Probabilistic Approach to Stochastic Differential Games

René Carmona, François Delarue

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This chapter offers a crash course on the theory of nonzero sum stochastic differential games. Its goal is to introduce the jargon and the notation of this class of game models. As the main focus of the text is the probabilistic approach to the solution of stochastic games, we review the strategy based on the stochastic Pontryagin maximum principle and show how BSDEs and FBSDEs can be brought to bear in the search for Nash equilibria. We emphasize the differences between open loop and closed loop or Markov equilibria and we illustrate the results of the chapter with detailed analyses of some of the models introduced in Chapter 1

Original languageEnglish (US)
Title of host publicationProbability Theory and Stochastic Modelling
PublisherSpringer Nature
Pages67-127
Number of pages61
DOIs
StatePublished - 2018

Publication series

NameProbability Theory and Stochastic Modelling
Volume83
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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