Maximum principle for stochastic optimal control problem of finite state forward-backward stochastic difference systems
Abstract
In this paper, we study the maximum principle for stochastic optimal control problems 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. The first one is described by a partially coupled forward-backward stochastic difference equation (FBS{\Delta}E) and the second one is described by a fully coupled FBS{\Delta}E. By adopting an appropriate representation of the product rule and an appropriate formulation of the backward stochastic difference equation (BS{\Delta}E), we deduce the adjoint difference equation. Finally, the maximum principle for this optimal control problem with the control domain being convex is established.
Cite
@article{arxiv.1907.04209,
title = {Maximum principle for stochastic optimal control problem of finite state forward-backward stochastic difference systems},
author = {Shailin Ji and Haodong Liu},
journal= {arXiv preprint arXiv:1907.04209},
year = {2019}
}
Comments
26 pages. arXiv admin note: substantial text overlap with arXiv:1812.11283