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

Part of: Mathematical economics Stochastic processes

Published online by Cambridge University Press:  04 April 2017

Onno J. Boxma ,
Esther Frostig  and
David Perry
Onno J. Boxma*
Affiliation:
Eindhoven University of Technology
Esther Frostig*
Affiliation:
University of Haifa
David Perry*
Affiliation:
University of Haifa Western Galilee College
*
* Postal address: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands.
** Postal address: Department of Statistics, University of Haifa, Haifa, 31905, Israel.
** Postal address: Department of Statistics, University of Haifa, Haifa, 31905, Israel.
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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 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.

Keywords

Spectrally negative Lévy processscale functionruin probabilityclaim refraction

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes
Secondary: 91B30: Risk theory, insurance

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 1 , March 2017 , pp. 267 - 285
Copyright
Copyright © Applied Probability Trust 2017 

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