Biogeography-Based Optimization of the Portfolio Optimization Problem with Second Order Stochastic Dominance Constraints

The portfolio optimization problem is the central problem of modern economics and decision theory; there is the Mean-Variance Model and Stochastic Dominance Model for solving this problem. In this paper, based on the second order stochastic dominance constraints, we propose the improved biogeography-based optimization algorithm to optimize the portfolio, which we called εBBO. In order to test the computing power of εBBO, we carry out two numerical experiments in several kinds of constraints. In experiment 1, comparing the Stochastic Approximation (SA) method with the Level Function (LF) algorithm and Genetic Algorithm (GA), we get a similar optimal solution by εBBO in [0, 0.6] and [0, 1] constraints with the return of 1.174% and 1.178%. In [−1, 2] constraint, we get the optimal return of 1.3043% by εBBO, while the return of SA and LF is 1.23% and 1.26%. In experiment 2, we get the optimal return of 0.1325% and 0.3197% by εBBO in [0, 0.1] and [−0.05, 0.15] constraints. As a comparison, the return of FTSE100 Index portfolio is 0.0937%. The results prove that εBBO algorithm has great potential in the field of financial decision-making, it also shows that εBBO algorithm has a better performance in optimization problem.