{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T21:21:58Z","timestamp":1762377718953,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,4]],"date-time":"2025-08-04T00:00:00Z","timestamp":1754265600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["71771008","72271013"],"award-info":[{"award-number":["71771008","72271013"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In portfolio optimization, investors often overlook asymmetric preferences for gains and losses. We propose a distributionally robust two-stage portfolio optimization (DR-TSPO) model, which is suitable for scenarios where the loss reference point is adaptively updated based on prior decisions. For analytical convenience, we further reformulate the DR-TSPO model as an equivalent second-order cone programming counterpart. Additionally, we develop a deep learning-based constraint correction algorithm (DL-CCA) trained directly on problem descriptions, which enhances computational efficiency for large-scale non-convex distributionally robust portfolio optimization. Our empirical results obtained using global market data demonstrate that during COVID-19, the DR-TSPO model outperformed traditional two-stage optimization in reducing conservatism and avoiding extreme losses.<\/jats:p>","DOI":"10.3390\/sym17081236","type":"journal-article","created":{"date-parts":[[2025,8,4]],"date-time":"2025-08-04T15:30:06Z","timestamp":1754321406000},"page":"1236","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Two-Stage Distributionally Robust Optimization for an Asymmetric Loss-Aversion Portfolio via Deep Learning"],"prefix":"10.3390","volume":"17","author":[{"given":"Xin","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Economics and Management, Beihang University, No. 37, Xueyuan Road, Beijing 100191, China"}]},{"given":"Shancun","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beihang University, No. 37, Xueyuan Road, Beijing 100191, China"}]},{"given":"Jingrui","family":"Pan","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Beihang University, No. 37, Xueyuan Road, Beijing 100191, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"263","DOI":"10.2307\/1914185","article-title":"Prospect Theory: An Analysis of Decision under Risk","volume":"47","author":"Kahneman","year":"1979","journal-title":"Econometrica"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1162\/003355301556310","article-title":"Prospect theory and asset prices","volume":"116","author":"Barberis","year":"2001","journal-title":"Q. J. Econ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"835","DOI":"10.1016\/j.jebo.2009.08.003","article-title":"Prospect theory for stock markets: Empirical evidence with time-series data","volume":"72","author":"Zhang","year":"2009","journal-title":"J. Econ. Behav. Organ."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1111\/j.1540-6261.2009.01448.x","article-title":"What drives the disposition effect? An analysis of a long-standing preference-based explanation","volume":"64","author":"Barberis","year":"2009","journal-title":"J. Financ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.jedc.2015.10.002","article-title":"Discrete-time behavioral portfolio selection under cumulative prospect theory","volume":"61","author":"Shi","year":"2015","journal-title":"J. Econ. Dyn. Control"},{"key":"ref_6","first-page":"3927","article-title":"Consumption and portfolio choice under loss aversion and endogenous updating of the reference level","volume":"66","author":"Laeven","year":"2020","journal-title":"Manag. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"103103","DOI":"10.1016\/j.omega.2024.103103","article-title":"Multi-period portfolio choice under loss aversion with dynamic reference point in serially correlated market","volume":"127","author":"Gao","year":"2024","journal-title":"Omega"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1162\/0034653043125167","article-title":"Optimal portfolio choice under loss aversion","volume":"86","author":"Berkelaar","year":"2004","journal-title":"Rev. Econ. Stat."},{"key":"ref_9","first-page":"385","article-title":"Behavioral portfolio selection in continuous time","volume":"18","author":"Jin","year":"2008","journal-title":"Math. Financ. Int. J. Math. Stat. Financ. Econ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1080\/14697688.2014.917805","article-title":"Myopic loss aversion, reference point, and money illusion","volume":"14","author":"He","year":"2014","journal-title":"Quant. Financ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1287\/mnsc.1100.1269","article-title":"Portfolio choice under cumulative prospect theory: An analytical treatment","volume":"57","author":"He","year":"2011","journal-title":"Manag. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"951","DOI":"10.1016\/j.jedc.2012.01.010","article-title":"Dynamic portfolio choice and asset pricing with narrow framing and probability weighting","volume":"36","author":"Legg","year":"2012","journal-title":"J. Econ. Dyn. Control"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1287\/opre.2015.1399","article-title":"Dynamic trading with reference point adaptation and loss aversion","volume":"63","author":"Shi","year":"2015","journal-title":"Oper. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s11579-017-0186-z","article-title":"Optimal investment with transaction costs under cumulative prospect theory in discrete time","volume":"11","author":"Zou","year":"2017","journal-title":"Math. Financ. Econ."},{"key":"ref_15","first-page":"87","article-title":"Two important improvements of prospect theory\u2014Study of the loss aversion coefficient \u03bb and the reference point","volume":"16","author":"Zou","year":"2007","journal-title":"Oper. Res. Manag. Sci."},{"key":"ref_16","first-page":"71","article-title":"Portfolio Selection","volume":"7","author":"Markowitz","year":"1952","journal-title":"J. Financ."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"506","DOI":"10.1287\/mnsc.1100.1286","article-title":"Reference-point formation and updating","volume":"57","author":"Baucells","year":"2011","journal-title":"Manag. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1287\/opre.2019.1872","article-title":"Failing to foresee the updating of the reference point leads to time-inconsistent investment","volume":"68","author":"Strub","year":"2020","journal-title":"Oper. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1016\/j.insmatheco.2020.02.004","article-title":"Dynamic consumption and portfolio choice under prospect theory","volume":"91","author":"Laeven","year":"2020","journal-title":"Insur. Math. Econ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3035","DOI":"10.1287\/opre.2022.2309","article-title":"How endogenization of the reference point affects loss aversion: A study of portfolio selection","volume":"70","author":"He","year":"2022","journal-title":"Oper. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2058","DOI":"10.1287\/ijoc.2021.1145","article-title":"Target-Oriented Distributionally Robust Optimization and Its Applications to Surgery Allocation","volume":"34","author":"Chow","year":"2022","journal-title":"INFORMS J. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1287\/ijoc.2021.1096","article-title":"Distributionally robust optimization under a decision-dependent ambiguity set with applications to machine scheduling and humanitarian logistics","volume":"34","author":"Noyan","year":"2022","journal-title":"INFORMS J. Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1361","DOI":"10.1287\/ijoc.2022.0113","article-title":"Distributionally Robust Chance-Constrained p-Hub Center Problem","volume":"35","author":"Zhao","year":"2023","journal-title":"INFORMS J. Comput."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1093\/rfs\/hhl003","article-title":"Portfolio selection with parameter and model uncertainty: A multi-prior approach","volume":"20","author":"Garlappi","year":"2007","journal-title":"Rev. Financ. Stud."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1155","DOI":"10.1287\/opre.1080.0684","article-title":"Worst-case conditional value-at-risk with application to robust portfolio management","volume":"57","author":"Zhu","year":"2009","journal-title":"Oper. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1861","DOI":"10.3934\/jimo.2019032","article-title":"CVaR-based robust models for portfolio selection","volume":"16","author":"Sun","year":"2020","journal-title":"J. Ind. Manag. Optim."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1080\/14697688.2018.1466057","article-title":"Data-driven robust mean-CVaR portfolio selection under distribution ambiguity","volume":"19","author":"Kang","year":"2019","journal-title":"Quant. Financ."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1080\/14697680701455410","article-title":"Ambiguity in portfolio selection","volume":"7","author":"Pflug","year":"2007","journal-title":"Quant. Financ."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s10479-010-0812-0","article-title":"A framework for optimization under ambiguity","volume":"193","author":"Wozabal","year":"2012","journal-title":"Ann. Oper. Res."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1177","DOI":"10.1287\/opre.2022.2383","article-title":"Wasserstein distributionally robust optimization and variation regularization","volume":"72","author":"Gao","year":"2024","journal-title":"Oper. Res."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"6382","DOI":"10.1287\/mnsc.2021.4155","article-title":"Distributionally robust mean-variance portfolio selection with Wasserstein distances","volume":"68","author":"Blanchet","year":"2022","journal-title":"Manag. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/j.ejor.2020.07.063","article-title":"Machine learning for combinatorial optimization: A methodological tour d\u2019horizon","volume":"290","author":"Bengio","year":"2021","journal-title":"Eur. J. Oper. Res."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Hasan, F., Kargarian, A., and Mohammadi, A. (2020, January 6\u20137). A survey on applications of machine learning for optimal power flow. Proceedings of the 2020 IEEE Texas Power and Energy Conference (TPEC), College Station, TX, USA.","DOI":"10.1109\/TPEC48276.2020.9042547"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Koziel, S., and Leifsson, L. (2013). Surrogate-Based Modeling and Optimization, Springer.","DOI":"10.1007\/978-1-4614-7551-4"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Baker, K. (2019, January 13\u201316). Learning warm-start points for AC optimal power flow. Proceedings of the 2019 IEEE 29th International Workshop on Machine Learning for Signal Processing (MLSP), Pittsburgh, PA, USA.","DOI":"10.1109\/MLSP.2019.8918690"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Dong, W., Xie, Z., Kestor, G., and Li, D. (2020, January 9\u201319). Smart-PGSim: Using neural network to accelerate AC-OPF power grid simulation. Proceedings of the SC20: International Conference for High Performance Computing, Networking, Storage and Analysis, Atlanta, GA, USA.","DOI":"10.1109\/SC41405.2020.00067"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1287\/ijoc.2020.1037","article-title":"Learning for constrained optimization: Identifying optimal active constraint sets","volume":"34","author":"Misra","year":"2022","journal-title":"INFORMS J. Comput."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","article-title":"On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming","volume":"106","author":"Biegler","year":"2006","journal-title":"Math. Program."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Amiri, M.H., Mehrabi Hashjin, N., Montazeri, M., Mirjalili, S., and Khodadadi, N. (2024). Hippopotamus optimization algorithm: A novel nature-inspired optimization algorithm. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-54910-3"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1236\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:23:05Z","timestamp":1760034185000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1236"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,4]]},"references-count":39,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["sym17081236"],"URL":"https:\/\/doi.org\/10.3390\/sym17081236","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,8,4]]}}}