{
  "id": "2110.06907",
  "version": "v3",
  "published": "2021-10-13T17:44:20.000Z",
  "updated": "2022-02-02T18:33:50.000Z",
  "title": "One-dimensional reflected BSDEs with quadratic growth generators",
  "authors": [
    "Shiqiu Zheng",
    "Lidong Zhang",
    "Xiangbo Meng"
  ],
  "comment": "37 pages, Uniqueness theorems for solutions of RBSDEs and BSDEs with convex generators are added in Section 5. Comments are welcome",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study the existence, uniqueness and comparison theorem for solutions of one-dimensional reflected backward stochastic differential equations (RBSDEs) with one continuous obstacle. The generators of such RBSDEs have a quadratic growth in $z$, with the quadratic term taking the form $f(y)|z|^2$, where the function $f$ is defined on an open interval $D$ and local integral. The corresponding results on BSDEs are also obtained. Our proofs mainly depend on a transformation based on $f$ and a domination method based on RBSDEs with two obstacles. As applications, we give a probabilistic interpretation of an obstacle problem for a quadratic PDE with local integral coefficient, and study an optimal stopping problem for the payoff of American options.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2022-02-02T18:33:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic growth generators",
      "one-dimensional reflected bsdes",
      "one-dimensional reflected backward stochastic differential",
      "local integral coefficient",
      "reflected backward stochastic differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}