NEW RESULTS ON THE DISTRIBUTION OF DISCOUNTED COMPOUND POISSON SUMS

Zhehao Zhang*

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-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 languageEnglish
Pages (from-to)169-187
Number of pages19
JournalASTIN Bulletin
Volume49
Issue number1
DOIs
Publication statusPublished - 1 Jan 2019
Externally publishedYes

Keywords

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

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