This diploma thesis is concerned with the evaluation, in which way companies, that invest into the market, can develop a optimal dividend strategy. For this particular matter we have discussed value functions which involve the payment of the dividends, as well as the time of ruin. Therefore a short look at the most important facts about risk and ruin theory has been taken previously. In addition, this paper involves restricted and unrestricted dividend payments. Furthermore the value function, as well as the probability of ruin has been described with the assistance of the infinitesimal generator and two examples have been studied with those results. In the following section, a short insight of the evaluation of the value function and the ruin probability, through a time dependend barrier has been given. At the end of this diploma thesis, the theoretical results of the diffusion model have been verified through Monte-Carlo-simulations which have been realized with the program language Matlab.