Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.08735 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918215970455552 |
|---|---|
| author | Molla, Hasib Uddin Backhouse, Matthew Banarjee, Ankit Qiu, Jinniao |
| author_facet | Molla, Hasib Uddin Backhouse, Matthew Banarjee, Ankit Qiu, Jinniao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications Molla, Hasib Uddin Backhouse, Matthew Banarjee, Ankit Qiu, Jinniao Mathematical Finance Machine Learning 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. |
| title | A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications |
| topic | Mathematical Finance Machine Learning |
| url | https://arxiv.org/abs/2511.08735 |