A hybrid FA–SA algorithm for fuzzy portfolio selection with transaction costs

Based on possibility theory, this paper deals with the portfolio adjusting problem for an existing portfolio under the assumption that the returns of risky assets are fuzzy numbers and there exists transaction costs in portfolio adjusting process. We propose a possibilistic mean-semi-absolute deviation portfolio model with V-shaped transaction costs, which are associated with a shift from the current portfolio to an adjusted one. In the proposed model, we take the possibilistic mean of the return as the investment return and possibilistic semi-absolute deviation of the return as the investment risk. To solve the proposed portfolio problem, a hybrid technique named as FA–SA algorithm combining firefly algorithm (FA) and simulated annealing algorithm (SA) is developed by taking the advantage of both FA and SA. In this algorithm, FA operates in the direction of enhancing the exploitation ability while SA improves the exploration using the lévy flight. Finally, a numerical example is given to demonstrate the effectiveness of the proposed model and the hybrid algorithm.