Portfolio selection problem with the third-order stochastic dominance constraints

The paper deals with portfolio selection problems which maximize mean portfolio return under constraints that the random return outperform a random benchmark. The outperformance can be understood in several different ways. In this paper, we focus on the mean maximization under third-order stochastic dominance constraints. The third-order stochastic dominance constraints are approximated by so called "super-convex" third-order stochastic dominance constraints which compare the semivariance functions in various grid points. First, we compute the optimal solution of the problem when an ultra-fine grid is used, i.e. super-convex third-order stochastic dominance is a very good approximation of the third-order stochastic dominance. Then, we decrease the number of grid (partition) points (and consequently increase the speed of computations) and we compare the optimal solutions and optimal objective values for various numbers of partition points between each other. Finally, we use the second-order stochastic dominance constraints instead of the third-order ones and we again analyze the changes in the optimal solution and the optimal objective value.