How HJB Market-Making Models Inform Practice

Summary

The document discusses whether stochastic-control models built around the Hamilton–Jacobi–Bellman equation have practical value in market making and algorithmic trading. It describes their role as research and teaching tools for reasoning about quote widths, volatility, inventory risk, and portfolio allocation. These models can help establish intuition about how a market maker might adjust quotes as conditions change.

The response distinguishes that conceptual value from direct use in live trading. It says the models are generally not deployed in their simplified academic form, because production trading must also account for signals, latency, market impact, and other fine-grained effects. This is a practitioner’s qualitative perspective rather than empirical evidence about industry adoption, and it does not specify a model, calibration procedure, or measured performance. The main lesson is to treat HJB formulations as useful starting points for intuition, while recognizing that implementation requires substantial additional work.

Key ideas

• HJB models can formalize how volatility and inventory risk affect market-making quotes.
• They provide a useful starting point for research, teaching, and building trading intuition.
• The response says simplified versions are generally not used directly in live trading.
• Practical systems must also account for signals, latency, and market impact.
• The assessment is qualitative and provides no adoption data or performance results.

Tags

# Is stochastic control with the HJB equation used in market making/algo trading at institutions?


# Is stochastic control with the HJB equation used in market making/algo trading at institutions?












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?

## Answer by ltrd (score 2, accepted)

https://quant.stackexchange.com/a/77848

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

- Research purpose

- 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.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.