Portfolio optimization under different risk measures and returns distributions with usage of genetic algorithm

There is a normally distributed assets returns assumption in majority of optimization models. In reality those returns are not normally distributed, which affects measure of risk and found solution. This thesis is focused on alternative distributions, which are possibly better for modeling assets returns and their potential usage in portfolio optimization. Further in thesis, there are described different measures of risk often used in portfolio theory and their application to Markowitz model. This model is with its normally distributed returns assumption described and other existing models, that emphasizes on violation of this assumption are presented. The core of this thesis is then presenting of genetic algorithm, that lets us in its each step estimate best possible distribution of returns and compute required statistics on estimated distribution, which should lead to possibly more accurate results in comparison with classical Markowitz model. Abbilities of genetic algorithm are then shown on real data of returns of selected assets from Czech and American assets. Effect of violation of normally distributed returns assumptions is shown on different risk measures. In the end of thesis, portfolio with complex but rational conditions is found. This portfolio serves not only as possible quide for investing, but also as a proof of ability of genetic algorithm of solving complex model.