A novel hybrid heuristic algorithm for a new uncertain mean-variance-skewness portfolio selection model with real constraints

Abstract

This paper discusses a portfolio selection problem under the mean-variance-skewness framework wherein the security returns are obtained through evaluation of the experts instead of historical data. By treating security returns as the uncertain variables, an uncertain mean-variance-skewness model is proposed for portfolio selection under consideration of the transaction costs, bounds on holdings, cardinality of the portfolio, and minimum transaction lots constraints. To solve the resultant portfolio selection problem, which is an NP-Complete nonlinear integer programming problem, a hybrid solution method termed the FA-GA is developed by combining features of the firefly algorithm (FA) and genetic algorithm (GA). In the proposed method, the crossover and mutation operators of the GA are integrated into the FA to strike an optimal balance between the exploration and exploitation. A numerical example of portfolio selection is given to demonstrate effectiveness of the proposed model and solution algorithm. Furthermore, a detailed performance analysis and comparison are done to establish superiority of the proposed model and solution method.