考虑现实约束的模糊多准则投资组合优化模型

针对模糊环境中资产收益和换手率均为模糊变量的投资组合问题, 考虑了资产组合的基数约束、投资比例的边界约束、资产的流动性以及分散化程度约束, 建立了一个以资产组合收益、偏度最大, 同时资产组合风险、不确定性以及模糊性最小为目标的多准则投资组合优化模型. 然后, 利用加权极大-极小模糊目标规划方法将所提出的模型转化为单目标规划问题, 进而设计了一个遗传算法来对其进行求解. 最后, 通过一个实例来阐明所提出模型的实用性以及算法的有效性. 研究结果表明: 本模型能够有效地刻画不同投资者的投资意图, 所设计的算法是有效的.

Fuzzy multiple criteria portfolio selection optimization model under real constrains

This paper deals with a portfolio selection problem in fuzzy environment in which returns and turnover rates of assets are represented by fuzzy variables. A fuzzy multiple criteria portfolio selection optimization model is proposed with the objectives to maximize the return and the skewness of portfolio, while the risk, the ambiguity and the fuzziness of portfolio are minimized. In the proposed model, the cardinality constraint, the bounds of constraints, the liquidity constraint and the diversification degree of portfolio are taken into consideration. A weighted max-min approach for fuzzy goal programming is employed to transform the proposed model into a single objective programming problem. Then, a genetic algorithm is designed for solutions. Finally, we use an empirical example to illustrate the practicability of our model and the efficiency of the designed algorithm. The results illustrate that our model is an effective approach for expressing investors' different investment intention and the designed algorithm is effective.