The Annals of Applied Probability

Numerical method for FBSDEs of McKean–Vlasov type

Jean-François Chassagneux, Dan Crisan, and François Delarue

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

Article information

Source
Ann. Appl. Probab., Volume 29, Number 3 (2019), 1640-1684.

Dates
Received: June 2017
Revised: March 2018
First available in Project Euclid: 19 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1550566839

Digital Object Identifier
doi:10.1214/18-AAP1429

Mathematical Reviews number (MathSciNet)
MR3914553

Zentralblatt MATH identifier
07057463

Subjects
Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 65C30: Stochastic differential and integral equations 91A13: Games with infinitely many players

Keywords
McKean–Vlasov master equation forward–backward SDE mean field games numerical approximation

Citation

Chassagneux, Jean-François; Crisan, Dan; Delarue, François. Numerical method for FBSDEs of McKean–Vlasov type. Ann. Appl. Probab. 29 (2019), no. 3, 1640--1684. doi:10.1214/18-AAP1429. https://projecteuclid.org/euclid.aoap/1550566839


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