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

• 成果类型: Article
• 署名作者: Delage, Erick; Kuhn, Daniel; Wiesemann, Wolfram
• 署名单位: Universite de Montreal; HEC Montreal; Universite de Montreal; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Imperial College London
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2018.3108
• 发表日期: 2019
• 页码: 3282-3301
• 关键词: stochastic programming; Risk measures; distributionally robust optimization; ambiguity aversion; randomizes decisions

摘要

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.