# Entropy-Regularized Mean-Variance Portfolio Optimization with Jumps

arXiv: https://arxiv.org/abs/2312.13409 · HTML: https://mlsanity.com/paper/2312.13409/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2023.

## Built on by (most cited first, 5 of 5)

- [On the grid-sampling limit SDE](https://mlsanity.com/paper/2410.07778/) (2024)
- [Reinforcement Learning for Jump-Diffusions, with Financial Applications](https://mlsanity.com/paper/2405.16449/) (2024)
- [Robust Reinforcement Learning under Diffusion Models for Data with Jumps](https://mlsanity.com/paper/2411.11697/) (2024)
- [A random measure approach to reinforcement learning in continuous time](https://mlsanity.com/paper/2409.17200/) (2024)
- [An Actor-Critic Framework for Continuous-Time Jump-Diffusion Controls with Normalizing Flows](https://mlsanity.com/paper/2604.05398/) (2026)

## Abstract (arXiv)

Motivated by the trade-off between exploitation and exploration in reinforcement learning, we study a continuous-time entropy-regularized mean variance portfolio selection problem in the presence of jumps. We propose an exploratory SDE for the wealth process associated with multiple risky assets which exhibit L'evy jumps. In contrast to the existing literature, we study the limiting behavior of the natural discrete-time formulation of the wealth process associated to a randomized control in order to derive the continuous-time dynamics. We then show that an optimal distributional control of the continuous-time entropy-regularized exploratory mean-variance problem is Gaussian. The respective optimal wealth process solves a linear SDE whose representation is explicitly obtained.