Abstract
We illustrate the classical Markowitz portfolio optimization theory in detail, and we give all essential proofs. Especially we show how to explicitly calculate the efficient border and the market portfolio in the case where short selling is possible without restrictions. In the case without short selling, we will work with Monte Carlo. We also introduce the single-index model as an alternative to estimate parameters needed for portfolio optimization. Then we formulate the optimal investment and consumption problem. We give a heuristic and intuitive introduction to the basic techniques of stochastic optimal control, especially to the Hamilton-Jacobi-Bellman equations and to their application. With the help of these concepts, we solve the optimal investment and consumption problem and discuss the results.
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