IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v27y2025i2d10.1007_s11009-025-10172-8.html
   My bibliography  Save this article

Simulation of Mckean-Vlasov Bsdes by Wiener Chaos Expansion

Author

Listed:
  • Céline Acary-Robert

    (Inria, CNRS, Grenoble INP, LJK)

  • Philippe Briand

    (CNRS, LAMA)

  • Abir Ghannoum

    (CNRS, LAMA
    LaMA-Liban)

  • Céline Labart

    (CNRS, LAMA)

Abstract

We present an algorithm to solve McKean-Vlasov BSDEs based on Wiener chaos expansion and Picard’s iterations and study its convergence. This paper extends the results obtained by Briand and Labart (The Annal Appl Probab 24(3):1129–1171, 2014) when standard BSDEs were considered. Here we are faced with the problem of the approximation of the law of (Y, Z) in the driver, that we solve by using a particle system. In order to avoid solving a system of BSDEs, which would not be feasible in practice, we use the same particles to approximate the law of (Y, Z) and to compute Monte Carlo approximations.

Suggested Citation

  • Céline Acary-Robert & Philippe Briand & Abir Ghannoum & Céline Labart, 2025. "Simulation of Mckean-Vlasov Bsdes by Wiener Chaos Expansion," Methodology and Computing in Applied Probability, Springer, vol. 27(2), pages 1-39, June.
    • Handle: RePEc:spr:metcap:v:27:y:2025:i:2:d:10.1007_s11009-025-10172-8
    DOI: 10.1007/s11009-025-10172-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-025-10172-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-025-10172-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Henry-Labordère, Pierre & Tan, Xiaolu & Touzi, Nizar, 2014. "A numerical algorithm for a class of BSDEs via the branching process," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1112-1140.
    2. Maximilien Germain & Joseph Mikael & Xavier Warin, 2022. "Numerical Resolution of McKean-Vlasov FBSDEs Using Neural Networks," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2557-2586, December.
    3. repec:dau:papers:123456789/5522 is not listed on IDEAS
    4. Geiss, Christel & Labart, Céline, 2016. "Simulation of BSDEs with jumps by Wiener Chaos expansion," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2123-2162.
    5. 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.
    6. Briand, Philippe & Delyon, Bernard & Mémin, Jean, 2002. "On the robustness of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 97(2), pages 229-253, February.
    7. Crisan, D. & Manolarakis, K. & Touzi, N., 2010. "On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1133-1158, July.
    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. Antonis Papapantoleon & Dylan Possamai & Alexandros Saplaouras, 2021. "Stability of backward stochastic differential equations: the general case," Papers 2107.11048, arXiv.org, revised Apr 2023.
    2. Jean-Franc{c}ois Chassagneux & Junchao Chen & Noufel Frikha, 2022. "Deep Runge-Kutta schemes for BSDEs," Papers 2212.14372, arXiv.org.
    3. Pagès, Gilles & Sagna, Abass, 2018. "Improved error bounds for quantization based numerical schemes for BSDE and nonlinear filtering," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 847-883.
    4. Jean-Franc{c}ois Chassagneux & Mohan Yang, 2021. "Numerical approximation of singular Forward-Backward SDEs," Papers 2106.15496, arXiv.org.
    5. Weinan E & Martin Hutzenthaler & Arnulf Jentzen & Thomas Kruse, 2021. "Multilevel Picard iterations for solving smooth semilinear parabolic heat equations," Partial Differential Equations and Applications, Springer, vol. 2(6), pages 1-31, December.
    6. Polynice Oyono Ngou & Cody Hyndman, 2014. "A Fourier interpolation method for numerical solution of FBSDEs: Global convergence, stability, and higher order discretizations," Papers 1410.8595, arXiv.org, revised May 2022.
    7. Qiang Han & Shaolin Ji, 2022. "A Multi-Step Algorithm for BSDEs Based On a Predictor-Corrector Scheme and Least-Squares Monte Carlo," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2403-2426, December.
    8. Steven Kou & Xianhua Peng & Xingbo Xu, 2016. "EM Algorithm and Stochastic Control in Economics," Papers 1611.01767, arXiv.org.
    9. Matoussi Anis & Sabbagh Wissal, 2016. "Numerical computation for backward doubly SDEs with random terminal time," Monte Carlo Methods and Applications, De Gruyter, vol. 22(3), pages 229-258, September.
    10. Ren, Zhenjie & Tan, Xiaolu, 2017. "On the convergence of monotone schemes for path-dependent PDEs," Stochastic Processes and their Applications, Elsevier, vol. 127(6), pages 1738-1762.
    11. Lucio Fiorin & Gilles Pagès & Abass Sagna, 2019. "Product Markovian Quantization of a Diffusion Process with Applications to Finance," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1087-1118, December.
    12. Geiss, Christel & Labart, Céline, 2016. "Simulation of BSDEs with jumps by Wiener Chaos expansion," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2123-2162.
    13. Agarwal, Ankush & Claisse, Julien, 2020. "Branching diffusion representation of semi-linear elliptic PDEs and estimation using Monte Carlo method," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5006-5036.
    14. Callegaro, Giorgia & Gnoatto, Alessandro & Grasselli, Martino, 2023. "A fully quantization-based scheme for FBSDEs," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    15. Guangbao Guo, 2018. "Finite Difference Methods for the BSDEs in Finance," IJFS, MDPI, vol. 6(1), pages 1-15, March.
    16. Yao, Song, 2017. "Lp solutions of backward stochastic differential equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3465-3511.
    17. Bouchard Bruno & Tan Xiaolu & Warin Xavier & Zou Yiyi, 2017. "Numerical approximation of BSDEs using local polynomial drivers and branching processes," Monte Carlo Methods and Applications, De Gruyter, vol. 23(4), pages 241-263, December.
    18. Zhang, Shen & Xu, Juanjuan & Zhang, Huanshui, 2024. "Decentralized control of forward and backward stochastic difference system with nested asymmetric information," Applied Mathematics and Computation, Elsevier, vol. 478(C).
    19. Andrew Lesniewski & Anja Richter, 2016. "Managing counterparty credit risk via BSDEs," Papers 1608.03237, arXiv.org, revised Aug 2016.
    20. Stefan Geiss & Emmanuel Gobet, 2010. "Fractional smoothness and applications in finance," Papers 1004.3577, arXiv.org.

    More about this item

    Keywords

    ;
    ;
    ;

    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:spr:metcap:v:27:y:2025:i:2:d:10.1007_s11009-025-10172-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.