IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2511.08735.html

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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2511.08735
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Qinwen Zhu & Gregoire Loeper & Wen Chen & Nicolas Langrené, 2021. "Markovian approximation of the rough Bergomi model for Monte Carlo option pricing," Post-Print hal-02910724, HAL.
    2. Etienne Chevalier & Sergio Pulido & Elizabeth Zúñiga, 2021. "American options in the Volterra Heston model," Working Papers hal-03178306, HAL.
    3. Etienne Chevalier & Sergio Pulido & Elizabeth Zúñiga, 2022. "American options in the Volterra Heston model," Post-Print hal-03178306, HAL.
    4. Etienne Chevalier & Sergio Pulido & Elizabeth Z'u~niga, 2021. "American options in the Volterra Heston model," Papers 2103.11734, arXiv.org, revised May 2022.
    5. Qinwen Zhu & Grégoire Loeper & Wen Chen & Nicolas Langrené, 2021. "Markovian Approximation of the Rough Bergomi Model for Monte Carlo Option Pricing," Mathematics, MDPI, vol. 9(5), pages 1-21, March.
    6. Christian Bayer & Peter K. Friz & Paul Gassiat & Jorg Martin & Benjamin Stemper, 2020. "A regularity structure for rough volatility," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 782-832, July.
    7. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Working Papers hal-02946146, HAL.
    8. Eduardo Abi Jaber & Donatien Hainaut & Edouard Motte, 2025. "The Volterra Stein-Stein model with stochastic interest rates," Papers 2503.01716, arXiv.org, revised Jul 2025.
    9. Eduardo Abi Jaber, 2022. "The characteristic function of Gaussian stochastic volatility models: an analytic expression," Finance and Stochastics, Springer, vol. 26(4), pages 733-769, October.
    10. Stefano De Marco, 2020. "On the harmonic mean representation of the implied volatility," Papers 2007.03585, arXiv.org.
    11. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2017. "Decoupling the short- and long-term behavior of stochastic volatility," CREATES Research Papers 2017-26, Department of Economics and Business Economics, Aarhus University.
    12. Aït-Sahalia, Yacine & Li, Chenxu & Li, Chen Xu, 2021. "Closed-form implied volatility surfaces for stochastic volatility models with jumps," Journal of Econometrics, Elsevier, vol. 222(1), pages 364-392.
    13. Florian Aichinger & Sascha Desmettre, 2025. "Pricing of geometric Asian options in the Volterra-Heston model," Review of Derivatives Research, Springer, vol. 28(1), pages 1-30, April.
    14. Calypso Herrera & Florian Krach & Pierre Ruyssen & Josef Teichmann, 2021. "Optimal Stopping via Randomized Neural Networks," Papers 2104.13669, arXiv.org, revised Dec 2023.
    15. Zhu, Qinwen & Diao, Xundi & Wu, Chongfeng, 2023. "Volatility forecast with the regularity modifications," Finance Research Letters, Elsevier, vol. 58(PA).
    16. Bastien Baldacci, 2020. "High-frequency dynamics of the implied volatility surface," Papers 2012.10875, arXiv.org.
    17. Archil Gulisashvili, 2022. "Multivariate Stochastic Volatility Models and Large Deviation Principles," Papers 2203.09015, arXiv.org, revised Nov 2022.
    18. Takaishi, Tetsuya, 2025. "Multifractality and sample size influence on Bitcoin volatility patterns," Finance Research Letters, Elsevier, vol. 74(C).
    19. Blanka Horvath & Antoine Jacquier & Aitor Muguruza & Andreas Søjmark, 2024. "Functional central limit theorems for rough volatility," Finance and Stochastics, Springer, vol. 28(3), pages 615-661, July.
    20. Masaaki Fukasawa & Tetsuya Takabatake & Rebecca Westphal, 2019. "Is Volatility Rough ?," Papers 1905.04852, arXiv.org, revised May 2019.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2511.08735. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.