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

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

Research output: Book/ReportReportAcademic

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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 ¿, 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 with proportional reinsurance.
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages22
Publication statusPublished - 2015

Publication series

NameReport Eurandom
Volume2015018
ISSN (Print)1389-2355

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