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

Published online by Cambridge University Press:  04 April 2017

Onno J. Boxma
Affiliation:
Eindhoven University of Technology
Esther Frostig
Affiliation:
University of Haifa
David Perry
Affiliation:
University of Haifa Western Galilee College
Corresponding
E-mail address:

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2017 

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References

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