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On Exact Solutions for Dividend Strategies of Threshold and Linear Barrier Type in a Sparre Andersen Model*

Published online by Cambridge University Press:  17 April 2015

Hansjörg Albrecher ,
Jürgen Hartinger  and
Stefan Thonhauser
Hansjörg Albrecher
Affiliation:
Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria, and Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria
Jürgen Hartinger
Affiliation:
Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria
Stefan Thonhauser
Affiliation:
Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria
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Abstract

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For the classical Cramér-Lundberg risk model, a dividend strategy of threshold type has recently been suggested in the literature. This strategy consists of paying out part of the premium income as dividends to shareholders whenever the free surplus is above a given threshold level. In contrast to the well-known horizontal barrier strategy, the threshold strategy can lead to a positive infinite-horizon survival probability, with reduced profit in terms of dividend payments. In this paper we extend several of these results to a Sparre Andersen model with generalized Erlang(n)-distributed interclaim times. Furthermore, we compare the performance of the threshold strategy to a linear dividend barrier model. In particular, (partial) integro-differential equations for the corresponding ruin probabilities and expected discounted dividend payments are provided for both models and explicitly solved for n = 2 and exponentially distributed claim amounts. Finally, the explicit solutions are used to identify parameter sets for which one strategy outperforms the other and vice versa.

Keywords

Sparre Andersen modeldividend paymentspiece-wise deterministic Markov processesruin probability
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 37 , Issue 2 , November 2007 , pp. 203 - 233
Copyright
Copyright © ASTIN Bulletin 2007

Footnotes

*

Supported by the Austrian Science Fund Project P-18392.

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