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

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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 intervalX AX 1X B, where the boundsX A,X B 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.

Zusammenfassung

Wir betrachten wirtschaftliche Entscheidungsprobleme mit Unsicherheit, in denen eine optimale EntscheidungX so getroffen werden soll, daß der Erwartungswert einer Zielfunktion, abhängig von einem stochastischen Parameterp, maximiert werden soll. In dieser Arbeit wird ein IntervallX AX 1X B für die optimale Politik angegeben, wobei die SchrankenX A,X B durch einfache Größen der Verteilung vonp ausgedrückt werden, im besonderen durch den Mittelwertμ und die mittlere absolute Abweichungd=E ¦p−μ ¦. Ferner wird gezeigt, daß die für die Herleitung der Schranken benötigten Konvexitätsannahmen in natürlicher Weise für einige klassische Produktionsprobleme mit Unsicherheit gelten.

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Supported by BARD Project No. I-10-79 and by Technion VPR Fund-Lawrence Deutsch Research Fund.

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Ben-Tal, A., Hochman, E. Approximation of expected returns and optimal decisions under uncertainty using mean and mean absolute deviation. Zeitschrift für Operations Research 29, 285–300 (1985). https://doi.org/10.1007/BF01918761

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  • DOI: https://doi.org/10.1007/BF01918761

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