{
  "id": "2401.04276",
  "version": "v1",
  "published": "2024-01-08T23:07:34.000Z",
  "updated": "2024-01-08T23:07:34.000Z",
  "title": "Ruin problems with investments on a finite interval: PIDEs and their viscosity solutions",
  "authors": [
    "Viktor Antipov",
    "Yuri Kabanov"
  ],
  "comment": "13 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The study deals with the ruin problem when an insurance company invests its reserve in a risky asset whose the price dynamics is given by a geometric L\\'evy process. Considering the ruin probability as a of the capital reserve we obtain for it a partial integro-differential equation understood in a viscosity sense and prove a result on the uniqueness of the viscosity solution for a corresponding boundary value problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-08T23:07:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "viscosity solution",
      "ruin problem",
      "finite interval",
      "partial integro-differential equation understood",
      "investments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}