Deep reinforcement learning in non-Markov market-making

We develop a deep reinforcement learning (RL) framework for an optimal market-making (MM) trading problem, specifically focusing on price processes with semi-Markov and Hawkes Jump-Diffusion dynamics. We begin by discussing the basics of RL and the deep RL framework used; we deployed the state-of-the-art Soft Actor–Critic (SAC) algorithm for the deep learning part. The SAC algorithm is an off-policy entropy maximization algorithm more suitable for tackling complex, high-dimensional problems with continuous state and action spaces, like those in optimal market-making (MM). We introduce the optimal MM problem considered, where we detail all the deterministic and stochastic processes that go into setting up an environment to simulate this strategy. Here, we also provide an in-depth overview of the jump-diffusion pricing dynamics used and our method for dealing with adverse selection within the limit order book, and we highlight the working parts of our optimization problem. Next, we discuss the training and testing results, where we provide visuals of how important deterministic and stochastic processes such as the bid/ask prices, trade executions, inventory, and the reward function evolved. Our study includes an analysis of simulated and real data. We include a discussion on the limitations of these results, which are important points for most diffusion style models in this setting.