Higher-order moment portfolio optimization via difference-of-convex programming and sums-of-squares.

We are interested in developing DC (Difference-of-Convex) programming approach for solving higher-order moment (Mean-Variance-Skewness-Kurtosis) portfolio selection problem. The portfolio selection with higher moments can be formulated as a nonconvex quartic multivariate polynomial optimization. Based on the recent development in Difference-of-Convex-Sums-of-Squares (DCSOS) decomposition techniques for polynomial optimization, we can reformulate this problem as a DC program which can be solved by a well-known DC algorithm - DCA. We have also proposed an improved DC algorithm called Boosted-DCA (BDCA) based on an Armijo type line search to accelerate the convergence of DCA. We introduce this acceleration technique to both DC algorithm based on DCSOS decomposition proposed in this paper and the DC algorithm based on universal DC decomposition proposed in our previous paper. Results in numerical simulation show good performance of our proposed algorithms in portfolio optimization.