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NEW RESULTS ON THE DISTRIBUTION OF DISCOUNTED COMPOUND POISSON SUMS

Published online by Cambridge University Press:  03 December 2018

Zhehao Zhang
Zhehao Zhang*
Affiliation:
Centre for Actuarial Studies, Department of Economics, The University of Melbourne, 111 Barry Street, Victoria 3010, Australia E-Mail: zhehaoz1@student.unimelb.edu.au
*
E-Mail: zhehaoz1@student.unimelb.edu.au
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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.

Keywords

Poisson risk processdiscounted aggregate claimsMittag-Leffler distributionheavy tailedcatastrophe insurance
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 1 , January 2019 , pp. 169 - 187
Copyright
Copyright © Astin Bulletin 2018 

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