Distributionally Robust Multivariate Stochastic Cone Order Portfolio Optimization: Theory and Evidence from Borsa Istanbul

Larissa Margerata Batrancea, Mehmet Ali Balcı, Ömer Akgüller () and Lucian Gaban ()
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Larissa Margerata Batrancea: Department of Business, Babeş-Bolyai University, 7 Horea Street, 400174 Cluj-Napoca, Romania
Mehmet Ali Balcı: Department of Mathematics, Faculty of Science, Mugla Sitki Kocman University, Muğla 48000, Turkey
Ömer Akgüller: Department of Mathematics, Faculty of Science, Mugla Sitki Kocman University, Muğla 48000, Turkey
Lucian Gaban: Faculty of Economics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania

Mathematics, 2025, vol. 13, issue 15, 1-41

Abstract: We introduce a novel portfolio optimization framework—Distributionally Robust Multivariate Stochastic Cone Order (DR-MSCO)—which integrates partial orders on random vectors with Wasserstein-metric ambiguity sets and adaptive cone structures to model multivariate investor preferences under distributional uncertainty. Grounded in measure theory and convex analysis, DR-MSCO employs data-driven cone selection calibrated to market regimes, along with coherent tail-risk operators that generalize Conditional Value-at-Risk to the multivariate setting. We derive a tractable second-order cone programming reformulation and demonstrate statistical consistency under empirical ambiguity sets. Empirically, we apply DR-MSCO to 23 Borsa Istanbul equities from 2021–2024, using a rolling estimation window and realistic transaction costs. Compared to classical mean–variance and standard distributionally robust benchmarks, DR-MSCO achieves higher overall and crisis-period Sharpe ratios (2.18 vs. 2.09 full sample; 0.95 vs. 0.69 during crises), reduces maximum drawdown by 10%, and yields endogenous diversification without exogenous constraints. Our results underscore the practical benefits of combining multivariate preference modeling with distributional robustness, offering institutional investors a tractable tool for resilient portfolio construction in volatile emerging markets.

Keywords: distributionally robust optimization; multivariate stochastic cone order; Wasserstein ambiguity; portfolio optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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