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.

We introduce an axiom of disappointment-concordance aversion for a preference relation over acts in an Anscombe-Aumann setting. This axiom characterizes preference relations represented by a new class of functionals belonging to the Gilboa-Schmeidler family, which we call the duet expectiled utilities, and it is connected to Gul's disappointment-averse preferences.

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).