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<p>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, <CitationRef CitationID="CR13">2014</CitationRef>) when standard BSDEs were considered. Here we are faced with the problem of the approximation of the law of (<i>Y</i>,&#xa0;<i>Z</i>) 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 (<i>Y</i>,&#xa0;<i>Z</i>) and to compute Monte Carlo approximations.</p>

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Simulation of Mckean-Vlasov Bsdes by Wiener Chaos Expansion

  • 期刊论文

  • 发表日期：

    2025年5月30日

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  • Céline Acary-Robert,
  • Philippe Briand,
  • Abir Ghannoum,
  • Céline Labart

摘要

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.