“Dice”-sion–Making Under Uncertainty: When Can a Random Decision Reduce Risk?

Erick Delage (), Daniel Kuhn () and Wolfram Wiesemann ()
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Erick Delage: HEC Montréal, Montreal, Quebec H3T 2A7, Canada; Groupe d'études et de recherche en analyse des décisions (GERAD), Montreal, Quebec H3T 1J4, Canada
Daniel Kuhn: École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
Wolfram Wiesemann: Imperial College London, London SW19 3SR, United Kingdom

Management Science, 2019, vol. 65, issue 7, 3282-3301

Abstract: Stochastic programming and distributionally robust optimization seek deterministic decisions that optimize a risk measure, possibly in view of the most adverse distribution in an ambiguity set. We investigate under which circumstances such deterministic decisions are strictly outperformed by random decisions, which depend on a randomization device producing uniformly distributed samples that are independent of all uncertain factors affecting the decision problem. We find that, in the absence of distributional ambiguity, deterministic decisions are optimal if both the risk measure and the feasible region are convex or alternatively, if the risk measure is mixture quasiconcave. We show that some risk measures, such as mean (semi-)deviation and mean (semi-)moment measures, fail to be mixture quasiconcave and can, therefore, give rise to problems in which the decision maker benefits from randomization. Under distributional ambiguity, however, we show that, for any ambiguity-averse risk measure satisfying a mild continuity property, we can construct a decision problem in which a randomized decision strictly outperforms all deterministic decisions.

Keywords: stochastic programming; risk measures; distributionally robust optimization; ambiguity aversion; randomized decisions (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (10)

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