{
  "id": "2211.00913",
  "version": "v1",
  "published": "2022-11-02T06:27:15.000Z",
  "updated": "2022-11-02T06:27:15.000Z",
  "title": "A unified approach to global solvability for FBSDEs with diagonal generators",
  "authors": [
    "Tianjiao Hua",
    "Peng Luo"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study the global solvability of multidimensional forwar-backward stochastic differential equations (FBSDEs) with diagonally Lipschitz, quadratic or super-quadratic generators. Under a certain \"monotonicity\" condition, we provide a unified approach which shows that there exists a decoupling field that is uniformly Lipschitz in its spatial variable. This decoupling field is closely related to bounded solution to an associated characteristic BSDE. Applications to stochastic optimal controls and stochastic differential games are investigated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-02T06:27:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H30",
      "93E20"
    ],
    "keywords": [
      "global solvability",
      "unified approach",
      "diagonal generators",
      "multidimensional forwar-backward stochastic differential equations",
      "decoupling field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}