Robust Preferences and Convex Measures of Risk

Abstract

We prove robust representation theorems for monetary measures of risk in a situation of uncertainty, where no probability measure is given a priori. They are closely related to a robust extension of the Savage representation of preferences on a space of financial positions which is due to Gilboa and Schmeidler. We discuss the problem of computing the monetary measure of risk induced by the subjective loss functional which appears in the robust Savage representation.