Essays on risk and ambiguity

This thesis comprises five research papers on risk measures and decision-making under ambiguity. The first three research papers focus on the risk measures in the multiplicative setting. The first paper provides fundamental theoretical results and definitions for the geometrically convex functionals and demonstrates their use for the risk measures in the multiplicative setting. The second paper focuses on the Orlicz premia, that is, a special class of multiplicative risk measures, by generalizing its definition in the literature, analyzing its properties, and showing that this class is the only elicitable return risk measures. The next paper examines the elicitability property further and provides a plethora of scoring functions for the multiplicative risk measures. The last two papers concentrate more on the decision under ambiguity. Hence, the next paper introduces a risk aversion index for the second degree and higher orders under Yaari’s dual theory and provides a characterization result for these indices. Finally, the last paper suggests model-free and testable definitions of ambiguity aversion and prudence, and characterizes these definitions under the several ambiguity models in the literature.