Before revision:  The penalized problem is solvable by a quadratically-constrained quadratic program, and can be interpreted as a chance-constrained program. We show the original and penalized solutions follow the Central Limit Theorem with computable covariance by extending M-estimation results from statistics. The second method is parametric : solve the empirical Markowitz problem instead if the log-return distribution is in the elliptical family (which includes Gaussian and t distributions), as then the population frontiers of the Markowitz and mean-CVaR problems are equivalent . Numerical simulations show both methods improve upon the empirical mean-CVaR solution under an elliptical model, with the Markowitz solution dominating.
After revision:  The parametric PBR method solves the empirical Markowitz problem instead if the log-return distribution is in the elliptical family (which includes Gaussian and t distributions), as then the population frontiers of the Markowitz and mean-CVaR problems are equivalent . Numerical simulations show both methods improve upon the empirical mean-CVaR solution under an elliptical model, with the Markowitz solution dominating.