{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,6]],"date-time":"2026-07-06T11:15:12Z","timestamp":1783336512221,"version":"3.54.6"},"reference-count":75,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"7","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Management Science"],"published-print":{"date-parts":[[2026,7]]},"abstract":"<jats:p>We introduce a new approach for prudent risk evaluation based on stochastic dominance, and it is called the model aggregation (MA) approach. In contrast to the classic worst case risk (WR) approach, the MA approach produces not only a robust value of risk evaluation but also a robust distributional model, independent of any specific risk measure. The MA risk evaluation can be computed through explicit formulas in the lattice theory of stochastic dominance, and under some standard assumptions, the MA robust optimization admits a convex program reformulation. The MA approach for Wasserstein and mean-variance uncertainty sets admits explicit formulas for the obtained robust models. Via an equivalence property between the MA and WR approaches, new axiomatic characterizations are obtained for the value at risk and the expected shortfall (also known as conditional value at risk). The new approach is illustrated with various risk measures and examples from portfolio optimization.<\/jats:p>\n                  <jats:p>This paper was accepted by Chung Piaw Teo, optimization.<\/jats:p>\n                  <jats:p>Funding: This research was supported by the National Natural Science Foundation of China [Grants 12371476, 71921001, 71671176, 71871208], the Natural Sciences and Engineering Research Council of Canada [Grants CRC-2022-00141, RGPIN-2024-03728, RGPAS-2018-522590, RGPIN-2018-03823], and the Society of Actuaries Center of Actuarial Excellence Research Grant.<\/jats:p>\n                  <jats:p>Supplemental Material: The online appendix and data files are available at https:\/\/doi.org\/10.1287\/mnsc.2023.03523 .<\/jats:p>","DOI":"10.1287\/mnsc.2023.03523","type":"journal-article","created":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T18:06:44Z","timestamp":1762538804000},"page":"6350-6367","source":"Crossref","is-referenced-by-count":1,"title":["Model Aggregation for Risk Evaluation and Robust Optimization"],"prefix":"10.1287","volume":"72","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3428-004X","authenticated-orcid":false,"given":"Tiantian","family":"Mao","sequence":"first","affiliation":[{"name":"Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3849-4555","authenticated-orcid":false,"given":"Ruodu","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2268-5285","authenticated-orcid":false,"given":"Qinyu","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"109","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1142\/S0219024917500261"},{"key":"B2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9965.00068"},{"key":"B3","volume-title":"Minimum Capital Requirements for Market Risk","author":"Basel Committee on Banking Supervision","year":"2019"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2013.10.015"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718829"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2018.0936"},{"key":"B7","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.2021.4155"},{"key":"B8","doi-asserted-by":"publisher","DOI":"10.1017\/jpr.2019.49"},{"key":"B9","doi-asserted-by":"publisher","DOI":"10.1111\/mafi.12097"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1093\/restud\/rdaf046"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9965.2009.00369.x"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1110.0950"},{"key":"B13","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/hhn081"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.1080\/14697681003685597"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1090.0741"},{"key":"B16","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.2018.3108"},{"issue":"1","key":"B17","first-page":"49","volume":"49","author":"Dentcheva D","year":"2023","journal-title":"Serdica Math. 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