PSO and ABC: comparisons for two-sided risk measures in portfolio selection problem.

One of the most studied problems in finance is the portfolio selection problem. In the classical porfolio selection model, proposed by Markowitz, the risk is measured by the variance of returns. This is good only in few cases, otherwise this will lead to an innacurate investment decision. In order to overcome this issue many alternative measures of risk have been proposed. In this work we will focus on a class of measures that take into account both, positive and negative deviations from the expected returns. We consider a realistic portfolio selection model, that considers several constraints used in the investment practice. This problem is considered to be NP-Hard. To approximatly solve this problem two population-based metaheuristic approaches have been proposed, Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC), and their performances are compared.