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

Author

Listed:
  • Hasib Uddin Molla
  • Matthew Backhouse
  • Ankit Banarjee
  • Jinniao Qiu

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.

Suggested Citation

  • Hasib Uddin Molla & Matthew Backhouse & Ankit Banarjee & Jinniao Qiu, 2025. "A Deep Learning-Based Method for Fully Coupled Non-Markovian FBSDEs with Applications," Papers 2511.08735, arXiv.org, revised Nov 2025.
    • Handle: RePEc:arx:papers:2511.08735
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    References listed on IDEAS

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    1. Christian Bayer & Jinniao Qiu & Yao Yao, 2020. "Pricing Options Under Rough Volatility with Backward SPDEs," Papers 2008.01241, arXiv.org.
    2. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    3. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.
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