{
  "id": "1708.06785",
  "version": "v1",
  "published": "2017-08-19T19:53:33.000Z",
  "updated": "2017-08-19T19:53:33.000Z",
  "title": "Parisian ruin for the dual risk process in discrete-time",
  "authors": [
    "Zbigniew Palmowski",
    "Lewis Ramsden",
    "Apostolos D. Papaioannou"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we consider the Parisian ruin probabilities for the dual risk model in a discrete-time setting. By exploiting the strong Markov property of the risk process we derive a recursive expression for the fnite-time Parisian ruin probability, in terms of classic discrete-time dual ruin probabilities. Moreover, we obtain an explicit expression for the corresponding infnite-time Parisian ruin probability as a limiting case. In order to obtain more analytic results, we employ a conditioning argument and derive a new expression for the classic infinite-time ruin probability in the dual risk model and hence, an alternative form of the infnite-time Parisian ruin probability. Finally, we explore some interesting special cases, including the Binomial/Geometric model, and obtain a simple expression for the Parisian ruin probability of the Gambler's ruin problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-19T19:53:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62P05"
    ],
    "keywords": [
      "dual risk process",
      "dual risk model",
      "classic discrete-time dual ruin probabilities",
      "expression",
      "corresponding infnite-time parisian ruin probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}