{
  "id": "1103.1460",
  "version": "v2",
  "published": "2011-03-08T08:23:14.000Z",
  "updated": "2012-09-11T07:49:36.000Z",
  "title": "On the drawdown of completely asymmetric Levy processes",
  "authors": [
    "Aleksandar Mijatovic",
    "Martijn R. Pistorius"
  ],
  "comment": "applications added, 26 pages, 3 figures, to appear in SPA",
  "categories": [
    "math.PR",
    "q-fin.RM"
  ],
  "abstract": "The {\\em drawdown} process $Y$ of a completely asymmetric L\\'{e}vy process $X$ is equal to $X$ reflected at its running supremum $\\bar{X}$: $Y = \\bar{X} - X$. In this paper we explicitly express in terms of the scale function and the L\\'{e}vy measure of $X$ the law of the sextuple of the first-passage time of $Y$ over the level $a>0$, the time $\\bar{G}_{\\tau_a}$ of the last supremum of $X$ prior to $\\tau_a$, the infimum $\\unl X_{\\tau_a}$ and supremum $\\ovl X_{\\tau_a}$ of $X$ at $\\tau_a$ and the undershoot $a - Y_{\\tau_a-}$ and overshoot $Y_{\\tau_a}-a$ of $Y$ at $\\tau_a$. As application we obtain explicit expressions for the laws of a number of functionals of drawdowns and rallies in a completely asymmetric exponential L\\'{e}vy model.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-11T07:49:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60G17"
    ],
    "keywords": [
      "asymmetric levy processes",
      "asymmetric exponential",
      "explicit expressions",
      "first-passage time",
      "scale function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.1460M"
    }
  }
}