数学物理学报 ›› 2011, Vol. 31 ›› Issue (2): 415-421.

• 论文 • 上一篇    下一篇

带扰动的经典风险模型中贴现罚函数的渐近估计

张振中1,2|邹捷中2|刘源远2   

  1. 1.东华大学 理学院 上海 201620|2.中南大学数学科学与计算技术学院 长沙 410075
  • 收稿日期:2008-12-04 修回日期:2010-01-08 出版日期:2011-04-25 发布日期:2011-04-25
  • 基金资助:

    国家自然科学基金(10901164)、重庆市教委自然科学基金(2009BB8221)和中央高校基本科研业务费专项资金资助

Asymptotic Estimates of the Discounted Penalty Function in a Perturbed Risk Model

 ZHANG Zhen-Zhong1,2, ZU Jie-Zhong2, LIU Yuan-Yuan2   

  1. 1.Department of Mathematics, School of Science, Donghua University, Shanghai 201620|2. School of Mathematical Science and Computing Technology, Central South University, Changsha 410075
  • Received:2008-12-04 Revised:2010-01-08 Online:2011-04-25 Published:2011-04-25
  • Supported by:

    国家自然科学基金(10901164)、重庆市教委自然科学基金(2009BB8221)和中央高校基本科研业务费专项资金资助

摘要:

该文主要讨论带扰动的经典风险模型中当索赔服从次指数分布时贴现罚函数的渐近表达式. 得到两种情形下由索赔引起的贴现罚函数的精确表达式. 此外, 证明当初始盈余趋近无穷时由扰动引起的贴现罚函数可以忽略.

关键词: 次指数, 贴现罚函数, 扩散

Abstract:

In this paper, the authors focus on asymptotic behavior of the discounted penalty function in the classical risk model perturbed by diffusion when the claim size is sub-exponentially distributed. They obtain the exact asymptotic expressions for  the discounted penalty function caused by  a claim, in two cases: δ>0 and δ=0, where δ denotes the interest force. Moreover, it is showed  that the discounted penalty function caused by oscillation vanishes when the initial reserve goes to infinity.

Key words: Sub-exponential distributions, Discounted penalty function, Diffusion

中图分类号: 

  • 91B30