{
  "id": "1409.6773",
  "version": "v1",
  "published": "2014-09-23T23:36:58.000Z",
  "updated": "2014-09-23T23:36:58.000Z",
  "title": "On a Stopping Game in continuous time",
  "authors": [
    "Erhan Bayraktar",
    "Zhou Zhou"
  ],
  "comment": "Keywords: A new type of optimal stopping game, non-anticipative stopping strategies, Dynkin games, saddle point",
  "categories": [
    "math.PR",
    "math.OC",
    "q-fin.MF"
  ],
  "abstract": "On a filtered probability space $(\\Omega,\\mathcal{F},P,\\mathbb{F}=(\\mathcal{F}_t)_{0\\leq t\\leq T})$, we consider stopper-stopper games $\\bar C:=\\inf_{\\Rho}\\sup_{\\tau\\in\\T}\\E[U(\\Rho(\\tau),\\tau)]$ and $\\underline C:=\\sup_{\\Tau}\\inf_{\\rho\\in\\T}\\E[U(\\Rho(\\tau),\\tau)]$ in continuous time, where $U(s,t)$ is $\\mathcal{F}_{s\\vee t}$-measurable (this is the new feature of our stopping game), $\\T$ is the set of stopping times, and $\\Rho,\\Tau:\\T\\mapsto\\T$ satisfy certain non-anticipativity conditions. We show that $\\bar C=\\underline C$, by converting these problems into a corresponding Dynkin game.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-23T23:36:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G40",
      "93E20",
      "91A10",
      "91A60",
      "60G07"
    ],
    "keywords": [
      "continuous time",
      "stopping game",
      "corresponding dynkin game",
      "filtered probability space",
      "non-anticipativity conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.6773B"
    }
  }
}