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An Approximation Model of the Collective Risk Model with INAR(1) Claim Process

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  • Haifang Shi
  • Dehui Wang

Abstract

Cossette et al. (2010, 2011) gave a novel collective risk model where the total numbers of claims satisfy the first-order integer-valued autoregressive process. For a risk model, it is interesting to investigate the upper bound of ruin probability. However, the loss increments of the above model are dependent; it is difficult to derive the upper bound of ruin probability. In this article, we propose an approximation model with stationary independent increments. The upper bound of ruin probability and the adjustment coefficient are derived. The approximation model is illustrated via four simulated examples. Results show that the gap of the approximation model and dependent model can be ignored by adjusting values of parameters.

Suggested Citation

  • Haifang Shi & Dehui Wang, 2014. "An Approximation Model of the Collective Risk Model with INAR(1) Claim Process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(24), pages 5305-5317, December.
    • Handle: RePEc:taf:lstaxx:v:43:y:2014:i:24:p:5305-5317
    DOI: 10.1080/03610926.2012.729636
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    Cited by:

    1. Kai Yang & Han Li & Dehui Wang & Chenhui Zhang, 2021. "Random coefficients integer-valued threshold autoregressive processes driven by logistic regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(4), pages 533-557, December.
    2. Kai Yang & Yao Kang & Dehui Wang & Han Li & Yajing Diao, 2019. "Modeling overdispersed or underdispersed count data with generalized Poisson integer-valued autoregressive processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(7), pages 863-889, October.

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