Risk Neutrality Regions

Abstract

The notion of risk neutrality is a basic element in standard textbook treatments of the economics of risk. In the single variable case, it is well known that an Expected Utility maximizer will be risk neutral toward all distributions if and only if her NM (von Neumann Morgenstern) index is linear. In the multivariate case, an individual can be risk neutral over a set of non-degenerate distributions even if her NM index is not linear. We provide necessary and sufficient conditions for when an individual with a nonlinear NM index is risk neutral and characterize the regions of the choice space over which risk neutrality is exhibited. The least concave decomposition of the NM index introduced by Debreu [4] plays an important role in our analysis as do the notions of minimum concavity points and minimum concavity directions. For the special case where one choice variable is certain, the analysis of risk neutrality requires modification of the Debreu decomposition. The existence of risk neutrality regions are shown to have potentially important implications for classic consumption-savings, consumption-leisure and representative agent equilibrium asset pricing models.

Keywords: Risk Neutrality, Expected Utility, Least Concave Utility and Minimum Concavity Points