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

Abstract

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.