English

Numerical Method for FBSDEs of McKean-Vlasov Type

Probability 2017-03-07 v1

Abstract

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-bakward SDE (or equivalently the solution of the PDE) satisfies mild regularity conditions. We also provide numerical illustrations.

Keywords

Cite

@article{arxiv.1703.02007,
  title  = {Numerical Method for FBSDEs of McKean-Vlasov Type},
  author = {Jean-François Chassagneux and Dan Crisan and François Delarue},
  journal= {arXiv preprint arXiv:1703.02007},
  year   = {2017}
}

Comments

33 pages, 3 figures