Research

Abstract: We axiomatize the Choquet rank-dependent utility model within a Savage framework with an exogenous source of pure risk. This model is a decision model under ambiguity, serving as a conceptual generalization of the Choquet expected utility model. The model unifies risk and ambiguity and reduces to the rank-dependent utility for pure risks. Our axiomatization uses two main axioms for biseparable preferences, along with some regularity axioms. A benefit of this axiomatization is that the fairly weak regularity axioms guarantee the existence of matching probabilities. Further, we discuss ambiguity attitudes for the CRDU model. We characterize these attitudes by properties of the associated matching probabilities and show that the supermodularity of the matching probability provides a robust representation. Finally, we show that under an additional Property, this model has a different representation using act-dependent distortion functions.

Abstract: We distinguish two frameworks for decisions under ambiguity: evaluate-then-aggregate (ETA) and aggregate-then-evaluate (ATE). Given a statistic that represents the decision maker's pure-risk preferences (such as expected utility) and an ambiguous act, an ETA model first evaluates the act under each plausible probabilistic model using this statistic and then aggregates the resulting evaluations according to ambiguity attitudes. In contrast, an ATE model first aggregates ambiguity by assigning the act a single representative distribution and then evaluates that distribution using the statistic. These frameworks differ in the order in which risk and ambiguity are processed, and they coincide when there is no ambiguity. While most existing ambiguity models fall within the ETA framework, our study focuses on the ATE framework, which is conceptually just as compelling and has been relatively neglected in the literature. We develop a Choquet ATE model, which generalizes the Choquet expected utility model by allowing arbitrary pure-risk preferences. We provide an axiomatization of this model in a Savage setting with an exogenous source of unambiguous events. The Choquet ATE framework allows us to analyze a wide range of ambiguity attitudes and their interplay with risk attitudes.

Abstract: We introduce the concept of partial law invariance, generalizing the concepts of law invariance and probabilistic sophistication widely used in decision theory, as well as statistical and financial applications. This new concept is motivated by practical considerations of decision making under uncertainty, thus connecting the literature on decision theory and that on financial risk management. We fully characterize partially law-invariant coherent risk measures via a novel representation formula. Strong partial law invariance is defined to bridge the gap between the above characterization and the classic representation formula of Kusuoka. We propose a few classes of new risk measures, including partially law-invariant versions of the Expected Shortfall and the entropic risk measures, and illustrate their applications in risk assessment under different types of uncertainty. We provide a tractable optimization formula for computing a class of partially law-invariant coherent risk measures and give a numerical example.