FBSDEs and the Solution of MFGs Without Common Noise

René Carmona, François Delarue

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations


The goal of this chapter is to develop a general methodology for the purpose of solving mean field games using the forward-backward SDE formulations introduced in Chapter 3 We first proceed with a careful analysis of forward-backward mean field SDEs, that is of McKean-Vlasov type, which shows how Schauder’s fixed point theorem can be used to prove existence of a solution. As a by-product, we derive two general solvability results for mean field games: first from the FBSDE representation of the value function, and then from the stochastic Pontryagin maximum principle. In the last section, we revisit some of the examples introduced in the first chapter, and illustrate how our general existence results can be applied.

Original languageEnglish (US)
Title of host publicationProbability Theory and Stochastic Modelling
PublisherSpringer Nature
Number of pages131
StatePublished - 2018

Publication series

NameProbability Theory and Stochastic Modelling
ISSN (Print)2199-3130
ISSN (Electronic)2199-3149

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Modeling and Simulation
  • Statistics and Probability


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