{
  "id": "2001.11861",
  "version": "v1",
  "published": "2020-01-31T14:17:20.000Z",
  "updated": "2020-01-31T14:17:20.000Z",
  "title": "Revisiting integral functionals of geometric Brownian motion",
  "authors": [
    "Elena Boguslavskaya",
    "Lioudmila Vostrikova"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "q-fin.CP",
    "q-fin.GN",
    "q-fin.PR",
    "stat.TH"
  ],
  "abstract": "In this paper we revisit the integral functional of geometric Brownian motion $I_t= \\int_0^t e^{-(\\mu s +\\sigma W_s)}ds$, where $\\mu\\in\\mathbb{R}$, $\\sigma > 0$, and $(W_s )_s>0$ is a standard Brownian motion. Specifically, we calculate the Laplace transform in $t$ of the cumulative distribution function and of the probability density function of this functional.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-31T14:17:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "geometric brownian motion",
      "revisiting integral functionals",
      "probability density function",
      "standard brownian motion",
      "laplace transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}