Distributionally robust expectation inequalities for structured distributions
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10107_2017_1220_ReferencePDF.pdf
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Author(s)
Morari, Manfred
Goulart, Paul J.
Van Parys, Bart Paul Gerard
Date Issued
December 2017
Journal
Mathematical Programming
Publisher
Springer Berlin Heidelberg
Citation
Van Parys, Bart P. G., Paul J. Goulart, and Manfred Morari. “Distributionally Robust Expectation Inequalities for Structured Distributions.” Mathematical Programming 173, no. 1–2 (December 23, 2017): 251–280.
Version
Author's final manuscript
Abstract
Quantifying the risk of unfortunate events occurring, despite limited distributional information, is a basic problem underlying many practical questions. Indeed, quantifying constraint violation probabilities in distributionally robust programming or judging the risk of financial positions can both be seen to involve risk quantification under distributional ambiguity. In this work we discuss worst-case probability and conditional value-at-risk problems, where the distributional information is limited to second-order moment information in conjunction with structural information such as unimodality and monotonicity of the distributions involved. We indicate how exact and tractable convex reformulations can be obtained using standard tools from Choquet and duality theory. We make our theoretical results concrete with a stock portfolio pricing problem and an insurance risk aggregation example. Keywords: Optimal inequalities, Extreme distributions, Convex optimisation, Choquet representation, CVaR
MIT Department
Massachusetts Institute of Technology. Operations Research Center
Sloan School of Management
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10107-017-1220-x
