Maximum principle for stochastic discrete-time ito equations

Abstract

In this chapter, a new version of maximum principle for discrete-time stochastic optimal control problem governed by stochastic a difference Ito equation is established. A new backward stochastic difference Ito equation is introduced, and it is shown that stochastic the discrete-time maximum principle is associated with the solution of a backward stochastic difference Ito equation. Based on the backward stochastic difference Ito equation discretetime stochastic maximum principle for the stochastic discrete optimal control problem is obtained. A sufficient condition for the problem is also given, and the solution of discrete time stochastic linear-quadratic optimal control problem is presented. © 2017 Nova Science Publishers, Inc.