Abstract
This paper deals with new types of optimization problems when minimizing a risk of a portfolio under a condition on portfolio mean return and over portfolios which are classified as efficient with respect to second-order stochastic dominance (SSD) criterion. These problems can be seen as generalizations of classical mean-risk models where a risk measure is minimized under condition on portfolio mean return.
The crucial condition on the second order stochastic dominance efficiency is expressed in terms of existence of "optimal" utility function which obeys SSD rules. It means that new problems find portfolios having minimal particular risk measure (variance, Value at Risk, conditional Value at Risk), with at least minimal required mean return and being the optimal solution of maximization expected utility problems for at least one non-decreasing and concave utility function.
This study reformulates these new problems in linear, nonlinear, mixed-integer programs. Moreover, using US stock market data, paper compares the classical mean-risk frontiers with optimal portfolios of the new problems with SSD efficiency constraints.