Maximum principle for stochastic optimal control problem of finite state forward-backward stochastic difference systems
arXiv:1907.04209
Abstract
In this paper, we study the maximum principle for stochastic optimal control problems of forward-backward stochastic difference systems (FBSΔSs) where the uncertainty is modeled by a discrete time, finite state process, rather than white noises. Two types of FBSΔSs are investigated. The first one is described by a partially coupled forward-backward stochastic difference equation (FBSΔE) and the second one is described by a fully coupled FBSΔE. By adopting an appropriate representation of the product rule and an appropriate formulation of the backward stochastic difference equation (BSΔE), we deduce the adjoint difference equation. Finally, the maximum principle for this optimal control problem with the control domain being convex is established.
26 pages. arXiv admin note: substantial text overlap with arXiv:1812.11283