Distributionally robust expectation inequalities for structured distributions
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2019
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| Online Access: | http://hdl.handle.net/1721.1/120735 https://orcid.org/0000-0003-4177-4849 |
| _version_ | 1826212389789368320 |
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| author | Morari, Manfred Goulart, Paul J. Van Parys, Bart Paul Gerard |
| author2 | Massachusetts Institute of Technology. Operations Research Center |
| author_facet | Massachusetts Institute of Technology. Operations Research Center Morari, Manfred Goulart, Paul J. Van Parys, Bart Paul Gerard |
| author_sort | Morari, Manfred |
| collection | MIT |
| description | 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 |
| first_indexed | 2024-09-23T15:20:38Z |
| format | Article |
| id | mit-1721.1/120735 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T15:20:38Z |
| publishDate | 2019 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1207352022-09-29T14:22:38Z Distributionally robust expectation inequalities for structured distributions Morari, Manfred Goulart, Paul J. Van Parys, Bart Paul Gerard Massachusetts Institute of Technology. Operations Research Center Sloan School of Management Van Parys, Bart Paul Gerard 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 2019-03-05T18:11:03Z 2019-03-05T18:11:03Z 2017-12 2019-01-29T04:43:29Z Article http://purl.org/eprint/type/JournalArticle 0025-5610 1436-4646 http://hdl.handle.net/1721.1/120735 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. https://orcid.org/0000-0003-4177-4849 en https://doi.org/10.1007/s10107-017-1220-x Mathematical Programming 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. Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Morari, Manfred Goulart, Paul J. Van Parys, Bart Paul Gerard Distributionally robust expectation inequalities for structured distributions |
| title | Distributionally robust expectation inequalities for structured distributions |
| title_full | Distributionally robust expectation inequalities for structured distributions |
| title_fullStr | Distributionally robust expectation inequalities for structured distributions |
| title_full_unstemmed | Distributionally robust expectation inequalities for structured distributions |
| title_short | Distributionally robust expectation inequalities for structured distributions |
| title_sort | distributionally robust expectation inequalities for structured distributions |
| url | http://hdl.handle.net/1721.1/120735 https://orcid.org/0000-0003-4177-4849 |
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