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The first moment and second central moments of the portfolio return, a.k.a.mean and variance, have been widely employed to assess the expected profit andrisk of the portfolio. Investors pursue higher mean and lower variance whendesigning the portfolios. The two moments can well describe the distribution ofthe portfolio return when it follows the Gaussian distribution. However, thereal world distribution of assets return is usually asymmetric andheavy-tailed, which is far from being a Gaussian distribution. The asymmetryand the heavy-tailedness are characterized by the third and fourth centralmoments, i.e., skewness and kurtosis, respectively. Higher skewness and lowerkurtosis are preferred to reduce the probability of extreme losses. However,incorporating high-order moments in the portfolio design is very difficult dueto their non-convexity and rapidly increasing computational cost with thedimension. In this paper, we propose a very efficient and convergence-provablealgorithm framework based on the successive convex approximation (SCA)algorithm to solve high-order portfolios. The efficiency of the proposedalgorithm framework is demonstrated by the numerical experiments.

Solving High-Order Portfolios via Successive Convex Approximation Algorithms