Partial derivatives, comparative risk behavior and concavity of utility functions

Abstract

We use the comparative risk behavior of the partial derivatives to address a long standing problem in mean-variance analysis: What does the concavity of utility functions mean? It is well known that, when mean-variance preferences are derived from expected utility and normal distributions, concavity is equivalent to decreasing prudence. In this paper, we derive conditions that link concavity to prudence in a general mean-standard deviation case.