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In this paper, we study the maximum principle for stochastic optimal controlproblems of forward-backward stochastic difference systems (FBS{\Delta}Ss)where the uncertainty is modeled by a discrete time, finite state process,rather than white noises. Two types of FBS{\Delta}Ss are investigated. Thefirst one is described by a partially coupled forward-backward stochasticdifference equation (FBS{\Delta}E) and the second one is described by a fullycoupled FBS{\Delta}E. By adopting an appropriate representation of the productrule and an appropriate formulation of the backward stochastic differenceequation (BS{\Delta}E), we deduce the adjoint difference equation. Finally, themaximum principle for this optimal control problem with the control domainbeing convex is established.

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