Comprehensive Robustness via Moment-based Optimization : Theory and Applications

The use of a stochastic model to predict the likelihood of future outcomes forms an integral part of decision optimization under uncertainty. In classical stochastic modeling uncertain parameters are often assumed to be driven by a particular form of probability distribution. In practice however, the distributional form is often difficult to infer from the observed data, and the incorrect choice of distribution can lead to significant quality deterioration of resultant decisions and unexpected losses. In this thesis, we present new approaches for evaluating expected future performance that do not rely on an exact distributional specification and can be robust against the errors related to committing to a particular specification. The notion of comprehensive robustness is promoted, where various degrees of model misspecification are studied. This includes fundamental one such as unknown distributional form and more involved ones such as stochastic moments and moment outliers. The approaches are developed based on the techniques of moment-based optimization, where bounds on the expected performance are sought based solely on partial moment information. They can be integrated into decision optimization and generate decisions that are robust against model misspecification in a comprehensive manner. In the first part of the thesis, we extend the applicability of moment-based optimization to incorporate new objective functions such as convex risk measures and richer moment information such as higher-order multivariate moments. In the second part, new tractable optimization frameworks are developed that account for various forms of moment uncertainty in the context of decision analysis and optimization. Financial applications such as portfolio selection and option pricing are studied.Ph