{
  "id": "1904.03286",
  "version": "v1",
  "published": "2019-04-05T21:35:06.000Z",
  "updated": "2019-04-05T21:35:06.000Z",
  "title": "Draw-down Parisian ruin for spectrally negative Lévy process",
  "authors": [
    "Wenyuan Wang",
    "Xiaowen Zhou"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we study the draw-down related Parisian ruin problem for spectrally negative L\\'{e}vy risk processes. We introduce the draw-down Parisian ruin time and solve the corresponding two-sided exit time via excursion theory. We also obtain an expression of the potential measure for the process killed at the draw-down Parisian time. As applications, new results are obtained for spectrally negative L\\'{e}vy risk process with dividend barrier and Parisian ruin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-05T21:35:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60E10",
      "60J35"
    ],
    "keywords": [
      "spectrally negative lévy process",
      "draw-down parisian ruin time",
      "draw-down related parisian ruin problem",
      "risk process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}