A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications
This work addresses complex stochastic control problems in finance, such as utility maximization under rough volatility, but appears incremental as it extends existing deep learning methods to a more general FBSDE setting.
The authors tackled the problem of solving fully coupled forward-backward stochastic differential equations (FBSDEs) in a non-Markovian framework using deep learning methods, achieving numerical solutions with provided error estimates and convergence results. They demonstrated practical applicability by solving utility maximization problems under rough volatility.
In this work, we extend deep learning-based numerical methods to fully coupled forward-backward stochastic differential equations (FBSDEs) within a non-Markovian framework. Error estimates and convergence are provided. In contrast to the existing literature, our approach not only analyzes the non-Markovian framework but also addresses fully coupled settings, in which both the drift and diffusion coefficients of the forward process may be random and depend on the backward components $Y$ and $Z$. Furthermore, we illustrate the practical applicability of our framework by addressing utility maximization problems under rough volatility, which are solved numerically with the proposed deep learning-based methods.