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A Risk Model with Multilayer Dividend Strategy
Authors:Hansjörg Albrecher PhD  Jürgen Hartinger PhD
Institution:1. Graz University of Technology , Steyrergasse 30 , 8010 Graz , Austria;2. Financial Mathematics at the Radon Institute, Austrian Academy of Sciences , Linz;3. Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences , Altenbergerstrasse 69, A-4040 Linz;4. K?rntner Landesversicherung , Domgasse 12, 9020 Klagenfurt , Austria
Abstract:Abstract

In recent years various dividend payment strategies for the classical collective risk model have been studied in great detail. In this paper we consider both the dividend payment intensity and the premium intensity to be step functions depending on the current surplus level. Algorithmic schemes for the determination of explicit expressions for the Gerber-Shiu discounted penalty function and the expected discounted dividend payments are derived. This enables the analytical investigation of dividend payment strategies that, in addition to having a sufficiently large expected value of discounted dividend payments, also take the solvency of the portfolio into account. Since the number of layers is arbitrary, it also can be viewed as an approximation to a continuous surplus-dependent dividend payment strategy. A recursive approach with respect to the number of layers is developed that to a certain extent allows one to improve upon computational disadvantages of related calculation techniques that have been proposed for specific cases of this model in the literature. The tractability of the approach is illustrated numerically for a risk model with four layers and an exponential claim size distribution.
Keywords:
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