Approximation of expected returns and optimal decisions under uncertainty using mean and mean absolute deviation

Abstract

We consider economic decision problems under uncertainty consisting of choosing an optimal decisionX, so as to maximize to expected value of an objective function depending on a stochastic parameterp. The paper establishes an optimal policy intervalXA ⩽X1 ⩽XB, where the boundsXA,XB are given in terms of simple parameters of the distribution ofp, in particular the meanμ, and the mean absolute deviationd=E ¦p−μ ¦. The convexity assumptions needed to establish such bounds are shown to hold naturally in some classical problems of production under uncertainty.