Solving extended mean-variance models using tensor analysis

We demonstrate how tensor analysis serves as a powerful tool for determining the optimal weights in extended versions of Markowitz's Mean-Variance model, particularly when addressing risks characterized by multivariate skew-elliptical probability distributions. Our approach preserves the familiar structure of the original mean-variance model while incorporating a risk aversion parameter that reflects the distribution of portfolio returns. This extension offers a more comprehensive representation of optimal portfolio selection problems. Consequently, the proposed model paves the way for advanced analytical solutions of extended versions of the mean-variance model.