{
  "id": "1806.11290",
  "version": "v1",
  "published": "2018-06-29T08:01:06.000Z",
  "updated": "2018-06-29T08:01:06.000Z",
  "title": "On The Ruin Problem With Investment When The Risky Asset Is A Semimartingale",
  "authors": [
    "Lioudmila Vostrikova",
    "Jérôme Spielmann"
  ],
  "categories": [
    "math.PR",
    "q-fin.CP",
    "q-fin.RM"
  ],
  "abstract": "In this paper, we study the ruin problem with investment in a general framework where the business part X is a L{\\'e}vy process and the return on investment R is a semimartingale. We obtain upper bounds on the finite and infinite time ruin probabilities that decrease as a power function when the initial capital increases. When R is a L{\\'e}vy process, we retrieve the well-known results. Then, we show that these bounds are asymptotically optimal in the finite time case, under some simple conditions on the characteristics of X. Finally, we obtain a condition for ruin with probability one when X is a Brownian motion with negative drift and express it explicitly using the characteristics of R.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-29T08:01:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ruin problem",
      "risky asset",
      "investment",
      "semimartingale",
      "vy process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}