A Reinforcement Learning-Based Method for Solving High-Dimensional Integro-Differential Equations

Explore a reinforcement learning framework for solving high-dimensional partial integro-differential equations that commonly arise in finance and real-world applications. Learn how this innovative deep learning approach overcomes the curse of dimensionality that plagues traditional finite difference and finite element methods. Discover the construction of Levy processes and corresponding reinforcement learning models that utilize deep neural networks to represent both solutions and non-local terms of complex equations. Understand the training methodology using temporal difference error, termination conditions, and non-local term properties as loss functions. Examine the computational advantages, robustness, and rigorous error estimates that validate this method's effectiveness across problems with varying forms and intensities of jumps. Gain insights into practical extensions of this approach to stochastic controls and multi-agent relative investment games, demonstrating its versatility in addressing challenging mathematical problems in finance and beyond.