The Myopic Property in Decision Models

Abstract

We examine conditions under which decisions made in isolation provide an optimal strategy for the multiperiod problem. We focus on investment decisions with constant returns to scale. We first consider the framework of subjective expected utility. Under minimal assumptions (i.e., without assuming utility is concave), we prove that only log utility is myopically optimal when returns are serially correlated. When returns are serially independent, we generalize Mossin’s result [Mossin J (1968) Optimal multiperiod portfolio policies. J. Bus. 41(2):215–229.] that only log and power, including linear and convex, possess the myopic property. Finally, we extend the inquiry when probabilities are uncertain and the decision maker uses the recursive smooth model of ambiguity to identify an optimal strategy. We show that with serial correlation, preferences including ambiguity concerns cannot be myopic and optimal. Without correlation, we identify the exact pairs of utility and ambiguity functions that permit myopic decision rules.