数学物理学报 ›› 2011, Vol. 31 ›› Issue (3): 737-751.

• 论文 • 上一篇    下一篇

一类基于进入过程的风险模型的精细大偏差

唐风琴1|李泽慧2|陈进源2   

  1. 1.淮北师范大学数学科学学院 安徽淮北 235000;  2.兰州大学数学与统计学院 兰州 730000
  • 收稿日期:2009-03-01 修回日期:2010-05-09 出版日期:2011-06-25 发布日期:2011-06-25
  • 基金资助:

    国家自然科学基金(10871086)和高等学校博士学科点专项科研基金(20050730002)资助

The Precise Large Deviations for a Risk Model Based on the Policy Entrance Process

 TANG Feng-Qin1, LI Ze-Hui2, CHEN Jin-Yuan2   

  1. 1.School of Mathematics Sciences, Huaibei |Normal University, Anhui Huaibei 235000|2.School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000
  • Received:2009-03-01 Revised:2010-05-09 Online:2011-06-25 Published:2011-06-25
  • Supported by:

    国家自然科学基金(10871086)和高等学校博士学科点专项科研基金(20050730002)资助

摘要:

Li和Kong[1]提出了一类基于进入过程的具有多种独立保单的风险模型并在时间趋于无穷大时对保险公司盈余资产的渐进分布作了研究. 该文探讨了这类模型的大偏差. 当索赔尾部为C(consistently varying)族时, 分别得到了具有单种保单和多种独立保单的模型的大偏差, 所得结果丰富了相应的发射噪声过程的大偏差.

关键词: 大偏差, 风险过程, Consistently varying, 发射噪声过程, 重尾分布

Abstract:

Li and Kong[1] constructed a new risk model based on the policy entrance process which involves multiple kinds of independent policies, and studied the asymptotic behavior of the surplus when time goes to infinity. In this paper the authors investigate large derivations for this model. The authors obtain the precise large deviations with both single and multiple kinds of independent
policies when the tail of the claim size is consistently varying. The  results extend the related large deviation results for shot noise processes.

Key words: Large deviations, Risk process, Consistently varying, Shot noise process, Heavy-tailed distribution

中图分类号: 

  • 60F10