# Reinforcement Learning for Jump-Diffusions, with Financial Applications

arXiv: https://arxiv.org/abs/2405.16449 · HTML: https://mlsanity.com/paper/2405.16449/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Adversarial robustness and RL in finance, one of 15 directions in Deep reinforcement learning methods.
- Builds on 11 of its 51 references that are in the map.
- First posted on arXiv 26 May 2024.

## Placed in

- Deep reinforcement learning methods / [Adversarial robustness and RL in finance](https://mlsanity.com/deeprl/adversarial-robustness-and-rl-in-finance/)

## Builds on (most cited first, 11 of 11)

- [Policy Gradient and Actor-Critic Learning in Continuous Time and Space: Theory and Algorithms](https://mlsanity.com/paper/2111.11232/) (2021)
- [q-Learning in Continuous Time](https://mlsanity.com/paper/2207.00713/) (2022)
- [Policy Evaluation and Temporal-Difference Learning in Continuous Time and Space: A Martingale Approach](https://mlsanity.com/paper/2108.06655/) (2021)
- [Making Deep Q-learning methods robust to time discretization](https://mlsanity.com/paper/1901.09732/) (2019)
- [Entropy Regularization for Mean Field Games with Learning](https://mlsanity.com/paper/2010.00145/) (2020)
- [Reinforcement learning for linear-convex models with jumps via stability analysis of feedback controls](https://mlsanity.com/paper/2104.09311/) (2021)
- [Time Discretization-Invariant Safe Action Repetition for Policy Gradient Methods](https://mlsanity.com/paper/2111.03941/) (2021)
- [State-Dependent Temperature Control for Langevin Diffusions](https://mlsanity.com/paper/2011.07456/) (2020)
- [Regularity and stability of feedback relaxed controls](https://mlsanity.com/paper/2001.03148/) (2020)
- [Control randomisation approach for policy gradient and application to reinforcement learning in optimal switching](https://mlsanity.com/paper/2404.17939/) (2024)
- [Entropy-Regularized Mean-Variance Portfolio Optimization with Jumps](https://mlsanity.com/paper/2312.13409/) (2023)

## Built on by (most cited first, 2 of 2)

- [Reinforcement Learning for Intensity Control: An Application to Choice-Based Network Revenue Management](https://mlsanity.com/paper/2406.05358/) (2024)
- [Exploratory Mean-Variance with Jumps: An Equilibrium Approach](https://mlsanity.com/paper/2512.09224/) (2025)

## Abstract (arXiv)

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.