Two-stage portfolio optimization with higher-order conditional measures of risk

OF THE DISSERTATION Two-Stage Portfolio Optimization with Higher-Order Conditional Measures of Risk by Sıtkı Gülten Dissertation Director: Dr. Andrzej Ruszczyński In this study, an application of novel risk modeling and optimization techniques to daily portfolio management will be described. In the first part, I develop and compare specialized methods for scenario generation and scenario tree construction. The quality of multi-stage stochastic optimization models depends heavily on the quality of the underlying scenario model. First, multivariate GO-GARCH model is used to generate adequate number of scenarios. Then, five different methods, a multi-facility location based backward scenario tree generation method, and forward and backward modified K-Means and Two-Step Cluster methods are used to generate scenario trees. Next, these five methods are tested on two-stage portfolio problems with different number of scenario sets. Finally, a Monge-Kantorovich transportation model is developed to compare the probability distribution of the GARCH-generated scenarios with the probability distribution in the constructed scenario trees.