The thesis is concerned with the so called "dividend payout criterion" for evaluation of reserve-processes of insurance companies.
In this context we consider the Compound-Poisson-model and the Diffusion-model. The "dividend payout criterion" leads to the problem of maximization of the expected dividend payout up to the time ruin occurs -- this also means that we have to find the optimal dividend strategy.
This problem is examined in the discrete and the continous case. In the Compound-Poisson-model the thesis is mainly concerned with barrier-strategies and the derivation of the integro-differential-equation, which is satisfied by the function of the expected dividends for barrier-strategies in dependence of the initial capital of the insurance company. In the Diffusion-model the thesis gives the solution for the problem of maximizing the dividend payout for the case of restricted and unrestricted payout-intensity. In this context the methods of controll-theory and the formula of Tanaka are explained. The aim of the section about controll-theory is the presentation of the hamilton-jacobi-bellman-algorithm, which can be applied under some certain conditions. These conditions are also discussed and stated by the so called verification theorems. Finally the case of finite time horizon in the Diffusion-model is considered. In this section three types of barrier-strategies are compared by Monte-Carlo-simulations.