23
IRUS Total
Downloads

"Dice"-sion making under uncertainty: when can a random decision reduce risk?

File Description SizeFormat 
5582.pdfAccepted version417.93 kBAdobe PDFView/Open
Title: "Dice"-sion making under uncertainty: when can a random decision reduce risk?
Authors: Delage, E
Kuhn, D
Wiesemann, W
Item Type: Journal Article
Abstract: Stochastic programming and distributionally robust optimization seek deterministic deci- sions that optimize a risk measure, possibly in view of the most adverse distribution in an am- biguity 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 several 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, on the other hand, 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.
Issue Date: 1-Jul-2019
Date of Acceptance: 11-Apr-2018
URI: http://hdl.handle.net/10044/1/59142
DOI: https://doi.org/10.1287/mnsc.2018.3108
ISSN: 0025-1909
Publisher: Informs
Start Page: 2947
End Page: 3448
Journal / Book Title: Management Science
Volume: 65
Issue: 7
Copyright Statement: © 2019, INFORMS.
Sponsor/Funder: Engineering & Physical Science Research Council (E
Funder's Grant Number: EP/M028240/1
Keywords: Social Sciences
Science & Technology
Technology
Management
Operations Research & Management Science
Business & Economics
stochastic programming
risk measures
distributionally robust optimization
ambiguity aversion
randomizes decisions
DISTRIBUTIONALLY ROBUST OPTIMIZATION
WORST-CASE VALUE
STOCHASTIC CHOICE
EXPECTED UTILITY
PREFERENCES
RANDOMIZATION
PROBABILITY
CONSISTENCY
COMMITMENT
Operations Research
08 Information and Computing Sciences
15 Commerce, Management, Tourism and Services
Publication Status: Published
Online Publication Date: 2019-05-02
Appears in Collections:Imperial College Business School