Deep Reinforcement Learning for Optimal Stopping with Application in Financial Engineering

Abderrahim Fathan, Erick Delage

Keywords: Reinforcement learning, deep learning, financial engineering, optimal stopping.

Abstract: Optimal stopping is the problem of deciding the right time at which to take a particular action in a stochastic system, in order to maximize an expected reward. It has many applications in areas such as finance, healthcare, and statistics. In this paper, we employ deep Reinforcement Learning (RL) to learn optimal stopping policies in two financial engineering applications: namely option pricing, and optimal option exercise. We present for the first time a comprehensive empirical evaluation of the quality of optimal stopping policies identified by three state of the art deep RL algorithms: double deep Q-learning (DDQN), categorical distributional RL (C51), and Implicit Quantile Networks (IQN). In the case of option pricing, our findings indicate that in a theoretical Black-Schole environment, IQN successfully identifies nearly optimal prices. On the other hand, it is slightly outperformed by C51 when confronted to real stock data movements in a put option exercise problem that involves assets from the S&P500 index. More importantly, the C51 algorithm is able to identify an optimal stopping policy that achieves 8% more out-of-sample returns than the best of four natural benchmark policies. We conclude with a discussion of our findings which should pave the way for relevant future research.

One-sentence Summary: We present the first comprehensive empirical evaluation of optimal stopping policies identified by deep RL algorithms in financial engineering, with evidence that distributional RL is the best approach for tackling real stock market data.

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