{
  "id": "1709.10295",
  "version": "v1",
  "published": "2017-09-29T09:16:06.000Z",
  "updated": "2017-09-29T09:16:06.000Z",
  "title": "Classification of the Bounds on the Probability of Ruin for L{é}vy Processes with Light-tailed Jumps",
  "authors": [
    "Jérôme Spielmann"
  ],
  "categories": [
    "math.PR",
    "q-fin.RM"
  ],
  "abstract": "In this note, we study the ultimate ruin probabilities of a real-valued L{\\'e}vy process X with light-tailed negative jumps. It is well-known that, for such L{\\'e}vy processes, the probability of ruin decreases as an exponential function with a rate given by the root of the Laplace exponent, when the initial value goes to infinity. Under the additional assumption that X has integrable positive jumps, we show how a finer analysis of the Laplace exponent gives in fact a complete description of the bounds on the probability of ruin for this class of L{\\'e}vy processes. This leads to the identification of a case that is not considered in the literature and for which we give an example. We then apply the result to various risk models and in particular the Cram{\\'e}r-Lundberg model perturbed by Brownian motion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-29T09:16:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vy process",
      "light-tailed jumps",
      "probability",
      "classification",
      "laplace exponent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}