NEW RESULTS ON THE DISTRIBUTION OF DISCOUNTED COMPOUND POISSON SUMS

Zhehao Zhang

ASTIN Bulletin, 2019, vol. 49, issue 1, 169-187

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.

Date: 2019
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