Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Hansjörg Albrecher
Université de Lausanne
Insurance Risk Theory with Tax and Dividend Payments
In this talk it is shown how a mixture of analytical and probabilistic techniques can be used to assess the
effect of dividend and tax payments on the solvency of an insurance portfolio. This will be illustrated both
for the classical risk model and some of its extensions. It will also be discussed how symbolic techniques
and links between risk theory and queueing theory can enrich the set of tools for these investigations.
Nicole Bäuerle
Karlsruhe Institute of Technology (KIT), Karlsruhe
Optimal Dividend-Payout in Random Discrete Time
We 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 so-called 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. Some numerical examples are presented for which the optimal bands
can be calculated explicitly. This is joint work with H. Albrecher and S. Thonhauser.
Julia Eisenberg
Technische Universität Wien
Optimal Control of Capital Injections by Reinsurance With and Without Regime Switching
We consider an insurance company, where the claims are reinsured by some reinsurance. Concerning the
surplus of the insurance company two different cases are studied. In the first case the surplus process is
supposed to follow a diffusion; in the second case we let the drift and the volatility of the diffusion-surplus
depend on an observable continuous-time Markov chain. This Markov chain represents regime switching
- the macroeconomic changes impacting the parameters of our model.
Our objective is to minimize the value of expected discounted capital injections, which are necessary to
keep the risk process above zero. Thus, we goal to find the value function defined as the infimum of
expected discounted capital injections over all reinsurance strategies; and to derive the optimal strategy
leading to the value function.
Whereas in the case of a “simple” diffusion the value function is an exponential function, things are
different in the case of regime switching. A general form explicit solution could not be given. However,
we illustrate how the value function can be calculated by a simple example with a two states Markov chain.
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