In this thesis we integrate discrete dividends into the stock model, estimate future outstanding dividend payments and solve different portfolio optimization problems. Therefore, we discuss three well-known stock models, including discrete dividend payments and evolve a model, which also takes early announcement into account. In order to estimate the future outstanding dividend payments, we develop a general estimation framework. First, we investigate a model-free, no-arbitrage methodology, which is based on the put-call parity for European options. Our approach integrates all available option market data and simultaneously calculates the market-implied discount curve. We illustrate our method using stocks of European blue-chip companies and show within a statistical assessment that the estimate performs well in practice. As American options are more common, we additionally develop a methodology, which is based on market prices of American at-the-money options. This method relies on a linear combination of no-arbitrage bounds of the dividends, where the corresponding optimal weight is determined via a historical least squares estimation using realized dividends. We demonstrate our method using all Dow Jones Industrial Average constituents and provide a robustness check with respect to the used discount factor. Furthermore, we backtest our results against the method using European options and against a so called simple estimate. In the last part of the thesis we solve the terminal wealth portfolio optimization problem for a dividend paying stock. In the case of the logarithmic utility function, we show that the optimal strategy is not a constant anymore but connected to the Merton strategy. Additionally, we solve a special optimal consumption problem, where the investor is only allowed to consume dividends. We show that this problem can be reduced to the before solved terminal wealth problem.