拟凸函数
模棱两可
风险度量
度量(数据仓库)
数学优化
一致性风险度量
数学
随机规划
最优决策
计算机科学
计量经济学
正多边形
凸优化
决策树
经济
凸组合
人工智能
数据挖掘
金融经济学
几何学
程序设计语言
文件夹
作者
Erick Delage,Daniel Kühn,Wolfram Wiesemann
出处
期刊:Management Science
[Institute for Operations Research and the Management Sciences]
日期:2019-07-01
卷期号:65 (7): 3282-3301
被引量:27
标识
DOI:10.1287/mnsc.2018.3108
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. This paper was accepted by Teck Ho, optimization.
科研通智能强力驱动
Strongly Powered by AbleSci AI