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

Onno J. Boxma, Esther Frostig, David Perry

Research output: Contribution to journalArticlepeer-review

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
StatePublished - 1 Mar 2017

Bibliographical note

Funding Information:
The research of David Perry was partially supported by the German-Israel Science Foundation (grant number 1-1184-31.4/2012) and the Israel Science Foundation (grant number 1071/14).

Publisher Copyright:
Copyright © 2017 Applied Probability Trust.

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (all)
  • Statistics, Probability and Uncertainty

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