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

Jiayi Xie, Wenguang Yu, Zhimin Zhang, Zhenyu Cui

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Pages (from-to)324-356
Number of pages33
JournalProbability in the Engineering and Informational Sciences
Volume37
Issue number2
DOIs
StatePublished - 1 Apr 2023

Keywords

  • Compound Poisson model
  • Gerber-Shiu function
  • Laguerre series expansion
  • Periodic observation

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