p.1447

Ambiguity Aversion, Robustness, and the Variational Representation of Preferences

Fabio Maccheroni
Massimo Marinacci
Aldo Rustichini

Abstract

We characterize, in the Anscombe–Aumann framework, the preferences for which there are a utility functionu on outcomes and an ambiguity indexc on the set of probabilities on the states of the world such that, for all acts f and g, $f\succsim g\quad\Leftrightarrow\quad\min_{p}\biggl(\int u(f)\,dp+c(p)\biggr)\geq \min_{p}\biggl(\int u(g)\,dp+c(p)\biggr)$f≿g⇔minp(∫u(f)dp+c(p))⩾minp(∫u(g)dp+c(p)). The function u represents the decision maker's risk attitudes, while the index c captures his ambiguity attitudes. These preferences include the multiple priors preferences of Gilboa and Schmeidler and the multiplier preferences of Hansen and Sargent. This provides a rigorous decision-theoretic foundation for the latter model, which has been widely used in macroeconomics and finance.