Maximum principle for stochastic optimal control problem of finite state forward‐backward stochastic difference systems

Abstract

AbstractThis article studies the maximum principle for stochastic optimal control problems of forward‐backward stochastic difference systems (FBSSs) where the uncertainty is modeled by a discrete time, finite state process, rather than white noises. Two distinct forms of FBSSs are investigated. The first one is described by a partially coupled forward‐backward stochastic difference equation (FBSE) and the second one is described by a fully coupled FBSE. We deduce the adjoint difference equation by adopting an appropriate representation of the product rule and a proper formulation of the backward stochastic difference equation (BSE). Finally, the maximum principle for this optimal control problem with the convex control domain is established.