Optimal Control Of Neutral Stochastic Delay Differential Equations

Neutral stochastic differential equation are often used to describe the systemswhich not only but also depend on present and past state but also involve derivativewith delay. In this paper, we study a scheme which the coefficients and control pro-cess are discreted in time of controlled neutral stochastic differential equations withbounded memory. By discretising time in two steps, we study the optimal control ofneutral stochastic delay equations.This paper has three chapters, in chapter 1, the author introduces the historicalbackground and the recent development of problems to be studied and some prepara-tions are given here.In chapter 2, the author introduces the optimal control for stochastic differentialequations.In chapter 3, we study the optimal control of neutral stochastic delay equations.Keywords: neutral stochastic differential equations; optimal control; delay; ap-proximation.