Fuzzy multi-period portfolio selection model with discounted transaction costs

In this paper, we discuss a multi-period portfolio selection with discounted transaction costs in a fuzzy uncertain investment environment, which has not been given much attention before. We assume that an investor’s motivation is to find the portfolio with maximizing terminal wealth and the cumulative skewness on portfolios, and minimizing the cumulative risk on portfolios. We consider the major criteria including wealth, risk, skewness, transaction costs, proportion entropy, transaction lots, the maximum holding number of assets in the portfolio and budge constraint. We propose a possbilistic mean-semivariance-skewness model with discounted transaction costs for multi-period fuzzy portfolio selection. To solve the multi-objective portfolio selection model, we first introduce a weighted max–min fuzzy goal programming approach to take investor’s different investment preferences into account and transform it into a single-objective programming problem and then design a dynamic differential evolution algorithm for solution. Finally, we provide an empirical study with the sample data from Chinese stock market to analyze the application of the model and the performance of the solution algorithm.