Mean variance preferences and the heat equation

Abstract

Chipman (1979) proves that for an expected utility maximizer choosing from a domain of normal distributions with mean μ and variance σ2 the induced preference function V(μ, σ) satisfies a differential equation known as the heat equation. The purpose of this note is to provide a generalization and simple proof of this result which does not depend on the normality assumption. © 1993 Kluwer Academic Publishers.