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Norm Constrained Empirical Portfolio Optimization with Stochastic Dominance: Robust Optimization Non-Asymptotics

Author

Listed:
  • Stelios Arvanitis

    (Department of Economics, AUEB)

Abstract

The present note provides an initial theoretical explanation of the way norm regularizations may provide a means of controlling the non-asymptotic probability of False Dominance classification for empirically optimal portfolios satisfying empirical Stochastic Dominance restrictions in an iid setting. It does so via a dual characterization of the norm-constrained problem, as a problem of Distributional Robust Optimization. This enables the use of concentration inequalities involving the Wasserstein distance from the empirical distribution, to obtain an upper bound for the non-asymptotic probability of False Dominance classification. This leads to information about the minimal sample size required for this probability to be dominated by a predetermined significance level.

Suggested Citation

  • Stelios Arvanitis, 2025. "Norm Constrained Empirical Portfolio Optimization with Stochastic Dominance: Robust Optimization Non-Asymptotics," Working Paper 1533, Economics Department, Queen's University.
    • Handle: RePEc:qed:wpaper:1533
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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/wpaper/qed_wp_1533.pdf
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    More about this item

    Keywords

    Portfolio optimization; Stochastic dominance; â„“p regularization; Wasserstein distance; Distributionally robust optimization; Concentration inequality; False dominance classification;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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