On the ruin probability of a generalized Cramér–Lundberg model driven by mixed Poisson processes

IF 0.7 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Applied Probability Pub Date : 2022-09-01 DOI:10.1017/jpr.2021.99

Masashi Tomita, Koichiro Takaoka, Motokazu Ishizaka

引用次数: 0

Abstract

Abstract We propose a generalized Cramér–Lundberg model of the risk theory of non-life insurance and study its ruin probability. Our model is an extension of that of Dubey (1977) to the case of multiple insureds, where the counting process is a mixed Poisson process and the continuously varying premium rate is determined by a Bayesian rule on the number of claims. We use two proofs to show that, for each fixed value of the safety loading, the ruin probability is the same as that of the classical Cramér–Lundberg model and does not depend on either the distribution of the mixing variable of the driving mixed Poisson process or the number of claim contracts.

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混合泊松过程驱动下的广义cram - lundberg模型的破产概率

摘要提出了一种非寿险风险理论的广义cram r - lundberg模型，并对其破产概率进行了研究。我们的模型是Dubey(1977)的模型的扩展，适用于多个被保险人的情况，其中计数过程是混合泊松过程，连续变化的保费率由索赔数量的贝叶斯规则决定。我们用两个证明表明，对于每一个固定的安全荷载值，破产概率与经典的cram r - lundberg模型相同，并且不依赖于驱动混合泊松过程的混合变量的分布或索赔合同的数量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Applied Probability 数学-统计学与概率论

CiteScore

1.50

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.