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

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

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 distributi...

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Bibliographic Details
Main Authors: Larissa Margerata Batrancea, Mehmet Ali Balcı, Ömer Akgüller, Lucian Gaban
Format: Article
Language:English
Published: MDPI AG 2025-07-01
Series:Mathematics
Subjects:
distributionally robust optimization
multivariate stochastic cone order
Wasserstein ambiguity
portfolio optimization
Online Access:https://www.mdpi.com/2227-7390/13/15/2473
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Summary: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.
ISSN:2227-7390

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