恒定观测间隔时间的复合泊松模型中的Gerber-Shiu分析

IF 0.7 3区工程技术 Q4 ENGINEERING, INDUSTRIAL

Probability in the Engineering and Informational Sciences Pub Date : 2022-06-06 DOI:10.1017/S0269964822000092

Jiayi Xie, Wenguang Yu, Zhimin Zhang, Zhenyu Cui

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引用次数: 2

摘要

本文研究了周期观测下的经典复合泊松模型。与文献中广泛使用的随机观测假设不同，我们假设观测间时间为常数。在该模型中，利用Laguerre级数展开方法研究了有限时间和无限时间Gerber-Shiu函数。我们证明了膨胀系数可以递归确定，并详细分析了逼近误差。给出了几种索赔尺寸密度函数的数值结果，验证了该方法的有效性，并对一些参数的影响进行了研究。

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Gerber-Shiu analysis in the compound Poisson model with constant inter-observation times

In this paper, the classical compound Poisson model under periodic observation is studied. Different from the random observation assumption widely used in the literature, we suppose that the inter-observation time is a constant. In this model, both the finite-time and infinite-time Gerber-Shiu functions are studied via the Laguerre series expansion method. We show that the expansion coefficients can be recursively determined and also analyze the approximation errors in detail. Numerical results for several claim size density functions are given to demonstrate effectiveness of our method, and the effect of some parameters is also studied.

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来源期刊

Probability in the Engineering and Informational Sciences 数学-工程：工业

CiteScore

2.20

自引率

18.20%

发文量

审稿时长

>12 weeks

期刊介绍： The primary focus of the journal is on stochastic modelling in the physical and engineering sciences, with particular emphasis on queueing theory, reliability theory, inventory theory, simulation, mathematical finance and probabilistic networks and graphs. Papers on analytic properties and related disciplines are also considered, as well as more general papers on applied and computational probability, if appropriate. Readers include academics working in statistics, operations research, computer science, engineering, management science and physical sciences as well as industrial practitioners engaged in telecommunications, computer science, financial engineering, operations research and management science.