{
  "id": "math/0508487",
  "version": "v1",
  "published": "2005-08-25T08:07:29.000Z",
  "updated": "2005-08-25T08:07:29.000Z",
  "title": "Some remarks on first passage of Levy processes, the American put and pasting principles",
  "authors": [
    "L. Alili",
    "A. E. Kyprianou"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/105051605000000377 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2005, Vol. 15, No. 3, 2062-2080",
  "doi": "10.1214/105051605000000377",
  "categories": [
    "math.PR",
    "q-fin.PR"
  ],
  "abstract": "The purpose of this article is to provide, with the help of a fluctuation identity, a generic link between a number of known identities for the first passage time and overshoot above/below a fixed level of a Levy process and the solution of Gerber and Shiu [Astin Bull. 24 (1994) 195-220], Boyarchenko and Levendorskii [Working paper series EERS 98/02 (1998), Unpublished manuscript (1999), SIAM J. Control Optim. 40 (2002) 1663-1696], Chan [Original unpublished manuscript (2000)], Avram, Chan and Usabel [Stochastic Process. Appl. 100 (2002) 75-107], Mordecki [Finance Stoch. 6 (2002) 473-493], Asmussen, Avram and Pistorius [Stochastic Process. Appl. 109 (2004) 79-111] and Chesney and Jeanblanc [Appl. Math. Fin. 11 (2004) 207-225] to the American perpetual put optimal stopping problem. Furthermore, we make folklore precise and give necessary and sufficient conditions for smooth pasting to occur in the considered problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-08-25T08:07:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G40",
      "60J75",
      "91B70",
      "60G51"
    ],
    "keywords": [
      "levy processes",
      "pasting principles",
      "stochastic process",
      "first passage time",
      "unpublished manuscript"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......8487A"
    }
  }
}