Reinforcement Learning for Jump‐Diffusions, With Financial Applications

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., 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, originally developed for controlled diffusions, without needing to check a priori whether the underlying data come from a pure diffusion or a jump‐diffusion. 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.