数学物理学报 ›› 2010, Vol. 30 ›› Issue (1): 31-41.

• 论文 • 上一篇    下一篇

绝对破产下具有贷款利息及常数分红界的扰动复合Poisson风险模型

王春伟, 尹传存   

  1. 1.河南科技大学理学院 河南洛阳 471003|2.曲阜师范大学数学科学学院 山东曲阜 273165
  • 收稿日期:2008-05-18 修回日期:2009-06-19 出版日期:2010-01-01 发布日期:2010-01-01
  • 基金资助:

    国家自然科学基金(10771119)、山东省自然科学基金(Y2004A06)和教育部科学技术研究重点项目(209091)资助

On the Perturbed Compound Poisson Risk Model under Absolute Ruin with Debit Interest and a Constant Dividend Barrier

WANG Chun-Wei, YIN Chuan-Cun   

  1. 1.School of Mathematics and Statistics, Henan University of Science and Technology, Henan Luoyang 471003;
    2.School of Mathematical Sciences, Qufu Normal University, Shandong Qufu 273165
  • Received:2008-05-18 Revised:2009-06-19 Online:2010-01-01 Published:2010-01-01
  • Supported by:

    国家自然科学基金(10771119)、山东省自然科学基金(Y2004A06)和教育部科学技术研究重点项目(209091)资助

摘要:

该文研究了绝对破产下具有贷款利息及常数分红界的扰动复合Poisson风险模型, 得到了折现分红总量的均值函数, 及其矩母函数以及此模型的期望折现罚金函数(Gerber-Shiu函数)满足的积分--微分方程及边值条件, 并求出了某些特殊情形下的具体表达式.

关键词: 绝对破产, Brown运动, 分红量, 贷款利息, 期望折现罚金函数

Abstract:

In this paper, we consider the perturbed compound Poisson risk model under absolute ruin  with debit interest and a constant dividend barrier.  Integro-differential equations satisfied by the expectation of discounted dividend payments, the moment generating function and the expected discounted penalty function (Gerber-Shiu function) with certain boundary conditions are obtained. For some special cases, explicit  expressions are obtained.

Key words: Absolute ruin, Brownian motion, Dividend payments, Debit interest, Expected discounted penalty function

中图分类号: 

  • 60J75