{
  "id": "1705.00369",
  "version": "v1",
  "published": "2017-04-30T19:54:04.000Z",
  "updated": "2017-04-30T19:54:04.000Z",
  "title": "Optimal stopping of a Brownian bridge with an unknown pinning point",
  "authors": [
    "Erik Ekström",
    "Juozas Vaicenavicius"
  ],
  "comment": "20 pages, 5 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "The problem of stopping a Brownian bridge with an unknown pinning point to maximise the expected value at the stopping time is studied. A few general properties such as continuity of the value function are established. Structural properties of an optimal stopping region are shown to crucially depend on the prior. However, we provide a general condition for a one-sided stopping region. More detailed analysis is conducted in the cases of the two-point and the mixed Gaussian priors, revealing a rich structure present in the problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-30T19:54:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G40",
      "60G35",
      "60J25"
    ],
    "keywords": [
      "unknown pinning point",
      "brownian bridge",
      "optimal stopping",
      "stopping region",
      "rich structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}