Comparative Risk Aversion with Two Risks

Abstract

This paper characterizes aversion to one risk in the presence of another, which is invulnerable to the size of exposure to the former risk and consistent with the common bivariate risk preferences for combining good with bad. We show that all bivariate utility functions that satisfy bivariate risk apportionment exhibit risk aversion with two risks if, and only if, the dependence structure of the two risks is characterized by the notion of expectation dependence. We then propose an intensity measure of risk aversion with two risks that is based on the utility premium normalized by the marginal utility evaluated at an arbitrarily chosen pair. We show that the intensity measure being uniformly larger is equivalent to the concept of greater generalized Ross risk aversion. An application for optimal prevention in a two-period model is presented when the dependence structure of the underlying random variables is governed by the notion of expectation dependence.