On the complete monotonicity of the compound geometric convolution with applications in risk theory

Sung Nok CHIU, Chuancun Yin

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

We prove that the complete monotonicity is preserved under mixed geometric compounding, and hence show that the ruin probability, the Laplace transform of the ruin time, and the density of the tail of the joint distribution of ruin and the deficit at ruin in the Sparre Andersen model are completely monotone if the claim size distribution has a completely monotone density.

Original languageEnglish
Pages (from-to)116-124
Number of pages9
JournalScandinavian Actuarial Journal
Issue number2
DOIs
Publication statusPublished - 2014

Scopus Subject Areas

  • Statistics and Probability
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • complete monotonicity
  • compound geometric convolution
  • Pollaczeck-Khinchine formula
  • ruin probability
  • Sparre Andersen model

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