{
  "id": "1302.7128",
  "version": "v1",
  "published": "2013-02-28T09:58:40.000Z",
  "updated": "2013-02-28T09:58:40.000Z",
  "title": "Explicit construction of a dynamic Bessel bridge of dimension 3",
  "authors": [
    "Luciano Campi",
    "Umut Çetin",
    "Albina Danilova"
  ],
  "journal": "Electronic Journal of Probability, v. 18, 2013",
  "categories": [
    "math.PR"
  ],
  "abstract": "Given a deterministically time-changed Brownian motion $Z$ starting from 1, whose time-change $V(t)$ satisfies $V(t) > t$ for all $t > 0$, we perform an explicit construction of a process $X$ which is Brownian motion in its own filtration and that hits zero for the first time at $V(\\tau)$, where $\\tau := \\inf\\{t>0: Z_t =0\\}$. We also provide the semimartingale decomposition of $X$ under the filtration jointly generated by $X$ and $Z$. Our construction relies on a combination of enlargement of filtration and filtering techniques. The resulting process $X$ may be viewed as the analogue of a 3-dimensional Bessel bridge starting from 1 at time 0 and ending at 0 at the random time $V(\\tau)$. We call this {\\em a dynamic Bessel bridge} since $V(\\tau)$ is not known in advance. Our study is motivated by insider trading models with default risk, where the insider observes the firm's value continuously on time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-28T09:58:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dynamic bessel bridge",
      "explicit construction",
      "filtration",
      "first time",
      "deterministically time-changed brownian motion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1302.7128C"
    }
  }
}