Deep Learning for Continuous-time Stochastic Control with Jumps
ArXiv ID: 2505.15602 “View on arXiv”
Authors: Patrick Cheridito, Jean-Loup Dupret, Donatien Hainaut
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.
Keywords: Stochastic Control, Hamilton-Jacobi-Bellman (HJB), Deep Reinforcement Learning, Value Function Approximation, Jumps, Derivatives
Complexity vs Empirical Score
- Math Complexity: 9.2/10
- Empirical Rigor: 6.5/10
- Quadrant: Holy Grail
- Why: The paper employs dense advanced mathematics including stochastic calculus, Hamilton-Jacobi-Bellman PIDEs, and continuous-time dynamic programming, while also demonstrating empirical rigor with specific algorithms (GPI-PINN/CBU), code availability, and comparative backtests against established methods.
flowchart TD
A["Research Goal: Solve continuous-time stochastic control with jumps"] --> B["Method: Model-based deep learning<br/>Continuous-time dynamic programming"]
B --> C["Data/Inputs: Problem parameters<br/>(dynamics, horizon, cost functions)"]
C --> D["Computational Process:<br/>Iterative training of two NNs"]
D --> E["NN1: Policy Network<br/>Optimal control approximation"]
D --> F["NN2: Value Network<br/>Value function approximation"]
D --> G["Training: HJB equation<br/>based objectives"]
E & F & G --> H["Outcomes:<br/>Accurate & scalable solution<br/>for high-dimensional problems"]