Van Oosten, Zachary2026-06-122026-06-122026-06-122026-05-21https://hdl.handle.net/10012/23600This thesis develops new decision models under ambiguity that accommodate arbitrary reductions in the absence of ambiguity, that is, models not restricted to expected utility (EU) under pure risk (no ambiguity). A central challenge is the identifiability problem: from preferences alone, one cannot distinguish which features of the representation functional reflect the decision maker's evaluation of pure risk from those that reflect their reaction to ambiguity. To resolve this, we exogenously specify a family of unambiguous events and employ the property of partial law invariance: the DM is indifferent between unambiguous acts with the same distribution. The resulting models developed across the four chapters outlined below are relevant to decision theory, quantitative risk management, mathematical finance, and operations research. Chapter 2 studies partial law invariance in the context of risk measures. We fully characterize partially law-invariant coherent risk measures via a novel representation formula and extend the classical Kusuoka representation. Additionally, we propose new risk measures, including partially law-invariant versions of Expected Shortfall and entropic risk measures, along with tractable formulas for their calculation. Chapter 3 axiomatizes the Choquet rank-dependent utility (CRDU) model, which cleanly separates pure risk from ambiguity and reduces to rank-dependent utility in the absence of ambiguity. We show that the coupling of ambiguity perception and ambiguity attitude can be fully characterized by the matching probability, and that the supermodularity of this matching probability gives CRDU a distributionally robust interpretation. Chapter 4 distinguishes two conceptual frameworks for processing ambiguity: evaluate-then-aggregate (ETA), which first evaluates an act under each plausible model and then aggregates, and aggregate-then-evaluate (ATE), which first reduces ambiguity to a single representative distribution before evaluation. As most existing ambiguity models fall within the ETA framework, we develop and axiomatize the Choquet ATE model that generalizes both Choquet expected utility and CRDU while accommodating arbitrary pure-risk evaluations. Afterward, we provide a rich analysis of the interplay between ambiguity attitudes and risk attitudes. Chapter 5 develops a distributionally robust optimization model whose ambiguity set is derived from a Bayesian second-order belief, providing a clear separation between pure risk, ambiguity perception, and ambiguity attitude. This chapter is motivated by the observation that the smooth ambiguity model does not satisfactorily generalize to arbitrary pure-risk evaluations. A canonical construction based on distorted second-order beliefs is introduced as a tractable instance of this model, with accompanying algorithms and numerical illustrations in the context of portfolio optimization.enDoctoral Thesis