{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,16]],"date-time":"2026-07-16T05:04:51Z","timestamp":1784178291439,"version":"3.55.0"},"reference-count":55,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2026,7,12]],"date-time":"2026-07-12T00:00:00Z","timestamp":1783814400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper investigates the stability of high-dimensional financial portfolios using concentration inequalities, information-theoretic measures, optimal transport metrics, and financial network analysis. Asset returns are generated under both multivariate Gaussian and multivariate Student-t distributions. Equal Weight and Regularized Minimum Variance portfolios are evaluated across alternative portfolio dimensions. The results show that increasing portfolio dimension reduces portfolio risk, tail probabilities, and risk estimation errors, indicating stronger concentration and higher stability in high-dimensional settings. Entropy and mutual information measures reveal improved diversification and weaker dependence structures as portfolio size increases. To assess distributional robustness, a novel Talagrand Stability Index (TSI), combining Wasserstein distance and Kullback\u2013Leibler divergence, is introduced. The results show that TSI decreases with portfolio dimension. Heavy-tailed Student-t returns generate weaker concentration effects, stronger dependence structures, and lower distributional stability than Gaussian returns. Mutual information-based financial networks reveal sparse and moderately interconnected dependence structures. To illustrate the practical applicability of the proposed framework, an empirical application based on daily returns of ten large U.S. equities during 2020\u20132025 is conducted, showing that the Regularized Minimum Variance portfolio achieves a marginally lower TSI than the Equal Weight portfolio. Robustness checks reported further indicate that this advantage is modest and outcome-dependent rather than decisive.<\/jats:p>","DOI":"10.3390\/e28070790","type":"journal-article","created":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T09:51:09Z","timestamp":1783936269000},"page":"790","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Concentration, Information, and Distributional Stability in High-Dimensional Portfolios: A Talagrand Stability Index Approach"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8536-5636","authenticated-orcid":false,"given":"Irina","family":"Georgescu","sequence":"first","affiliation":[{"name":"Department of Economic Informatics and Cybernetics, Bucharest University of Economic Studies, Calea Doroban\u021bi, 15-17, Sector 1, 010552 Bucharest, Romania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0154-6617","authenticated-orcid":false,"given":"Jani","family":"Kinnunen","sequence":"additional","affiliation":[{"name":"Department of Information Systems, \u00c5bo Akademi University, Tuomiokirkontori 3, 20500 Turku, Finland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,12]]},"reference":[{"key":"ref_1","unstructured":"Cao, H., Gu, H., Guo, X., and Rosenbaum, M. 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