NEW RESULTS ON THE DISTRIBUTION OF DISCOUNTED COMPOUND POISSON SUMS

Zhehao Zhang

doi:10.1017/asb.2018.28

NEW RESULTS ON THE DISTRIBUTION OF DISCOUNTED COMPOUND POISSON SUMS

Zhehao Zhang^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	169-187
Number of pages	19
Journal	ASTIN Bulletin
Volume	49
Issue number	1
DOIs	https://doi.org/10.1017/asb.2018.28
Publication status	Published - 1 Jan 2019
Externally published	Yes

Keywords

catastrophe insurance
discounted aggregate claims
heavy tailed
Mittag-Leffler distribution
Poisson risk process

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10.1017/asb.2018.28

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NEW RESULTS ON THE DISTRIBUTION OF DISCOUNTED COMPOUND POISSON SUMS

Abstract

Keywords

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