Fair value measurements - Schedule of Assets and Liabilities Measured at Fair Value on Recurring Basis (Details) - USD ($) $ in Thousands	Jun. 30, 2024	Dec. 31, 2023
ASSETS
Deposits with clearing organizations	$ 34,967	$ 34,789
Securities owned:
Securities owned, at fair value	1,043,256	795,312
Investments	18,656	18,785
Loans	689
Securities purchased under agreements to resell	4,079	5,842
Derivative contracts:
Derivative contracts, total	29	13
Total	1,097,597	854,741
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	177,251	31,676
Derivative contracts:
Derivative contracts, total	1,456	737
Total	178,707	32,413
U.S. Treasury securities
Securities owned:
Securities owned, at fair value	859,623	695,346
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	138,059	14,603
U.S. Agency securities
Securities owned:
Securities owned, at fair value	5,755	2
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	2
Sovereign obligations
Securities owned:
Securities owned, at fair value	424
Corporate debt and other obligations
Securities owned:
Securities owned, at fair value	18,104	5,769
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	7,279	1,508
Mortgage and other asset-backed securities
Securities owned:
Securities owned, at fair value	7,117	6,627
Municipal obligations
Securities owned:
Securities owned, at fair value	88,373	35,333
Convertible bonds
Securities owned:
Securities owned, at fair value	25,272	16,735
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	13,450	2,136
Corporate equities
Securities owned:
Securities owned, at fair value	29,622	27,170
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	18,461	13,427
Money markets
Securities owned:
Securities owned, at fair value	6,253	5,617
Auction rate securities
Securities owned:
Securities owned, at fair value	2,713	2,713
Futures
Derivative contracts:
Derivative contracts, total		2
Derivative contracts:
Derivative contracts, total	1,423	735
TBAs
Derivative contracts:
Derivative contracts, total	29	11
Derivative contracts:
Derivative contracts, total	33	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	34,967	34,789
Securities owned:
Securities owned, at fair value	894,995	727,916
Investments	1,369	1,872
Loans	0
Securities purchased under agreements to resell		0
Derivative contracts:
Derivative contracts, total	0	2
Total	931,331	764,579
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	156,520	28,030
Derivative contracts:
Derivative contracts, total	1,423	735
Total	157,943	28,765
Level 1 | U.S. Treasury securities
Securities owned:
Securities owned, at fair value	859,623	695,346
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	138,059	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	29,622	27,170
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	18,461	13,427
Level 1 | Money markets
Securities owned:
Securities owned, at fair value	5,750	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	1,423	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	145,548	64,683
Investments	17,287	16,913
Loans	689
Securities purchased under agreements to resell		5,842
Derivative contracts:
Derivative contracts, total	29	11
Total	163,553	87,449
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	20,731	3,646
Derivative contracts:
Derivative contracts, total	33	2
Total	20,764	3,648
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	5,755	2
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	2
Level 2 | Sovereign obligations
Securities owned:
Securities owned, at fair value	424
Level 2 | Corporate debt and other obligations
Securities owned:
Securities owned, at fair value	18,104	5,769
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	7,279	1,508
Level 2 | Mortgage and other asset-backed securities
Securities owned:
Securities owned, at fair value	7,117	6,627
Level 2 | Municipal obligations
Securities owned:
Securities owned, at fair value	88,373	35,333
Level 2 | Convertible bonds
Securities owned:
Securities owned, at fair value	25,272	16,735
Securities sold but not yet purchased:
Securities sold but not yet purchased, at fair value	13,450	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	503	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	29	11
Derivative contracts:
Derivative contracts, total	33	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	2,713	2,713
Investments	0	0
Loans	0
Securities purchased under agreements to resell		0
Derivative contracts:
Derivative contracts, total	0	0
Total	2,713	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 | 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	2,713	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