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.
QED Working Paper Number
1533
Keywords
Portfolio optimization
Stochastic dominance
ℓp regularization
Wasserstein distance
Distributionally robust optimization
Concentration inequality
False dominance classification
Working Paper