An enhanced model for portfolio choice with SSD criteria: a constructive approach

Abstract

We formulate a portfolio planning model that is based on second-order stochastic dominance as the choice criterion. This model is an enhanced version of the multi-objective model proposed by Roman et al. [Math. Progr. Ser. B, 2006, 108, 541–569]; the model compares the scaled values of the different objectives, representing tails at different confidence levels of the resulting distribution. The proposed model can be formulated as a risk minimization model where the objective function is a convex risk measure; we characterize this risk measure and the resulting optimization problem. Moreover, our formulation offers a natural generalization of the SSD-constrained model of Dentcheva and Ruszczyński [J. Bank. Finance, 2006, 30, 433–451]. A cutting plane-based solution method for the proposed model is outlined. We present a computational study showing: (a) the effectiveness of the solution methods and (b) the improved modeling capabilities: the resulting portfolios have superior return distributions.