Market-Making P&L Models and Stochastic Control Methods

Summary

The document points to three research approaches for modeling a market maker’s profit and loss, as extensions beyond the earlier Ho-Stoll treatment. They differ in the utility assumptions and level of solution: one presents a model with an approximate solution, another solves the case of linear utility, and a third offers a general solution for a broad class of utility functions.

The discussion gives no equations, empirical results, or comparison of model performance. Instead, it serves as a reading guide and notes the mathematical background needed to follow the papers: stochastic differential equations with jumps and stochastic control, particularly Hamilton-Jacobi-Bellman methods for jump processes. The stated preference for the most general approach is a personal view rather than evidence that it performs better in practice. The document does not explain implementation, market assumptions, or how any of the models account for real trading costs and changing market conditions.

Key ideas

• Market-making research models profit and loss using stochastic processes and control methods.
• The cited approaches vary in how broadly they handle utility functions and how completely they solve the model.
• One approach uses an approximate solution, while another treats linear utility.
• Studying these methods requires familiarity with jump processes and Hamilton-Jacobi-Bellman control equations.
• The discussion offers a reading path rather than empirical evidence or practical performance comparisons.

Tags

# academic papers about market making


# academic papers about market making












I am looking for academic articles which model the p&L of market makers. I have read the Ho-Stoll (1984) article. Is there any recent article on this subject?

## Answer by lehalle (score 26, accepted)

https://quant.stackexchange.com/a/8898

In fact you have three papers available to go further:

- The Avellaneda-Stoikov one, with proper model and an approximate solution

- The Bayraktar-Ludkovski one, with a solution for the linear utility function

- The L-Guéant-Fernandez one, with a full solution for a generic utility function

I prefer the last one ;{)}

To read them, you need to know Stochastic Differential Equations (with jumps) and Stochastic Control (especially Hamilton-Jacobi-Bellman expressions of Stochastic Control with jumps).

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