Arrow-Pratt-Type Measure of Ambiguity Aversion

Abstract

We define a measure of ambiguity aversion for ambiguity-averse utility functions in a way analogous to the Arrow-Pratt measure of risk aversion. The measure is determined by the second Peano derivative, which exists even for non-differentiable functions, such as maximin and Choquet expected utility functions. Unlike the standard notion of comparative ambiguity aversion, it allows us to compare ambiguity aversion between two utility functions exhibiting different risk attitudes. We introduce a notion of ambiguity premium and show that our measure is related to the second-order, as opposed to the first-order, ambiguity premium. We also show that it is related to the first-order impact on matching probabilities of the size of prizes.