Minimization of a Function of a Quadratic Functional with Application to Optimal Portfolio Selection

We present an explicit closed-form solution to the problem of minimizing the combination of linear functional and a function of quadratic functional, subject to a system of affine constraints. This is of interest for solving important problems in financial economics related to optimal portfolio selection. The new results essentially generalize previous results of the authors concerning optimal portfolio selection with translation invariant and positive homogeneous risk measures. The classical mean-variance model and the recently introduced and investigated tail mean-variance model are special cases of the problem discussed here.