In chapter 5 of https://www.maths.ed.ac.uk/~dsiska/LecNotesSCDAA.pdf, they use stochastic control and the Hamiltonian Jacobi Bellman (HJB) equation in attempt to measure bid-ask spreads and optimal portfolio allocation.

Is there any practical relevance that is used in industry, or is it another case of finance academia out of touch?


1 Answer 1


I would say that there are two things that we can talk about:

  1. Research purpose
  2. Real Trading

Those models are a good thing to start when you try to build something that has to have characteristics of market-making -> widen quotes if volatility spikes, asymmetry in quotes when you have inventory risk etc. All of these things that you should know and you have to have some intuition about are in those models.

In terms of real trading, these models are not used in this particular form. HFT and market-making are all about nuances and we can start with this kind of model but we have to work simultaneously on signals, latency, market impacts etc. A lot of things to consider that are not strictly in those models.

So, in my case, those models are a good thing to show for interns and to "play" with it and gain intuition. In real trading, a lot more work is done in latency, signals and other things.

  • $\begingroup$ Do you know any project ideas for market-making that could use the HJB equation and optimal control? I’ve scoured the internet for inspiration but have come up empty handed. My only ideas are limited by not having second by second tick data $\endgroup$ Dec 30, 2023 at 10:13

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