{
  "id": "1609.03954",
  "version": "v1",
  "published": "2016-09-13T17:57:23.000Z",
  "updated": "2016-09-13T17:57:23.000Z",
  "title": "On the controller-stopper problems with controlled jumps",
  "authors": [
    "Erhan Bayraktar",
    "Jiaqi Li"
  ],
  "comment": "Keywords: Controller-stopper problems, controlled jumps, stochastic target problems, stochastic Perron's method, viscosity solutions.}. arXiv admin note: text overlap with arXiv:1604.03906",
  "categories": [
    "math.OC",
    "math.PR"
  ],
  "abstract": "We analyze the continuous time zero-sum and cooperative controller-stopper games of Karatzas and Sudderth [Annals of Probability, 2001], Karatzas and Zamfirescu [Annals of Probability, 2008] and Karatzas and Zamfirescu [Applied Mathematics and Optimization, 2005] when the volatility of the state process is controlled as in Bayraktar and Huang [SIAM Journal on Control and Optimization, 2013] but additionally when the state process has controlled jumps. We perform this analysis by first resolving the stochastic target problems (of Soner and Touzi [SIAM Journal on Control and Optimization, 2002; Journal of European Mathematical Society, 2002]) with a cooperative or a non-cooperative stopper and then embedding the original problem into the latter set-up. Unlike in Bayraktar and Huang [SIAM Journal on Control and Optimization, 2013] our analysis relies crucially on the Stochastic Perron method of Bayraktar and Sirbu [SIAM Journal on Control and Optimization, 2013] but not the dynamic programming principle, which is difficult to prove directly for games.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-13T17:57:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93E20",
      "49L25",
      "60J75",
      "60G40"
    ],
    "keywords": [
      "controlled jumps",
      "controller-stopper problems",
      "siam journal",
      "optimization",
      "state process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}