{
  "id": "1907.04209",
  "version": "v1",
  "published": "2019-07-06T00:05:21.000Z",
  "updated": "2019-07-06T00:05:21.000Z",
  "title": "Maximum principle for stochastic optimal control problem of finite state forward-backward stochastic difference systems",
  "authors": [
    "Shailin Ji",
    "Haodong Liu"
  ],
  "comment": "26 pages. arXiv admin note: substantial text overlap with arXiv:1812.11283",
  "categories": [
    "math.OC",
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-06T00:05:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic optimal control problem",
      "finite state forward-backward stochastic difference",
      "state forward-backward stochastic difference systems",
      "maximum principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}