Decisions under risk and ambiguity

The series of working papers contains recent advances on some aspects of decision theory, especially axiomatic foundations of decisions under risk and ambiguity. These papers study risk aversion, ambiguity aversion, stochastic dominance, cumulative prospect theory, rank-dependent utility theory, disappointment theory, and other decision-theoretic concepts and models.

A brief description of each working paper is provided below to explain its main results and the logical structure across papers.

This paper follows up on WP06 by introducing risk-insurance parity, which associates various classes of insurance contracts with different notions of risk aversion. We obtain full characterizations of the classes of insurance indemnity functions that correspond to weak and strong risk aversion. Risk-insurance parity allows us to define two new notions of risk aversion, between weak and strong, characterized by insurance propensity to deductible-only and limit-only contracts, respectively.

We distinguish two frameworks for decisions under ambiguity: evaluate-then-aggregate (ETA) and aggregate-then-evaluate (ATE). We focus on the ATE framework, which has been relatively neglected in the literature. A Choquet ATE model is proposed and axiomatized, which generalizes the Choquet expected utility model by allowing arbitrary pure-risk preferences.

This paper axiomatizes the Choquet rank-dependent utility model within a Savage framework with an exogenous source of pure risk, serving as a conceptual generalization of the Choquet expected utility model.

In a framework of bi-separable preferences, we axiomatize expectiled utilities and connect them to Gul's disappointment-averse preferences and to asymmetric linear regression.

We provide a new foundation of risk aversion by showing that this attitude is fully captured by the propensity to seize insurance opportunities. Both strong and weak notions of risk aversion, as well as their comparative notions, can be characterized by insurance behaviour. The journal version is accepted by American Economic Review (2025).

Comonotonicity is a key concept that characterizes the ambiguity model of Schmeidler. We investigate anticomonotonicity, the natural counterpart to comonotonicity. Theorem 1 yields that, on a finite space, anticomonotonic additivity implies additivity; this is in sharp contrast to comonotonic additivity. The journal version is accepted by Theoretical Economics (2024).

This paper offers a full characterization of probabilistic risk aversion for generalized rank-dependent functions. The journal version is accepted by Economic Theory (2024).

We show the perhaps surprising inequality (Theorem 1) that the weighted average of iid extremly heavy-tailed (i.e., infinite mean) Pareto losses is larger than a standalone loss in the sense of first-order stochastic dominance. The main result applies to super-Pareto distributions and negative dependence. The journal version is accepted by Operations Research (2024).

This paper investigates whether and when fractional degree stochastic dominance rules can exhibit invariance properties, and obtained several characterization results of stochastic dominance rules.

We formulate a general class of fractional SD generated by a convex transform, which includes those built from absolute or relative risk aversion as special cases, and characterize them in rank-dependent utility and cumulative prospect theory. The journal version is published in Journal of Mathematical Economics (2022).