Stochastic Zero-Sum Differential Games for Forward-Backward SDEs

Jun Moon, Tamer Basar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider stochastic zero-sum differential games (SZSDGs) described by fully-coupled forward-backward stochastic differential equations (FBSDEs). The fully-coupled FBSDE means that the drift and diffusion terms of forward SDEs depend on the solution of the backward SDE (BSDE). The objective functional is modeled by the BSDE part of the FBSDE. For the lower and upper value functions of the SZSDG, we establish the dynamic programming principle via the generalized stochastic backward semigroup associated with the BSDE. We then show that the (lower and upper) value functions are viscosity solutions to the associated HamiltonJacobi-Isaacs partial differential equations together with an algebraic equation. This additional algebraic equation emerges due to dependence of the diffusion term on the solution of the BSDE. The problem formulation and the results of this paper generalize those in the existing literature on SZSDGs to the controlled FBSDE framework.

Original languageEnglish (US)
Title of host publication2019 IEEE 58th Conference on Decision and Control, CDC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6350-6355
Number of pages6
ISBN (Electronic)9781728113982
DOIs
StatePublished - Dec 2019
Event58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France
Duration: Dec 11 2019Dec 13 2019

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2019-December
ISSN (Print)0743-1546

Conference

Conference58th IEEE Conference on Decision and Control, CDC 2019
CountryFrance
CityNice
Period12/11/1912/13/19

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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