广义Polya-Aeppli分布下相依风险模型的破产概率

数学理论与应用 ›› 2017, Vol. 37 ›› Issue (2): 48-59.

广义Polya-Aeppli分布下相依风险模型的破产概率

刘元勋, 赵佃立

上海理工大学理学院

出版日期:2017-06-30 发布日期:2020-09-23
基金资助:
国家自然科学基金青年基金资助项目(11671260)

Ruin Probability of a Dependent Risk Model with Generalized Polya-Aeppli Distribution

Liu Yuanxun, Zhao Dianli

College of Science,University of Shanghai for Science and Technology

Online:2017-06-30 Published:2020-09-23

摘要/Abstract

摘要：

本文基于广义Polya-Aeppli分布研究两个赔偿过程具有相关性的破产概率问题.首先,结合Kocherlakota(1995)定义的概率母函数推导一类相依过程的联合概率分布函数及其各阶矩的具体表达式;然后,建立两种情况的破产模型,通过Laplace变换将求解破产概率转换为求解累积赔偿金额的概率分布函数,给出赔偿金额服从指数分布时两类风险模型的破产概率解析表达式.广义Polya-Aeppli分布定义了一类具有相关性的离散分布,克服了已有模型中使用Poisson过程模拟实际数据存在的过分分散问题,且易于进行参数估计,所以本文所得结论具有更广泛的适用性.

关键词: 广义Polya-Aeppli分布, 风险模型, Laplace变换, 破产概率, 累积赔偿金额

Abstract:

In this paper,we study the ruin probability of a risk model with two dependent compensation processes based on the generalized Polya-Aeppli distribution.Firstly,the joint probability distribution function and the precise expressions of moments for a class of dependent processes are derived by applying the probability generating function defined by Kocherlakota (1995).Then two kinds of ruin models are formulated,and the corresponding ruin probabilities are obtained by using the Laplace transformation to covert computing ruin probability to calculating probability distribution function of the cumulative claims when the claims follow the exponential distribution.The generalized Polya-Aeppli distribution defines a class of discrete distributions with correlation.It overcomes the over-dispersion problem of the actual data which cannot be modeled by Poisson process,and is easy to estimate the parameters.Thus our approach has a wide range of applicability.

Key words:

"> , Generalized Polya-Aeppli distribution, Risk model, Laplace transform, Ruin probability, Cumulative claims

刘元勋, 赵佃立. 广义Polya-Aeppli分布下相依风险模型的破产概率[J]. 数学理论与应用, 2017, 37(2): 48-59.

Liu Yuanxun, Zhao Dianli.

Ruin Probability of a Dependent Risk Model with Generalized Polya-Aeppli Distribution [J]. Mathematical Theory and Applications, 2017, 37(2): 48-59.

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