A New Population Initialization Approach Based on Bordered Hessian for Portfolio Optimization Problems

In the portfolio optimization problems, the proportion-weighted combination in a portfolio is represented as a real-valued array between 0 and 1. While applying any evolutionary algorithm, however, the algorithm hardly takes the ends of a given real value. It means that the evolutionary algorithms have a problem that they cannot give the not-selected asset whose weight is represented as 0. In order to avoid this problem, we propose a new population initialization approach using the extreme point of the bordered Hessian and then apply our approach to the initial population of GA for the portfolio optimization problems in this paper. In the numerical experiments, we show that our method employing the population initialization approach and GA works very well for the portfolio optimizations even if the portfolio consists of the large number of assets.