{
  "id": "2308.08183",
  "version": "v1",
  "published": "2023-08-16T07:29:53.000Z",
  "updated": "2023-08-16T07:29:53.000Z",
  "title": "Refraction strategies in stochastic control: optimality for a general Lévy process model",
  "authors": [
    "Kei Noba",
    "José Luis Pérez",
    "Kazutoshi Yamazaki"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "We revisit an absolutely-continuous version of the stochastic control problem driven by a L\\'evy process. A strategy must be absolutely continuous with respect to the Lebesgue measure and the running cost function is assumed to be convex. We show the optimality of a refraction strategy, which adjusts the drift of the state process at a constant rate whenever it surpasses a certain threshold. The optimality holds for a general L\\'evy process, generalizing the spectrally negative case presented in Hern\\'andez-Hern\\'andez et al.(2016).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-16T07:29:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "93E20",
      "90B05"
    ],
    "keywords": [
      "general lévy process model",
      "refraction strategy",
      "optimality",
      "stochastic control problem driven",
      "general levy process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}