Deep reinforcement learning has recently been successfully applied to a plethora of diverse and difficult sequential decision-making tasks, ranging from the Atari games to robotic motion control. Among the foremost such tasks in quantitative finance is the problem of optimal market making. Market making is the process of simultaneously quoting limit orders on both sides of the limit order book of a security with the goal of repeatedly capturing the quoted spread while minimizing the inventory risk. Most of the existing analytical approaches to market making tend to be predicated on a set of strong, naïve assumptions, whereas current machine learning-based approaches either resort to crudely discretized quotes or fail to incorporate additional predictive signals. In this paper, we present a novel framework for market making with signals based on model-free deep reinforcement learning, addressing these shortcomings. A new state space formulation incorporating outputs from standalone signal generating units, as well as a novel action space and reward function formulation, are introduced. The framework is underpinned by both ideas from adversarial reinforcement learning and neuroevolution. Experimental results on historical data demonstrate the superior reward-to-risk performance of the proposed framework over several standard market making benchmarks. More specifically, the resulting reinforcement learning agent achieves between 20-30% higher terminal wealth than the benchmarks while being exposed to only around 60% of their inventory risks. Finally, an insight into its policy is provided for the sake of interpretability.INDEX TERMS Deep reinforcement learning, genetic algorithms, high-frequency trading, machine learning, market making, stochastic control.

Market making is the process whereby a market participant, called a market maker, simultaneously and repeatedly posts limit orders on both sides of the limit order book of a security in order to both provide liquidity and generate profit. Optimal market making entails dynamic adjustment of bid and ask prices in response to the market maker’s current inventory level and market conditions with the goal of maximizing a risk-adjusted return measure. This problem is naturally framed as a Markov decision process, a discrete-time stochastic (inventory) control process. Reinforcement learning, a class of techniques based on learning from observations and used for solving Markov decision processes, lends itself particularly well to it. Recent years have seen a very strong uptick in the popularity of such techniques in the field, fueled in part by a series of successes of deep reinforcement learning in other domains. The primary goal of this paper is to provide a comprehensive and up-to-date overview of the current state-of-the-art applications of (deep) reinforcement learning focused on optimal market making. The analysis indicated that reinforcement learning techniques provide superior performance in terms of the risk-adjusted return over more standard market making strategies, typically derived from analytical models.

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