Randomized observation periods for the compound Poisson risk model: the discounted penalty function

Hansjörg Albrecher*, Eric C.K. Cheung, Stefan Thonhauser

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

In the framework of collective risk theory, we consider a compound Poisson risk model for the surplus process where the process (and hence ruin) can only be observed at random observation times. For Erlang(n) distributed inter-observation times, explicit expressions for the discounted penalty function at ruin are derived. The resulting model contains both the usual continuous-time and the discrete-time risk model as limiting cases, and can be used as an effective approximation scheme for the latter. Numerical examples are given that illustrate the effect of random observation times on various ruin-related quantities.

Original languageEnglish
Pages (from-to)424-452
Number of pages29
JournalScandinavian Actuarial Journal
Issue number6
DOIs
Publication statusPublished - 1 Nov 2013
Externally publishedYes

Keywords

  • compound Poisson risk model
  • defective renewal equation
  • discounted density
  • Erlangization
  • Gerber-Shiu function

ASJC Scopus subject areas

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

Fields of Expertise

  • Information, Communication & Computing

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