Is time consistency compatible with risk aversion?

Abstract

Managerial decision models applied in operations research, finance, information management, and many other disciplines are typically both dynamic and stochastic. When decisions at different points in time are allowed, the question arises what conditions guarantee the absence of incentives to deviate from the ex ante optimal policy at later dates. We term such a policy time consistent. A well-known result states that additively separable objective functions ensure time consistency under risk neutrality. Unfortunately, this is no longer true when decision makers are risk averse. Then, (much) more restrictive assumptions are needed. The aim of this paper is to provide clear-cut conditions that ensure time consistency in an expected utility framework. Our main findings are twofold: on the one hand, constant absolute risk aversion can guarantee time consistency when final values are under consideration. On the other hand, time consistency and risk aversion are incompatible when intertemporal payments are aggregated by means of net present values.