Higher-Order Ambiguity Attitudes

TL;DR

This paper introduces a new model-free way to characterize ambiguity attitudes, providing simple definitions of ambiguity aversion and prudence, and explores their implications in various decision-making models.

Contribution

It proposes a novel, primitive trait-based framework for ambiguity attitudes, linking them to well-known models and decision problems under uncertainty.

Findings

New definition of ambiguity prudence linked to third derivatives in models

Equivalence of ambiguity prudence to derivatives in multiple models

Connection of ambiguity prudence to optimal insurance under ambiguity

Abstract

We introduce a model-free preference under ambiguity, as a primitive trait of behavior, which we apply once as well as repeatedly. Its single and double application yield simple, easily interpretable definitions of ambiguity aversion and ambiguity prudence. We derive their implications within canonical models for decision under risk and ambiguity. We establish in particular that our new definition of ambiguity prudence is equivalent to a positive third derivative of: (i) the capacity in the Choquet expected utility model, (ii) the dual conjugate of the divergence function under variational divergence preferences and (iii) the ambiguity attitude function in the smooth ambiguity model. We show that our definition of ambiguity prudent behavior may be naturally linked to an optimal insurance problem under ambiguity.