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

Chengguo Weng (), Yi Zhang () and Ken Seng Tan ()
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Chengguo Weng: University of Waterloo
Yi Zhang: Zhejiang University
Ken Seng Tan: University of Waterloo

Methodology and Computing in Applied Probability, 2013, vol. 15, issue 3, 655-682

Abstract: 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.

Keywords: Asymptotics; Poisson shot noise; Regular variation; Ruin probability; Stop-loss insurance; Tail probability; Upper tail dependence; 62E20; 62P05; 60F10 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s11009-011-9274-3

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