Explicit solution of a portfolio optimization problem by a general bivariate functional of the mean and variance

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We consider the problem of maximization of functional of expected portfolio return and variance portfolio return in its most general form and present an explicit closed-form solution of the optimal portfolio selection. This problem is closely related to expected utility maximization and two-moments decision models. We observe that all the optimization problems corresponding to the general functional considered here reduce to the same efficient frontier. We show that most known risk measures: mean-variance, expected short fall, Sharpe ratio and the recently introduced tail mean variance, are special cases of this functional. The new results essentially generalize previous results by the first two authors concerning the maximization of combination of expected portfolio return and a function of a variance portfolio return.

(Anyone who wish to look at the working paper before the talk, please email Yuval)