We analyze the international portfolio optimization problem by introducing the higher moments of the main financial index returns. We take especially account of their skewness and kurtosis. We introduce various decision criteria, based on these moments. In this framework, we solve different optimization problems: skewness maximization, kurtosis minimization, Polynomial Goal Programming (PGP), and finally, truncated utility maximization. For all of these objective functions, we determine, analyze and compare the optimal solutions, especially their degree of diversification.

We illustrate our results on monthly returns of eighteen major international stock market indexes, for the period January 1988 through December 2007.