Reinforcement Learning for Jump-Diffusions, with Financial Applications

TL;DR

This paper extends continuous-time reinforcement learning to jump-diffusion processes, demonstrating that existing algorithms can be applied without modification, and explores financial applications like portfolio optimization and option hedging.

Contribution

It generalizes RL algorithms to jump-diffusions, showing their invariance and applicability to complex financial models with jumps.

Findings

RL algorithms for diffusions apply to jump-diffusions without modification.

Jump presence influences actor-critic parameterizations but not the algorithms themselves.

Application to financial models confirms the invariance and effectiveness of the approach.

Abstract

We study continuous-time reinforcement learning (RL) for stochastic control in which system dynamics are governed by jump-diffusion processes. We formulate an entropy-regularized exploratory control problem with stochastic policies to capture the exploration--exploitation balance essential for RL. Unlike the pure diffusion case initially studied by Wang et al. (2020), the derivation of the exploratory dynamics under jump-diffusions calls for a careful formulation of the jump part. Through a theoretical analysis, we find that one can simply use the same policy evaluation and $q$-learning algorithms in Jia and Zhou (2022a, 2023), originally developed for controlled diffusions, without needing to check a priori whether the underlying data come from a pure diffusion or a jump-diffusion. However, we show that the presence of jumps ought to affect parameterizations of actors and critics in general. We investigate as an application the mean--variance portfolio selection problem with stock price modelled as a jump-diffusion, and show that both RL algorithms and parameterizations are invariant with respect to jumps. Finally, we present a detailed study on applying the general theory to option hedging.