Limit Theorems for Local Cumulative Shock Models with Cluster Shock Structure
Joint Authors
Bai, Jianming
Chen, Yun
Yuan, Chun
Yin, Xiaoling
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-03-25
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
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 andsecondary shocks.
Each primary shock causes a series of secondary shocks according tosome cluster pattern.
In reliability applications, a primary shock can represent an issueof insurance policies of an insurer company, and the secondary shocks then denote therelevant insurance claims generated by the policy.
We focus on the local cumulative shockprocess where only a certain number of the most recent primary and secondary shocksare accumulated.
This process is a very new topic in the available literature which ismore flexible and realistic in modeling some more complex reliability situations such asbankrupt behavior of an insurance company.
Based on the theory of infinite divisibilityand stable distributions, we establish a central limit theorem for the local cumulativeshock process and obtain the conditions for the process to converge to an infinitely divisibledistribution or to an α-stable law.
Also, by choosing the proper scale parameters, theprocess converges to a normal distribution.
American Psychological Association (APA)
Bai, Jianming& Chen, Yun& Yuan, Chun& Yin, Xiaoling. 2015. Limit Theorems for Local Cumulative Shock Models with Cluster Shock Structure. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-10.
https://search.emarefa.net/detail/BIM-1074835
Modern Language Association (MLA)
Bai, Jianming…[et al.]. Limit Theorems for Local Cumulative Shock Models with Cluster Shock Structure. Mathematical Problems in Engineering No. 2015 (2015), pp.1-10.
https://search.emarefa.net/detail/BIM-1074835
American Medical Association (AMA)
Bai, Jianming& Chen, Yun& Yuan, Chun& Yin, Xiaoling. Limit Theorems for Local Cumulative Shock Models with Cluster Shock Structure. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-10.
https://search.emarefa.net/detail/BIM-1074835
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074835