Models and Algorithms for Portfolio Optimization Under Uncertainty

This dissertation consists of four papers addressing different aspects of financial portfolio optimization problems. The first paper studies an extended set of Mean-Gini models and explores the properties of the reward-to-variability Mean-Gini Ratio performance measure. Compared to other mean-risk models, the performances of Gini-based models are evaluated via an empirical cross-validation test based on different market trend patterns. The second paper develops an interactive solution procedure to help an investor with implicit utility function search for the optimal portfolio among the efficient portfolios through a reasonable number of pari-wise comparisons. The effectiveness of the proposed interactive procedure and performance of optimal portfolios corresponding to a range of utility functions are assessed via computational tests. In the third paper, we propose a class of new stochastic risk budgeting multi-portfolio optimization models with marginal risk contribution constraints. Each model takes the form of chance-constrained stochastic programming problem using a joint chance constraint with random technology matrix. A sparse set of mixed-integer linear programming formulations based on a combinatorial modeling framework are developed to solve the problems efficiently. The numerical tests studies the performance of proposed models, the impacts of parameters and diversification types. The fourth paper analyze a class DRR of distributionally robust optimization problems, which include fractional functions risk-reward ratios. We develop a reformulation and algorithmic data-driven framework based on the Wasserstein metric to model ambiguity and to derive a probabilistic guarantee that the ambiguity set contains the true probability distribution. We design two bisection algorithms with finite convergence property to efficiently solve the reformulation. We specify ambiguous portfolio optimization models for the Sharpe, Sortino, Sortino-Satchel, and Omega ratios.