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Ruin excursions, the G/G/∞ queue, and tax payments in renewal risk models

Part of: Mathematical economics Special processes

Published online by Cambridge University Press:  14 July 2016

Hansjörg Albrecher ,
Sem C. Borst ,
Onno J. Boxma  and
Jacques Resing
Hansjörg Albrecher
Affiliation:
University of Lausanne and Swiss Finance Institute, Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, Quartier UNIL-Dorigny, 1015 Lausanne, Switzerland. Email address: hansjoerg.albrecher@unil.ch
Sem C. Borst
Affiliation:
Eindhoven University of Technology and Alcatel-Lucent, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
Onno J. Boxma
Affiliation:
Eindhoven University of Technology and EURANDOM, Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
Jacques Resing
Affiliation:
Eindhoven University of Technology, Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
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Abstract

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In this paper we investigate the number and maximum severity of the ruin excursion of the insurance portfolio reserve process in the Cramér–Lundberg model with and without tax payments. We also provide a relation of the Cramér–Lundberg risk model with the G/G/∞ queue and use it to derive some explicit ruin probability formulae. Finally, the renewal risk model with tax is considered, and an asymptotic identity is derived that in some sense extends the tax identity of the Cramér– Lundberg risk model.

Keywords

Classical risk modelruin probabilityG/G/∞ queuetaxrenewal model

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Part 1. Risk Theory
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 3 - 14
Copyright
Copyright © Applied Probability Trust 2011 

References

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