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

Hasib Uddin Molla; Matthew Backhouse; Ankit Banarjee; Jinniao Qiu

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arXiv · 2511.08735

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

Hasib Uddin Molla·Matthew Backhouse·Ankit Banarjee·Jinniao Qiu

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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.

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Hasib Uddin Molla, Matthew Backhouse, Ankit Banarjee, Jinniao Qiu. 2025-11-11. A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications. https://arxiv.org/abs/2511.08735

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