Limit theorems for local cumulative shock models with cluster shock structure
Bai, JM(白建明); Yun Chen; Chun Yuan; Xiaoling Yin
2015
发表期刊Mathematical Problems in Engineering
ISSN1024-123X
卷号2015期号:2015页码:1-11
出版者HINDAWI
摘要This paper considers a more general shock model with insurance and financial risk background, in which the system is subject to two types of shocks called primary shocks and secondary shocks. Each primary shock causes a series of secondary shocks according to some cluster pattern. In reliability applications, a primary shock can represent an issue of insurance policies of an insurer company, and the secondary shocks then denote the relevant insurance claims generated by the policy. We focus on the local cumulative shock process where only a certain number of the most recent primary and secondary shocks are accumulated. This process is a very new topic in the available literature which is more flexible and realistic in modeling some more complex reliability situations such as bankrupt behavior of an insurance company. Based on the theory of infinite divisibility and stable distributions, we establish a central limit theorem for the local cumulative shock process and obtain the conditions for the process to converge to an infinitely divisible distribution or to an α -stable law. Also, by choosing the proper scale parameters, the process converges to a normal distribution. © 2015 Jianming Bai et al.
出版地NEW YORK
关键词Insurance Normal distribution Central Limit Theorem Cumulative shock models Infinite divisibility Infinitely divisible distributions Insurance companies Insurance policies Reliability applications Stable distributions
作者部门兰州大学
DOI10.1155/2014/603863
文章类型Article
收录类别SCIE ; EI
所属项目编号国家自然科学基金
语种英语
资助项目国家自然科学基金项目
项目资助者NSFC
WOS记录号WOS:000354686000001
EI记录号20151500743480
IR记录号20151500743480
第一机构
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文献类型期刊论文
条目标识符http://ir.lzu.edu.cn/handle/262010/107818
Collection管理学院_工商管理&公共管理&信息管理
Recommended Citation:
GB/T 7714
Jianming Bai,Yun Chen,Chun Yuan,et al. Limit theorems for local cumulative shock models with cluster shock structure[J]. Mathematical Problems in Engineering,2015,2015(2015):1-11.
APA Jianming Bai,Yun Chen,Chun Yuan,&Xiaoling Yin.(2015).Limit theorems for local cumulative shock models with cluster shock structure.Mathematical Problems in Engineering,2015(2015),1-11.
MLA Jianming Bai,et al."Limit theorems for local cumulative shock models with cluster shock structure".Mathematical Problems in Engineering 2015.2015(2015):1-11.
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