{
  "id": "2409.13849",
  "version": "v1",
  "published": "2024-09-20T18:45:59.000Z",
  "updated": "2024-09-20T18:45:59.000Z",
  "title": "Optimality of a barrier strategy in a spectrally negative Lévy model with a level-dependent intensity of bankruptcy",
  "authors": [
    "Dante Mata",
    "Jean-François Renaud"
  ],
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "We consider de Finetti's stochastic control problem for a spectrally negative L\\'evy process in an Omega model. In such a model, the (controlled) process is allowed to spend time under the critical level but is then subject to a level-dependent intensity of bankruptcy. First, before considering the control problem, we derive some analytical properties of the corresponding Omega scale functions. Second, we prove that exists a barrier strategy that is optimal for this control problem under a mild assumption on the L\\'evy measure. Finally, we analyse numerically the impact of the bankruptcy rate function on the optimal strategy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-20T18:45:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "93E20",
      "45D05"
    ],
    "keywords": [
      "spectrally negative lévy model",
      "barrier strategy",
      "level-dependent intensity",
      "optimality",
      "finettis stochastic control problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}