{"ID":2843614,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.08735","arxiv_id":"2511.08735","title":"A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications","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.","short_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 bu...","url_abs":"https://arxiv.org/abs/2511.08735","url_pdf":"https://arxiv.org/pdf/2511.08735v2","authors":"[\"Hasib Uddin Molla\",\"Matthew Backhouse\",\"Ankit Banarjee\",\"Jinniao Qiu\"]","published":"2025-11-11T19:50:21Z","proceeding":"q-fin.MF","tasks":"[\"q-fin.MF\",\"cs.LG\"]","methods":"[\"Diffusion Model\"]","has_code":false}