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Optimal dividend-payout in random discrete time

Albrecher Hansjörg, Bäuerle Nicole and Thonhauser Stefan
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Bäuerle Nicole: University of Karlsruhe (TH), Institute für Stochastics, Karlsruhe, Deutschland
Thonhauser Stefan: University of Lausanne, Faculty of Business and Economics, Lausanne

Statistics & Risk Modeling, 2011, vol. 28, issue 3, 251-276

Abstract: Assume that the surplus process of an insurance company is described by a general Lévy process and that possible dividend pay-outs to shareholders are restricted to random discrete times which are determined by an independent renewal process. Under this setting we show that the optimal dividend pay-out policy is a band-policy. If the renewal process is a Poisson process, it is further shown that for Cramér–Lundberg risk processes with exponential claim sizes and its diffusion limit the optimal policy collapses to a barrier-policy. Finally, a numerical example is given for which the optimal bands can be calculated explicitly. The random observation procedure studied in this paper also allows for an interpretation in terms of a random walk model with a certain type of random discounting.

Date: 2011
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