A reinsurance risk model with a threshold coverage policy: The Gerber-Shiu penalty function

O.J. Boxma, E. Frostig, D. Perry

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
69 Downloads (Pure)

Abstract

We consider a Cramér-Lundberg insurance risk process with the added feature of reinsurance. If an arriving claim finds the reserve below a certain threshold γ, or if it would bring the reserve below that level, then a reinsurer pays part of the claim. Using fluctuation theory and the theory of scale functions of spectrally negative Lévy processes, we derive expressions for the Laplace transform of the time to ruin and of the joint distribution of the deficit at ruin and the surplus before ruin. We specify these results in much more detail for the threshold set-up in the case of proportional reinsurance.

Original languageEnglish
Pages (from-to)267-285
Number of pages19
JournalJournal of Applied Probability
Volume54
Issue number1
DOIs
Publication statusPublished - 1 Mar 2017

Keywords

  • claim refraction
  • ruin probability
  • scale function
  • Spectrally negative Lévy process

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