On the correspondence between multivariate risk aversion and risk aversion with state-dependent preferences

Abstract

This paper establishes the correspondence between multivariate risk aversion and risk aversion with state-dependent preferences. It shows that the prerequisite for comparability of risk aversion in the multivariate case, namely, identical ordinal preferences on the commodity space, corresponds to identical, properly defined, reference sets in the case of state-dependent preferences. For comparable decision makers the condition that the utility function of one is a concave transformation of that of the other on the commodity space corresponds to the condition that the expected utility of one is a concave transformation of that of the other on the reference set.