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

Published online by Cambridge University Press:  06 June 2022

Jiayi Xie ,
Wenguang Yu ,
Zhimin Zhang Open the ORCID record for Zhimin Zhang [Opens in a new window]  and
Zhenyu Cui Open the ORCID record for Zhenyu Cui [Opens in a new window]
Jiayi Xie
Affiliation:
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P.R. China. E-mail: zmzhang@cqu.edu.cn
Wenguang Yu
Affiliation:
School of Insurance, Shandong University of Finance and Economics, Jinan 250014, P.R. China.
Zhimin Zhang
Affiliation:
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, P.R. China. E-mail: zmzhang@cqu.edu.cn
Zhenyu Cui
Affiliation:
School of Business, Stevens Institute of Technology, Hoboken, NJ, USA
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Abstract

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.

Keywords

Compound Poisson modelGerber-Shiu functionLaguerre series expansionPeriodic observation
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Special Issue 2: Probability and stochastic modeling in actuarial science and related fields , April 2023 , pp. 324 - 356
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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