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In this paper, the authors address the global optimization of two interesting nonconvex problems in finance. They relax the normality assumption underlying the classical Markowitz mean-variance portfolio optimization model and consider the incorporation of skewness (third moment) and kurtosis (fourth moment). The investor seeks to maximize the expected return and the skewness of the portfolio and minimize its variance and kurtosis, subject to budget and no short selling constraints. In the first model, it is assumed that asset statistics are exact. The second model allows for uncertainty in asset statistics. They consider rival discrete estimates for the mean, variance, skewness and kurtosis of asset returns.
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