# Logarithmic regret in the ergodic Avellaneda-Stoikov market making model

arXiv: https://arxiv.org/abs/2409.02025 · HTML: https://mlsanity.com/paper/2409.02025/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2024.

## Built on by (most cited first, 2 of 2)

- [Learning Market Making with Closing Auctions](https://mlsanity.com/paper/2601.17247/) (2026)
- [Reinforcement Learning with Hawkes-Structured Networks for Market Making](https://mlsanity.com/paper/2610.16524/) (2026)

## Abstract (arXiv)

We analyse the regret arising from learning the price sensitivity parameter kappa of liquidity takers in the ergodic version of the Avellaneda-Stoikov market making model. We show that a learning algorithm based on a maximum-likelihood estimator for the parameter achieves the regret upper bound of order ln2 T in expectation. To obtain the result we need two key ingredients. The first is the twice differentiability of the ergodic constant under the misspecified parameter in the Hamilton-Jacobi-Bellman (HJB) equation with respect to kappa, which leads to a second--order performance gap. The second is the learning rate of the regularised maximum-likelihood estimator which is obtained from concentration inequalities for Bernoulli signals. Numerical experiments confirm the convergence and the robustness of the proposed algorithm.