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

• URL: http://arxiv.org/abs/2511.08735v1
• Date: Thu, 13 Nov 2025 01:04:46 GMT
• Title: A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications
• Authors: Hasib Uddin Molla, Ankit Banarjee, Matthew Backhouse, Jinniao Qiu,
• Abstract summary: In this work, we extend deep learning-based numerical methods to fully coupled forward-backward differential equations.<n>In contrast to the existing literature, our approach not only analyzes the non-Markovian framework but also addresses fully coupled coefficients.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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