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

arXiv: https://arxiv.org/abs/2511.08735 · HTML: https://mlsanity.com/paper/2511.08735/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 21 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Builds on (most cited first, 7 of 7)

- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations](https://mlsanity.com/paper/1706.04702/) (2017)
- [Convergence of the Deep BSDE Method for Coupled FBSDEs](https://mlsanity.com/paper/1811.01165/) (2018)
- [Three algorithms for solving high-dimensional fully-coupled FBSDEs through deep learning](https://mlsanity.com/paper/1907.05327/) (2019)
- [PDGM: a Neural Network Approach to Solve Path-Dependent Partial Differential Equations](https://mlsanity.com/paper/2003.02035/) (2020)
- [Deep Signature FBSDE Algorithm](https://mlsanity.com/paper/2108.10504/) (2021)
- [Numerical Approximations of Coupled Forward-Backward SPDEs](https://mlsanity.com/paper/2012.07879/) (2020)

## Abstract (arXiv)

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.