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山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (09): 78-83.doi: 10.6040/j.issn.1671-9352.0.2014.373

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带分红的稀疏风险模型的期望折现罚金函数

陈洁1, 吕玉华2   

  1. 1. 济宁学院数学系, 山东 济宁 273155;
    2. 曲阜师范大学数学科学学院, 山东 曲阜 273165
  • 收稿日期:2014-08-14 修回日期:2015-07-22 出版日期:2015-09-20 发布日期:2015-09-26
  • 作者简介:陈洁(1985-), 女, 硕士, 讲师, 研究方向为随机过程.E-mail:jiechen6688@163.com
  • 基金资助:
    国家自然科学基金资助项目(11171179);山东省自然科学基金资助项目(ZR2009AL015)

Discounted penalty function for a thinning risk model with dividend

CHEN Jie1, LÜ Yu-hua2   

  1. 1. Department of Mathematics, Jining University, Jining 273155, Shandong, China;
    2. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China
  • Received:2014-08-14 Revised:2015-07-22 Online:2015-09-20 Published:2015-09-26

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摘要： 考虑一类带分红的稀疏风险模型,得到了期望折现罚金函数的积分微分方程。当保费额与索赔额同为指数分布时,研究了积分微分方程的拉普拉斯变换的解以及破产概率、赤字分布、破产时刻的瞬间盈余分布的积分微分方程的显解。

关键词: 障碍分红, 稀疏, 拉普拉斯变换, 期望折现罚金函数, 积分微分方程

Abstract: The thinning risk model with barrier dividend was considered. The integro-differential equation for the expected discounted penalty function was obtained. If the premium and the claim sizes are exponentially distributed, some expressions for the Laplace transform of the integro-differential equation were founded. When the premium and the claim sizes are exponentially distributed, the closed-form solutions of the time of ruin, the deficit at ruin and the surplus before ruin were obtained.

Key words: barrier dividend, Laplace transform, integro-differential equation, thinning process, expected discounted penalty function

中图分类号: 

  • O211.6
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