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June 2019 Numerical method for FBSDEs of McKean–Vlasov type
Jean-François Chassagneux, Dan Crisan, François Delarue
Ann. Appl. Probab. 29(3): 1640-1684 (June 2019). DOI: 10.1214/18-AAP1429

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.

Citation

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Jean-François Chassagneux. Dan Crisan. François Delarue. "Numerical method for FBSDEs of McKean–Vlasov type." Ann. Appl. Probab. 29 (3) 1640 - 1684, June 2019. https://doi.org/10.1214/18-AAP1429

Information

Received: 1 June 2017; Revised: 1 March 2018; Published: June 2019
First available in Project Euclid: 19 February 2019

zbMATH: 07057463
MathSciNet: MR3914553
Digital Object Identifier: 10.1214/18-AAP1429

Subjects:
Primary: 60H10, 65C30, 91A13

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 3 • June 2019
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