{
  "id": "1907.09993",
  "version": "v1",
  "published": "2019-07-23T16:43:50.000Z",
  "updated": "2019-07-23T16:43:50.000Z",
  "title": "A note on Parisian ruin under a hybrid observation scheme",
  "authors": [
    "Mohamed Amine Lkabous"
  ],
  "categories": [
    "math.PR",
    "q-fin.RM"
  ],
  "abstract": "In this paper, we study the concept of Parisian ruin under the hybrid observation scheme model introduced by Li et al. \\cite{binetal2016}. Under this model, the process is observed at Poisson arrival times whenever the business is financially healthy and it is continuously observed when it goes below $0$. The Parisian ruin is then declared when the process stays below zero for a consecutive period of time greater than a fixed delay. We improve the result originally obtained in \\cite{binetal2016} and we compute other fluctuation identities. All identities are given in terms of second-generation scale functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-23T16:43:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parisian ruin",
      "hybrid observation scheme model",
      "poisson arrival times",
      "second-generation scale functions",
      "process stays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}