Maximum principle for differential games of forward-backward stochastic systems with applications

Chi Man Hui, Hua Xiao

Research output: Journal article publicationJournal articleAcademic researchpeer-review

14 Citations (Scopus)


This paper is concerned with a maximum principle for both zero-sum and nonzero-sum games. The most distinguishing feature, compared with the existing literature, is that the game systems are described by forward-backward stochastic differential equations. This kind of games is motivated by linear-quadratic differential game problems with generalized expectation. We give a necessary condition and a sufficient condition in the form of maximum principle for the foregoing games. Finally, an example of a nonzero-sum game is worked out to illustrate that the theories may find interesting applications in practice. In terms of the maximum principle, the explicit form of an equilibrium point is obtained.
Original languageEnglish
Pages (from-to)412-427
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 1 Feb 2012


  • Equilibrium point
  • Forward-backward stochastic differential equation
  • Maximum principle
  • Saddle point
  • Stochastic differential game

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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