{
  "id": "1912.08719",
  "version": "v1",
  "published": "2019-12-17T13:56:35.000Z",
  "updated": "2019-12-17T13:56:35.000Z",
  "title": "The risk model with stochastic premiums and a multi-layer dividend strategy",
  "authors": [
    "Olena Ragulina"
  ],
  "comment": "Published at https://doi.org/10.15559/19-VMSTA136 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/). arXiv admin note: text overlap with arXiv:1801.01006",
  "journal": "Modern Stochastics: Theory and Applications 2019, Vol. 6, No. 3, 285-309",
  "doi": "10.15559/19-VMSTA136",
  "categories": [
    "math.PR"
  ],
  "abstract": "The paper deals with a generalization of the risk model with stochastic premiums where dividends are paid according to a multi-layer dividend strategy. First of all, we derive piecewise integro-differential equations for the Gerber--Shiu function and the expected discounted dividend payments until ruin. In addition, we concentrate on the detailed investigation of the model in the case of exponentially distributed claim and premium sizes and find explicit formulas for the ruin probability as well as for the expected discounted dividend payments. Lastly, numerical illustrations for some multi-layer dividend strategies are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-17T13:56:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "multi-layer dividend strategy",
      "stochastic premiums",
      "risk model",
      "expected discounted dividend payments",
      "ruin probability"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}