Deep Learning for Continuous-Time Stochastic Control with Jumps

TL;DR

This paper presents a novel deep learning method for solving finite-horizon continuous-time stochastic control problems with jumps, using neural networks trained via dynamic programming principles to handle complex stochastic dynamics.

Contribution

It introduces a model-based deep learning framework that employs neural networks to approximate optimal policies and value functions in jump-diffusion control problems.

Findings

Accurate approximation of optimal policies and value functions.

Scalable to high-dimensional stochastic control tasks.

Effective in complex jump-diffusion scenarios.

Abstract

In this paper, we introduce a model-based deep-learning approach to solve finite-horizon continuous-time stochastic control problems with jumps. We iteratively train two neural networks: one to represent the optimal policy and the other to approximate the value function. Leveraging a continuous-time version of the dynamic programming principle, we derive two different training objectives based on the Hamilton-Jacobi-Bellman equation, ensuring that the networks capture the underlying stochastic dynamics. Empirical evaluations on different problems illustrate the accuracy and scalability of our approach, demonstrating its effectiveness in solving complex high-dimensional stochastic control tasks.