Static and dynamic quantile preferences

Abstract

This paper axiomatizes static and dynamic quantile preferences. Static quantile preferences specify that a prospect should be preferred if it has a higher $\tau$-quantile, for some $\tau \in (0,1)$, while its dynamic counterpart extends this to take into account a sequence of decisions and information disclosure. An important motivation for the axiomatization that leads to this preference is the separation of tastes and beliefs. We first axiomatize quantile preferences for the static case with finite state space and then extend the axioms to the dynamic context. The dynamic preferences induce an additively separable quantile model with standard discounting, that is, the recursive equation is characterized by the sum of the current period utility function and the discounted value of the certainty equivalent, which is a quantile function. These preferences are time consistent and have a simple quantile recursive representation, which gives the model the analytical tractability needed in several fields in financial and economic applications. Finally, we study the notion of risk attitude in both the static and recursive quantile models. In quantile models, the risk attitude is completely captured by the quantile $\tau$, a single-dimensional parameter. This is simpler than in expected utility models, where in general the risk attitude is determined by a function.