Robust Solutions of Optimization Problems Affected by Uncertain Probabilities

CentER Working Paper Series No. 2011-061

29 Pages Posted: 31 May 2011

See all articles by Aharon Ben-Tal

Aharon Ben-Tal

Technion-Israel Institute of Technology

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Anja De Waegenaere

Tilburg University - Center for Economic Research (CentER)

Bertrand Melenberg

Tilburg University - Center for Economic Research (CentER)

Gijs Rennen

Tilburg University - Department of Econometrics & Operations Research

Date Written: May 25, 2011

Abstract

In this paper we focus on robust linear optimization problems with uncertainty regions defined by ø-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on ø-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with ø-divergence uncertainty is tractable for most of the choices of ø typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach.

Keywords: robust optimization, ø-divergence, goodness-of-fit statistics

JEL Classification: C61

Suggested Citation

Ben-Tal, Aharon and den Hertog, Dick and De Waegenaere, Anja M.B. and Melenberg, Bertrand and Rennen, Gijs, Robust Solutions of Optimization Problems Affected by Uncertain Probabilities (May 25, 2011). CentER Working Paper Series No. 2011-061. Available at SSRN: https://ssrn.com/abstract=1853428 or http://dx.doi.org/10.2139/ssrn.1853428

Aharon Ben-Tal

Technion-Israel Institute of Technology ( email )

Technion City
Haifa 32000, Haifa 32000
Israel

Dick Den Hertog (Contact Author)

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

Anja M.B. De Waegenaere

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Bertrand Melenberg

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 466 2730 (Phone)

Gijs Rennen

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

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