Sparse High-Order Portfolios Via Proximal Dca And Sca

In this paper, we study the cardinality constrained mean-variance-skewness-kurtosis (MVSKC) model for sparse high order portfolio optimization. The MVSKC model is computationally challenging, as the objective function is non-convex and the cardinality constraint is discontinuous. Since the cardinality constraint has the difference-of-convex (DC) property, we transform it into a penalty term and then propose three algorithms, namely the proximal difference-of-convex algorithm (pDCA), pDCA with extrapolation (pDCAe), and the successive convex approximation (SCA), to handle the resulting penalized mean-variance-skewness-kurtosis (PMVSK) formulation. Moreover, we establish theoretical convergence results for pDCA and SCA. Numerical experiments on a real dataset demonstrate the superiority of our proposed methods in obtaining better objective values and sparser solutions efficiently.