A cubature based algorithm to solve decoupled McKean-Vlasov Forward Backward Stochastic Differential Equations

TL;DR

This paper introduces a deterministic cubature-based algorithm for solving decoupled McKean-Vlasov FBSDEs, achieving high-order convergence and applicable to mean field stochastic control problems.

Contribution

It presents a novel deterministic cubature method for McKean-Vlasov FBSDEs, with algorithms that attain convergence orders of one and two.

Findings

Algorithms achieve convergence of order one and two.

Method is deterministic, differing from particle-based approaches.

Applicable to stochastic control problems in mean field environments.

Abstract

We propose a new algorithm to approach 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 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.