Simulation of Mckean-Vlasov Bsdes by Wiener Chaos Expansion

Céline Acary-Robert (), Philippe Briand (), Abir Ghannoum () and Céline Labart ()
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Céline Acary-Robert: Inria, CNRS, Grenoble INP, LJK
Philippe Briand: CNRS, LAMA
Abir Ghannoum: CNRS, LAMA
Céline Labart: CNRS, LAMA

Methodology and Computing in Applied Probability, 2025, vol. 27, issue 2, 1-39

Abstract: 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.

Keywords: McKean-Vlasov backward stochastic differential equations; Wiener chaos expansion; Particle methods; 60H10; 65C35; 65C05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11009-025-10172-8

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