{
  "id": "1504.07061",
  "version": "v1",
  "published": "2015-04-27T12:43:21.000Z",
  "updated": "2015-04-27T12:43:21.000Z",
  "title": "On Parisian ruin over a finite-time horizon",
  "authors": [
    "Krzysztof Debicki",
    "Enkelejd Hashorva",
    "Lanpeng Ji"
  ],
  "comment": "20",
  "categories": [
    "math.PR"
  ],
  "abstract": "For a risk process $R_u(t)=u+ct-X(t), t\\ge 0$, where $u\\ge 0$ is the initial capital, $c>0$ is the premium rate and $X(t),t\\ge 0$ is an aggregate claim process, we investigate the probability of the Parisian ruin \\[ \\mathcal{P}_S(u,T_u)=\\mathbb{P}\\{\\inf_{t\\in[0,S]} \\sup_{s\\in[t,t+T_u]} R_u(s)<0\\}, \\] with a given positive constant $S$ and a positive measurable function $T_u$. We derive asymptotic expansion of $\\mathcal{P}_S(u,T_u)$, as $u\\to\\infty$, for the aggregate claim process $X$ modeled by Gaussian processes. As a by-product, we derive the exact tail asymptotics of the infimum of a standard Brownian motion with drift over a finite-time interval.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-27T12:43:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G70"
    ],
    "keywords": [
      "parisian ruin",
      "finite-time horizon",
      "aggregate claim process",
      "exact tail asymptotics",
      "standard brownian motion"
    ],
    "publication": {
      "doi": "10.1007/s11425-015-5073-6",
      "journal": "Science in China A: Mathematics",
      "year": 2016,
      "month": "Mar",
      "volume": 59,
      "number": 3,
      "pages": 557
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016ScChA..59..557D"
    }
  }
}