets and Liabilities Measured at Fair Value on Recurring Basis (Details) - USD ($) $ in Thousands	Sep. 30, 2024	Dec. 31, 2023
ASSETS
Deposits with clearing organizations	$ 35,480	$ 34,789
Securities owned:
Securities owned, at fair value	1,067,452	795,312
Investments	18,880	18,785
Trade claim	1,257
Loans	677
Securities purchased under agreements to resell	0	5,842
Derivative contracts:
Derivative contracts, total	38	13
Total	1,123,784	854,741
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	203,663	31,676
Derivative contracts:
Derivative contracts, total	4,978	737
Total	208,641	32,413
Sovereign obligations
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	1,678
U.S. Treasury securities
Securities owned:
Securities owned, at fair value	940,816	695,346
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	166,160	14,603
U.S. Agency securities
Securities owned:
Securities owned, at fair value	4,602	2
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	1
Sovereign obligations
Securities owned:
Securities owned, at fair value	5,390
Corporate debt and other obligations
Securities owned:
Securities owned, at fair value	15,040	5,769
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	5,406	1,508
Mortgage and other asset-backed securities
Securities owned:
Securities owned, at fair value	2,204	6,627
Municipal obligations
Securities owned:
Securities owned, at fair value	37,592	35,333
Convertible bonds
Securities owned:
Securities owned, at fair value	22,907	16,735
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	15,767	2,136
Corporate equities
Securities owned:
Securities owned, at fair value	29,375	27,170
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	14,651	13,427
Money markets
Securities owned:
Securities owned, at fair value	6,845	5,617
Auction rate securities
Securities owned:
Securities owned, at fair value	2,681	2,713
Futures
Derivative contracts:
Derivative contracts, total		2
Derivative contracts:
Derivative contracts, total	4,936	735
TBAs
Derivative contracts:
Derivative contracts, total	38	11
Derivative contracts:
Derivative contracts, total	42	2
Mortgage and other asset-backed securities
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value		2
Level 1
ASSETS
Deposits with clearing organizations	35,480	34,789
Securities owned:
Securities owned, at fair value	975,985	727,916
Investments	1,244	1,872
Trade claim	0
Loans	0
Securities purchased under agreements to resell		0
Derivative contracts:
Derivative contracts, total	0	2
Total	1,012,709	764,579
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	180,811	28,030
Derivative contracts:
Derivative contracts, total	4,936	735
Total	185,747	28,765
Level 1 | Sovereign obligations
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0
Level 1 | U.S. Treasury securities
Securities owned:
Securities owned, at fair value	940,816	695,346
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	166,160	14,603
Level 1 | U.S. Agency securities
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0
Level 1 | Sovereign obligations
Securities owned:
Securities owned, at fair value	0
Level 1 | Corporate debt and other obligations
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 1 | Mortgage and other asset-backed securities
Securities owned:
Securities owned, at fair value	0	0
Level 1 | Municipal obligations
Securities owned:
Securities owned, at fair value	0	0
Level 1 | Convertible bonds
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 1 | Corporate equities
Securities owned:
Securities owned, at fair value	29,375	27,170
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	14,651	13,427
Level 1 | Money markets
Securities owned:
Securities owned, at fair value	5,794	5,400
Level 1 | Auction rate securities
Securities owned:
Securities owned, at fair value	0	0
Level 1 | Futures
Derivative contracts:
Derivative contracts, total		2
Derivative contracts:
Derivative contracts, total	4,936	735
Level 1 | TBAs
Derivative contracts:
Derivative contracts, total	0	0
Derivative contracts:
Derivative contracts, total	0	0
Level 1 | Mortgage and other asset-backed securities
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value		0
Level 2
ASSETS
Deposits with clearing organizations	0	0
Securities owned:
Securities owned, at fair value	88,786	64,683
Investments	17,636	16,913
Trade claim	1,257
Loans	677
Securities purchased under agreements to resell		5,842
Derivative contracts:
Derivative contracts, total	38	11
Total	108,394	87,449
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	22,852	3,646
Derivative contracts:
Derivative contracts, total	42	2
Total	22,894	3,648
Level 2 | Sovereign obligations
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	1,678
Level 2 | U.S. Treasury securities
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 2 | U.S. Agency securities
Securities owned:
Securities owned, at fair value	4,602	2
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	1
Level 2 | Sovereign obligations
Securities owned:
Securities owned, at fair value	5,390
Level 2 | Corporate debt and other obligations
Securities owned:
Securities owned, at fair value	15,040	5,769
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	5,406	1,508
Level 2 | Mortgage and other asset-backed securities
Securities owned:
Securities owned, at fair value	2,204	6,627
Level 2 | Municipal obligations
Securities owned:
Securities owned, at fair value	37,592	35,333
Level 2 | Convertible bonds
Securities owned:
Securities owned, at fair value	22,907	16,735
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	15,767	2,136
Level 2 | Corporate equities
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 2 | Money markets
Securities owned:
Securities owned, at fair value	1,051	217
Level 2 | Auction rate securities
Securities owned:
Securities owned, at fair value	0	0
Level 2 | Futures
Derivative contracts:
Derivative contracts, total		0
Derivative contracts:
Derivative contracts, total	0	0
Level 2 | TBAs
Derivative contracts:
Derivative contracts, total	38	11
Derivative contracts:
Derivative contracts, total	42	2
Level 2 | Mortgage and other asset-backed securities
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value		2
Level 3
ASSETS
Deposits with clearing organizations	0	0
Securities owned:
Securities owned, at fair value	2,681	2,713
Investments	0	0
Trade claim	0
Loans	0
Securities purchased under agreements to resell		0
Derivative contracts:
Derivative contracts, total	0	0
Total	2,681	2,713
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Derivative contracts:
Derivative contracts, total	0	0
Total	0	0
Level 3 | Sovereign obligations
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0
Level 3 | U.S. Treasury securities
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 3 | U.S. Agency securities
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0
Level 3 | Sovereign obligations
Securities owned:
Securities owned, at fair value	0
Level 3 | Corporate debt and other obligations
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 3 | Mortgage and other asset-backed securities
Securities owned:
Securities owned, at fair value	0	0
Level 3 | Municipal obligations
Securities owned:
Securities owned, at fair value	0	0
Level 3 | Convertible bonds
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 3 | Corporate equities
Securities owned:
Securities owned, at fair value	0	0
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	0	0
Level 3 | Money markets
Securities owned:
Securities owned, at fair value	0	0
Level 3 | Auction rate securities
Securities owned:
Securities owned, at fair value	2,681	2,713
Level 3 | Futures
Derivative contracts:
Derivative contracts, total		0
Derivative contracts:
Derivative contracts, total	0	0
Level 3 | TBAs
Derivative contracts:
Derivative contracts, total	0	0
Derivative contracts:
Derivative contracts, total	$ 0	0
Level 3 | Mortgage and other asset-backed securities
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value		$ 0