{
  "id": "2212.01559",
  "version": "v1",
  "published": "2022-12-03T07:13:17.000Z",
  "updated": "2022-12-03T07:13:17.000Z",
  "title": "A Global Maximum Principle for Controlled Conditional Mean-field FBSDEs with Regime Switching",
  "authors": [
    "Tao Hao",
    "Jiaqiang Wen",
    "Jie Xiong"
  ],
  "comment": "28 pages",
  "categories": [
    "math.OC",
    "math.PR"
  ],
  "abstract": "This paper is devoted to a global stochastic maximum principle for conditional mean-field forward-backward stochastic differential equations (FBSDEs, for short) with regime switching. The control domain is unnecessarily convex and the driver of backward stochastic differential equations (BSDEs, for short) could depend on $Z$. Different from the case of non-recursive utility, the first-order and second-order adjoint equations are both high-dimensional linear BSDEs. Based on the adjoint equations, we reveal the relations among the terms of the first- and second-order Taylor's expansions. A general maximum principle is proved, which develops the work of Nguyen, Yin, and Nguyen [22] to recursive utility. As applications, the linear-quadratic problem is considered and a problem with state constraint is studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-03T07:13:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "60H30"
    ],
    "keywords": [
      "controlled conditional mean-field fbsdes",
      "global maximum principle",
      "regime switching",
      "forward-backward stochastic differential equations",
      "mean-field forward-backward stochastic differential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}