Disappointment concordance and duet expectiles

Résumé 0

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.