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Tail Behavior of Poisson Shot Noise Processes under Heavy-tailed Shocks and Actuarial Applications

Author

Listed:
  • Chengguo Weng

    (University of Waterloo)

  • Yi Zhang

    (Zhejiang University)

  • Ken Seng Tan

    (University of Waterloo
    Central University of Finance and Economics)

Abstract

This paper considers the tail behavior of Poisson shot noise processes where the shock random variables are generally dependent but bivariate upper tail independent. Some uniform asymptotic relations are established for tail probabilities of the process. As the Poisson shot noise process can capture the effects of delay factors and the interest factor in the insurance business, these established results are very useful in many insurance applications. As examples, they are applied to two important actuarial topics: ruin probabilities and insurance premium approximation.

Suggested Citation

  • Chengguo Weng & Yi Zhang & Ken Seng Tan, 2013. "Tail Behavior of Poisson Shot Noise Processes under Heavy-tailed Shocks and Actuarial Applications," Methodology and Computing in Applied Probability, Springer, vol. 15(3), pages 655-682, September.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:3:d:10.1007_s11009-011-9274-3
    DOI: 10.1007/s11009-011-9274-3
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    References listed on IDEAS

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    1. Cline, D. B. H. & Samorodnitsky, G., 1994. "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 75-98, January.
    2. Ken Tan & Chengguo Weng & Yi Zhang, 2009. "VAR and CTE Criteria for Optimal Quota-Share and Stop-Loss Reinsurance," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(4), pages 459-482.
    3. Torrisi, G. L., 2004. "Simulating the ruin probability of risk processes with delay in claim settlement," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 225-244, August.
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    Cited by:

    1. Yiqing Chen, 2019. "A Renewal Shot Noise Process with Subexponential Shot Marks," Risks, MDPI, vol. 7(2), pages 1-8, June.

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