Abstrakt
This paper deals with new types of optimization problems when minimizing variance of portfolios which have at least the required mean return and, moreover, are classified as efficient with respect to a particular order of stochastic dominance (SD) criterion. These problems can be seen as generalizations of classical mean-variance models, where a risk measure (variance) is minimized under condition on portfolio mean return.
The crucial condition on the stochastic dominance efficiency is expressed in terms of existence of "optimal" utility function, such that a feasible portfolio is a maximizer of expected utility when the "optimal" utility function is used. It means that new problems find portfolios having minimal variance with at least minimal required mean return and being the optimal solution of maximizing expected utility problems for at least one utility function that obeys the particular SD rules.