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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. repec:dau:papers:123456789/5522 is not listed on IDEAS
    5. 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.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

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