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New Results On The Distribution Of Discounted Compound Poisson Sums

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  • Zhang, Zhehao

Abstract

This paper focuses on the distribution of Poisson sums of discounted claims over a finite or infinite time period. It gives two new results when claim amounts follow Mittag-Leffler distributions and two new results when claim amounts follow gamma distributions. Further, as Mittag-Leffler distribution is of heavy-tailed nature and its moments only exist for order strictly smaller than one, this distribution can be used for modelling insurance whose claim amounts are extremely large, that is, catastrophe insurance.

Suggested Citation

  • Zhang, Zhehao, 2019. "New Results On The Distribution Of Discounted Compound Poisson Sums," ASTIN Bulletin, Cambridge University Press, vol. 49(1), pages 169-187, January.
    • Handle: RePEc:cup:astinb:v:49:y:2019:i:01:p:169-187_00
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    1. Zhang, Zhehao, 2019. "On the stochastic equation L(Z)=L[V(X+Z)] and properties of Mittag–Leffler distributions," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 365-376.

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