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A new risk model based on policy entrance process and its weak convergence properties

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  • Zehui Li
  • Xinbing Kong

Abstract

In this paper, we construct a new risk model based on the policy entrance process. The model is concerned with n kinds of independent policies, and each policy is allowed to claim more than once before it expires. As each kind of policy is issued according to a non‐homogeneous Poisson process, the long run behaviour of the new risk process is investigated. When the tail of the claim size distribution is regularly varying, the standardized risk process is proved to converge to a stable law. When each kind of policy is issued according to a homogeneous Poisson process, we also give a diffusion approximation of the new risk process. Copyright © 2007 John Wiley & Sons, Ltd.

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  • Zehui Li & Xinbing Kong, 2007. "A new risk model based on policy entrance process and its weak convergence properties," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 23(3), pages 235-246, May.
    • Handle: RePEc:wly:apsmbi:v:23:y:2007:i:3:p:235-246
    DOI: 10.1002/asmb.669
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    Cited by:

    1. Jian-Ming Bai & Zhe Zhang & Ze-Hui Li, 2014. "Lifetime properties of a cumulative shock model with a cluster structure," Annals of Operations Research, Springer, vol. 212(1), pages 21-41, January.
    2. Hongmin Xiao & Lin Xie, 2018. "Asymptotic Ruin Probability of a Bidimensional Risk Model Based on Entrance Processes with Constant Interest Rate," Risks, MDPI, vol. 6(4), pages 1-12, November.

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