Disappointment concordance and duet expectiles

TL;DR

This paper introduces duet expectiles, a new class of utility functionals based on disappointment-concordance, linking them to expectiles and risk measures, with implications for decision theory under uncertainty.

Contribution

It characterizes preference relations using a novel axiom of disappointment-concordance, leading to the development of duet expectiled utilities and their connection to expectiles.

Findings

Duet expectiles involve two endogenous probability measures.

When the measures coincide, duet expectiles reduce to standard expectiles.

The framework connects risk aversion and uncertainty aversion concepts.

Abstract

We introduce an axiom of disappointment-concordance (disco) aversion for a preference relation over acts in an Anscombe-Aumann setting. This axiom means that the decision maker, facing the sum of two acts, dislikes the situation where both acts realize simultaneously as disappointments. Our main result is that, under strict monotonicity and continuity, the axiom of disco aversion characterizes preference relations represented by a new class of functionals belonging to the Gilboa-Schmeidler family, which we call the duet expectiled utilities. When the outcome space is the real line, a duet expectiled utility becomes a duet expectile, which involves two endogenous probability measures. It further becomes a usual expectile, ,a statistical quantity popular in regression and risk measures, when these two probability measures coincide. We discuss properties of duet expectiles and connections with fundamental concepts including probabilistic sophistication, risk aversion, and uncertainty aversion.