An Impulse Control Approach to Market Making in a Hawkes LOB Market

TL;DR

This paper develops a novel impulse control framework for market making in a Hawkes process-based limit order book, integrating deep reinforcement learning to handle complex, high-dimensional control problems with promising empirical results.

Contribution

It introduces a new impulse control model for market making in Hawkes process markets and proposes a deep RL approach to approximate solutions, addressing computational challenges.

Findings

RL agent achieves Sharpe ratios above 30 in simulations

Deep learning methods effectively approximate complex HJB-QVI solutions

Impulse control combined with RL outperforms traditional models

Abstract

We study the optimal Market Making problem in a Limit Order Book (LOB) market simulated using a high-fidelity, mutually exciting Hawkes process. Departing from traditional Brownian-driven mid-price models, our setup captures key microstructural properties such as queue dynamics, inter-arrival clustering, and endogenous price impact. Recognizing the realistic constraint that market makers cannot update strategies at every LOB event, we formulate the control problem within an impulse control framework, where interventions occur discretely via limit, cancel, or market orders. This leads to a high-dimensional, non-local Hamilton-Jacobi-Bellman Quasi-Variational Inequality (HJB-QVI), whose solution is analytically intractable and computationally expensive due to the curse of dimensionality. To address this, we propose a novel Reinforcement Learning (RL) approximation inspired by auxiliary control formulations. Using a two-network PPO-based architecture with self-imitation learning, we demonstrate strong empirical performance with limited training, achieving Sharpe ratios above 30 in a realistic simulated LOB. In addition to that, we solve the HJB-QVI using a deep learning method inspired by Sirignano and Spiliopoulos 2018 and compare the performance with the RL agent. Our findings highlight the promise of combining impulse control theory with modern deep RL to tackle optimal execution problems in jump-driven microstructural markets.