{
  "id": "1904.11911",
  "version": "v1",
  "published": "2019-04-26T15:54:55.000Z",
  "updated": "2019-04-26T15:54:55.000Z",
  "title": "Optimally stopping at a given distance from the ultimate supremum of a spectrally negative Lévy process",
  "authors": [
    "Mónica B. Carvajal Pinto",
    "Kees van Schaik"
  ],
  "categories": [
    "math.PR",
    "math.OC",
    "q-fin.GN"
  ],
  "abstract": "We consider the optimal prediction problem of stopping a spectrally negative L\\'evy process as close as possible to a given distance $b \\geq 0$ from its ultimate supremum, under a squared error penalty function. Under some mild conditions, the solution is fully and explicitly characterised in terms of scale functions. We find that the solution has an interesting non-trivial structure: if $b$ is larger than a certain threshold then it is optimal to stop as soon as the difference between the running supremum and the position of the process exceeds a certain level (less than $b$), while if $b$ is smaller than this threshold then it is optimal to stop immediately (independent of the running supremum and position of the process). We also present some examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-26T15:54:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G40",
      "62M20"
    ],
    "keywords": [
      "spectrally negative lévy process",
      "ultimate supremum",
      "optimally stopping",
      "squared error penalty function",
      "optimal prediction problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}