Essays on distributionally robust portfolio optimization

Interest in distributionally robust optimization has been increasing recently. In this dissertation, we review recent developments in the literature in this field and propose a model for distributionally robust mean-risk portfolio optimization. The model optimizes a risk-averse objective function with the worst-case return as reward and worse-case conditional Value-at-Risk as the risk measure. The model considers ambiguity in the distribution of data used to estimate the asset returns in the optimization model by creating an ambiguity set using &phis;-divergence measures which measure the distance between vectors. A numerical example is shown using the Kullback-Leibler divergence measure as the &phis;-divergence measure. A model for distributionally robust portfolio optimization with transaction costs is used to compare the performance of a distributionally robust mean-CVaR portfolio with the nominal as well as equally-weighted portfolio. The result shows that, under certain conditions, the distributionally robust model performs better than both the nominal and equally-weighted portfolio.