NUMERICAL METHOD FOR FBSDES OF MCKEAN-VLASOV TYPE

• 成果类型: Article
• 署名作者: Chassagneux, Jean-Francois; Crisan, Dan; Delarue, Francois
• 署名单位: Universite Paris Cite; Imperial College London; Universite Cote d'Azur
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/18-AAP1429
• 发表日期: 2019
• 页码: 1640-1684
• 关键词: mean-field games; stochastic differential-equations; CONVERGENCE; algorithm

摘要

This paper is dedicated to the presentation and the analysis of a numerical scheme for forward-backward SDEs of the McKean-Vlasov type, or equivalently for solutions to PDEs on the Wasserstein space. Because of the mean field structure of the equation, earlier methods for classical forward- backward systems fail. The scheme is based on a variation of the method of continuation. The principle is to implement recursively local Picard iterations on small time intervals. We establish a bound for the rate of convergence under the assumption that the decoupling field of the forward-backward SDE (or equivalently the solution of the PDE) satisfies mild regularity conditions. We also provide numerical illustrations.