Linear-quadratic optimal control and nonzero-sum differential game of forward-backward stochastic system

Abstract

An existence and uniqueness result for one kind of forward-backward stochastic differential equations with double dimensions was obtained under some monotonicity conditions. Then this result was applied to the linear-quadratic stochastic optimal control and nonzero-sum differential game of forward-backward stochastic system. The explicit forms of the optimal control and the Nash equilibrium point are obtained respectively. We note that our method is effective in studying the uniqueness of Nash equilibrium point. Copyright © 2011 John Wiley and Sons Asia Pte Ltd.