A reinsurance risk model with a threshold coverage policy: the Gerber–Shiu penalty function. (4th April 2017)

• Record Type: Journal Article
• Authors: Boxma, Onno J.; Frostig, Esther; Perry, David
• Is Part Of: Journal of applied probability. Volume 54:Number 1(2017)
• Page Start: 267
• Page End: 285
• Publication Date: 2017-04-04
• Subjects: Spectrally negative Lévy process, -- scale function, -- ruin probability, -- claim refraction; Primary 60G51, -- Secondary 91B30; 519.2
• DOI: 10.1017/jpr.2016.99
• Languages: English
• ISSNs: 0021-9002

Abstract

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.