A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications

Hasib Uddin Molla, Matthew Backhouse, Ankit Banarjee and Jinniao Qiu

Papers from arXiv.org

Abstract: 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.

Date: 2025-11, Revised 2025-11
New Economics Papers: this item is included in nep-upt
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