Third-degree stochastic dominance and DEA efficiency – relations and numerical comparison

Dealing with uncertainty on financial markets is very difficult task. The investor’s decision is highly dependent on the selected criteria which should help him to select the best among available investment opportunities. Harry Markowitz, [12], introduced his mean-risk model more than 50 years ago where variance was used as the risk measure. Many other risk measures has been proposed since then. The axiomatic definition of coherent risk measures is accepted by theorists as well as by practitioners, cf. [1]. The purpose of the mean-risk models is to maximize the mean return and to minimize the risk at the same time under given constraints on portfolio composition leading to biobjective optimization problem.