A cubature based algorithm to solve decoupled McKean-Vlasov forward-backward stochastic differential equations

被引：21
作者：
de Raynal, P. E. Chaudru [1 ]
Trillos, C. A. Garcia [1 ]
机构：
[1] Univ Nice Sophia Antipolis, Lab Jean Alexandre Dieudonne, F-06108 Nice 02, France
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2015年 / 125卷 / 06期
关键词：
Cubature; McKean-Vlasov processes; BSDE; Mean field games; Non-local PDE; MEAN-FIELD GAMES; WIENER SPACE; QUADRATIC GROWTH; PARTICLE METHOD; CONVERGENCE;
D O I：
10.1016/j.spa.2014.11.018
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We propose a new algorithm to approximate weakly the solution of a McKean-Vlasov SDE. Based on the cubature method of Lyons and Victoir (2004), the algorithm is deterministic differing from the usual methods based on interacting particles. It can be parametrized in order to obtain a given order of convergence. Then, we construct implementable algorithms to solve decoupled Forward-Backward Stochastic Differential equations (FBSDE) of McKean-Vlasov type, which appear in some stochastic control problems in a mean field environment. We give two algorithms and show that they have convergence of order one and two under appropriate regularity conditions. (C) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码：2206 / 2255
页数：50
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