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

We consider economic decision problems under uncertainty consisting of choosing an optimal decision X, so as to maximize to expected value of an objective function depending on a stochastic parameter p. The paper establishes an optimal policy interval X_A ≤X¹ ≤X_B, where the bounds X_A, X_B are given in terms of simple parameters of the distribution of p, in particular the mean μ, and the mean absolute deviation d=E |p-μ |. The convexity assumptions needed to establish such bounds are shown to hold naturally in some classical problems of production under uncertainty.