Fair value measurements - Assets and Liabilities Measured at Fair Value on Recurring Basis (Details) - USD ($) $ in Thousands	Dec. 31, 2023	Dec. 31, 2022
ASSETS
Deposits with clearing organizations	$ 34,789	$ 24,937
Securities owned
Securities owned, at fair value	795,312	498,594
Investments	18,785	7,068
Securities purchased under agreements to resell	5,842	0
Derivative contracts:
Derivative contracts, total	13
Total	854,741	532,361
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	31,676	52,768
Derivative contracts:
Derivative contracts	737	1,805
Total	32,413	54,573
U.S. Treasury securities
Securities owned
Securities owned, at fair value	695,346	362,815
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	14,603	25,006
U.S. Agency securities
Securities owned
Securities owned, at fair value	2	6,012
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value		3
Sovereign obligations
Securities owned
Securities owned, at fair value		9,502
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value		9,048
Corporate debt and other obligations
Securities owned
Securities owned, at fair value	5,769	9,844
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	1,508	2,905
Mortgage and other asset-backed securities
Securities owned
Securities owned, at fair value	6,627	1,882
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value		2
Municipal obligations
Securities owned
Securities owned, at fair value	35,333	30,126
Convertible bonds
Securities owned
Securities owned, at fair value	16,735	21,800
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	2,136	4,428
Corporate equities
Securities owned
Securities owned, at fair value	27,170	24,837
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	13,427	11,378
Money markets
Securities owned
Securities owned, at fair value	5,617
Auction rate securities
Securities owned
Securities owned, at fair value	2,713	31,776
Futures
Derivative contracts:
Derivative contracts, total	2
Derivative contracts:
Derivative contracts	735	44
TBAs
Derivative contracts:
Derivative contracts, total	11	1,762
Derivative contracts:
Derivative contracts	2	1,761
Level 1
ASSETS
Deposits with clearing organizations	34,789	24,937
Securities owned
Securities owned, at fair value	727,916	387,652
Investments	1,872	0
Securities purchased under agreements to resell	0
Derivative contracts:
Derivative contracts, total	2
Total	764,579	412,589
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	28,030	36,384
Derivative contracts:
Derivative contracts	735	44
Total	28,765	36,428
Level 1 | U.S. Treasury securities
Securities owned
Securities owned, at fair value	695,346	362,815
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	14,603	25,006
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
Securities sold, but not yet purchased
Securities sold but not yet purchased, 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
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value		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	27,170	24,837
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	13,427	11,378
Level 1 | Money markets
Securities owned
Securities owned, at fair value	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	735	44
Level 1 | TBAs
Derivative contracts:
Derivative contracts, total	0	0
Derivative contracts:
Derivative contracts	0	0
Level 2
ASSETS
Deposits with clearing organizations	0	0
Securities owned
Securities owned, at fair value	64,683	79,166
Investments	16,913	7,068
Securities purchased under agreements to resell	5,842
Derivative contracts:
Derivative contracts, total	11
Total	87,449	87,996
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	3,646	16,384
Derivative contracts:
Derivative contracts	2	1,761
Total	3,648	18,145
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	2	6,012
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value		3
Level 2 | Sovereign obligations
Securities owned
Securities owned, at fair value		9,502
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value		9,048
Level 2 | Corporate debt and other obligations
Securities owned
Securities owned, at fair value	5,769	9,844
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	1,508	2,905
Level 2 | Mortgage and other asset-backed securities
Securities owned
Securities owned, at fair value	6,627	1,882
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value		2
Level 2 | Municipal obligations
Securities owned
Securities owned, at fair value	35,333	30,126
Level 2 | Convertible bonds
Securities owned
Securities owned, at fair value	16,735	21,800
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	2,136	4,428
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	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	0	0
Level 2 | TBAs
Derivative contracts:
Derivative contracts, total	11	1,762
Derivative contracts:
Derivative contracts	2	1,761
Level 3
ASSETS
Deposits with clearing organizations	0	0
Securities owned
Securities owned, at fair value	2,713	31,776
Investments	0	0
Securities purchased under agreements to resell	0
Derivative contracts:
Derivative contracts, total	0
Total	2,713	31,776
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value	0	0
Derivative contracts:
Derivative contracts	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
Securities sold, but not yet purchased
Securities sold but not yet purchased, 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
Securities sold, but not yet purchased
Securities sold but not yet purchased, at fair value		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
Level 3 | Auction rate securities
Securities owned
Securities owned, at fair value	2,713	31,776
Level 3 | Futures
Derivative contracts:
Derivative contracts, total	0
Derivative contracts:
Derivative contracts	0	0
Level 3 | TBAs
Derivative contracts:
Derivative contracts, total	0	0
Derivative contracts:
Derivative contracts	$ 0	$ 0