Numerical method for FBSDEs of McKean–Vlasov type

By Jean-François Chassagneux, D. Crisan, Franccois Delarue. The Annals of Applied Probability, 2017

64 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Mechanics, Finance

View Paper: https://www.semanticscholar.org/paper/0d61eedd7a4dd178cc67cdaf1a3450bbe8eb9a66

How researchers see this paper

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In Applied Mathematics

1. François Delarue
2. Franccois Delarue
3. Gordan vZitkovi'c
4. Hao Xing
5. Stéphane Menozzi

In Finance

1. Alekos Cecchin
2. Erhan Bayraktar
3. Asaf Cohen
4. François Delarue
5. René A. Carmona
6. Daniel Lacker
7. Franccois Delarue
8. Huyen Pham

Citations in the corpus

• Finite state mean field games with Wright–Fisher common noise (2019, methodology): “Although we provide a longer review on MFG later in the text, we feel useful to quote, at this early stage of the introduction, [33, 34] and [9, Chapter 7] as references on the master equation for finite state mean field games, and [7, 5, 10, 8, 16] as references for continuous state mean field game”