{
  "id": "0905.1975",
  "version": "v1",
  "published": "2009-05-12T22:06:13.000Z",
  "updated": "2009-05-12T22:06:13.000Z",
  "title": "On the first passage time density of a continuous Martingale over a moving boundary",
  "authors": [
    "Gerardo Hernandez-del-Valle"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "In this paper we derive the density $\\varphi$ of the first time $T$ that a continuous martingale $M$ with non-random quadratic variation $<M>_\\cdot:=\\int_0^\\cdot h^2(u)du$ hits a moving boundary $f$ which is twice continuously differentiable, and $f'/h\\in\\mathbb{C}^2[0,\\infty)$. Thus, this work is an extension to case in which $M$ is in fact a one-dimensional standard Brownian motion $B$, as studied in Hernandez-del-Valle (2007).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-12T22:06:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "45D05",
      "60J60",
      "45G15"
    ],
    "keywords": [
      "first passage time density",
      "moving boundary",
      "continuous martingale",
      "one-dimensional standard brownian motion",
      "non-random quadratic variation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.1975H"
    }
  }
}