Ph.D Thesis Defense: "Market Making in a Limit Order Book: Classical optimal control and Reinforcement Learning Approaches"

Abstract: In this thesis, we discuss two approaches to solve the high-frequency market making problem, which is one of crucial problems in algorithmic trading, with a conventional model-based method and a more modern model-free reinforcement learning (RL) technique.

We first solve a stochastic control problem with an end-of-day inventory liquidation cost. We extend the existing literature on market making modeling by allowing random demand and the possibility of simultaneous arrivals of buy and sell market orders. We also incorporate an innovative general forecast of future price changes in the pricing policy. A substantially improved performance of our model is validated based on a first-of-its kind empirical study. 

Secondly, we adopt model-free RL algorithms to solve the problem of high-frequency market making and manage to control the terminal inventory level by suitably incorporating the end-of-day inventory liquidation cost in the sequence of immediate rewards. We also conduct an insightful scrutiny on the influence of immediate rewards and state variables.

We finally propose two constrained linear demand models to take into account the upper and lower bound of the market demand. Two alternative sub-optimal solutions are derived and compared with policies obtained using RL methods, which reveal competitive performances.

Host: Jose Figueroa-Lopez