Separability, neutrality and certainty equivalence†

Abstract

Abstract Studies of optimal stochastic control problems have drawn attention to three properties: separability, neutrality and certainty equivalence. The relationships between these properties have not yet been fully explored. This paper gives definitions of all three properties, summarizes well-known results about them and discusses the relationships between them. It is shown that separability is not the same as, but is a necessary condition for, certainty equivalence. It is conjectured that neutrality is a sufficient condition for certainty equivalence.