Limit theorems for local cumulative shock models with cluster shock structure
type: Item
instance of: scholarly article
title: Limit theorems for local cumulative shock models with cluster shock structure
zbMATH Open document ID: 1394.91186
DOI: 10.1155/2015/828979
author: Yun Chen
author: Chun Yuan
author: Xiaoling Yin
author: Jianming Bai
published in: Mathematical Problems in Engineering
publication date: 2018-08-27T00:00:00Z
review text: Summary: 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 \(\alpha\)-stable law. Also, by choosing the proper scale parameters, the process converges to a normal distribution.
Mathematics Subject Classification ID: 91B30
zbMATH DE Number: 6927334
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/828979
OpenAlex ID: W1981982133
Wikidata QID: Q59119587
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description: scientific article; zbMATH DE number 6927334