Investment in real economic activities is generally uncertain and stochastic,and investors'choice of risky assets is of multi-stage in most cases.Based on this reality,multiple frictions in a fuzzy environment are considered and a base constraint is proposed on assets using transaction restrictions to develop a likelihood mean-lower half-variance-entropy multi-stage portfolio optimization model(V-S-M),which is a multi-stage mixed integer programming problem.A genetic differential co-evolutionary algorithm(GAHDE)for solving the model is presented to analyse the portfolio strategy under different risk attitudes,and the numerical re-sults are compared with the likelihood mean-lower half variance model(V-M)and the likelihood mean-entropy model(S-M),as well as with standard genetic algorithms(GA)and differential evolution algorithms(DE).The results validated the superiority and effectiveness of the model and algorithm designed in this paper.
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