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Limit Theorems for Local Cumulative Shock Models with Cluster Shock Structure

机译：具有簇冲击结构的局部累积冲击模型的极限定理

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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 alpha-stable law. Also, by choosing the proper scale parameters, the process converges to a normal distribution.
机译：本文考虑了一个具有保险和金融风险背景的更一般的冲击模型，其中该系统受到两种类型的冲击的影响，即主要冲击和次要冲击。每个主冲击会根据某些簇模式而导致一系列次冲击。在可靠性应用中，一次冲击可以代表一个保险公司的保险单问题，而二次冲击则表示该保单产生的相关保险索赔。我们专注于局部累积冲击过程，其中仅累积了一定数量的最新一次和二次冲击。在现有文献中，此过程是一个非常新的主题，在建模一些更复杂的可靠性情况（如保险公司的破产行为）时，该过程更加灵活和现实。基于无限可分和稳定分布的理论，我们为局部累积冲击过程建立了一个中心极限定理，并为该过程收敛到无限可分分布或α稳定定律提供了条件。同样，通过选择适当的比例参数，该过程收敛到正态分布。

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  • 来源
    《Mathematical Problems in Engineering》 |2015年第5期|828979.1-828979.10|共10页
  • 作者

    Bai Jianming; Chen Yun; Yuan Chun; Yin Xiaoling;

  • 作者单位

    Lanzhou Univ, Sch Management, Lanzhou 730000, Peoples R China.;

    Lanzhou Univ, Sch Management, Lanzhou 730000, Peoples R China.;

    Lanzhou Univ, Sch Management, Lanzhou 730000, Peoples R China.;

    Lanzhou Univ, Sch Management, Lanzhou 730000, Peoples R China.;

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