{
  "id": "1801.01006",
  "version": "v1",
  "published": "2018-01-03T14:04:10.000Z",
  "updated": "2018-01-03T14:04:10.000Z",
  "title": "The risk model with stochastic premiums, dependence and a threshold dividend strategy",
  "authors": [
    "Olena Ragulina"
  ],
  "comment": "Published at https://doi.org/10.15559/17-VMSTA89 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/)",
  "journal": "Modern Stochastics: Theory and Applications 2017, Vol. 4, No. 4, 315-351",
  "doi": "10.15559/17-VMSTA89",
  "categories": [
    "math.PR"
  ],
  "abstract": "The paper deals with a generalization of the risk model with stochastic premiums where dependence structures between claim sizes and inter-claim times as well as premium sizes and inter-premium times are modeled by Farlie--Gumbel--Morgenstern copulas. In addition, dividends are paid to its shareholders according to a threshold dividend strategy. We derive integral and integro-differential equations for the Gerber--Shiu function and the expected discounted dividend payments until ruin. Next, we concentrate on the detailed investigation of the model in the case of exponentially distributed claim and premium sizes. In particular, we find explicit formulas for the ruin probability in the model without either dividend payments or dependence as well as for the expected discounted dividend payments in the model without dependence. Finally, numerical illustrations are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-03T14:04:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "threshold dividend strategy",
      "stochastic premiums",
      "risk model",
      "dependence",
      "expected discounted dividend payments"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}