OPTIMIZATION FOR DECISION MAKERS WITH AMBIGUOUS PREFERENCES

Abstract

The fundamental goal of this thesis is to build optimization frameworks for decision makers with ambiguous preferences under different conditions. Specifically, we firstly propose a new stochastic dominance relationship in which utility functions are weighted against a reference utility for risk-averse decision makers. The necessary and sufficient conditions are provided. We then formulate our proposed weighted almost stochastic dominance in our optimization framework by convex function interpolation and subgradient characterization. We will resort to linear programming and its duality as our technique.

We next extend the concept of almost stochastic dominance to random variables with normal and log-normal probability distributions, and apply the results to mean-variance analysis and MGM strategy. We show how we could calculate the amount of dominance by which a normally or log-normally distributed reward dominates another by almost stochastic dominance and determine the set of utility functions such that one prospect dominates the other.

We then provide a more general optimization framework that considers the following four factors: multivariate prospects, preference uncertainty, computational tractability, target-oriented measure. Two approaches, subgradient characterization and acceptance set approach are considered.