基于可信性理论的均值-熵-偏度投资组合模型及其算法求解

Mean-Entropy-Skewness Portfolio Model Based on Credibility Theory and Its Algorithm Solution

本文考虑到证券市场的投资者往往面临着随机和模糊两种不确定性的情形,在模糊随机环境下把证券的收益率视作三角模糊变量,在可信性理论基础上建立了带融资约束条件的均值-熵-偏度三目标投资组合决策模型,拓展了基于可信性理论的投资组合决策模型的研究内容,同时通过对约束条件处理方法,外部档案维护方法等关键算子的改良,提出了一种新的约束多目标粒子群算法。本文运用该算法对模型进行求解,把得到的最优解与传统的多目标粒子群算法得到的最优解进行对比,结果表明新算法得到的最优解的质量会显著地优于传统的多目标粒子群算法的最优解,从而验证了算法的有效性和准确性。该算法可以在三维空间中得到一个分布性和逼近性较好的Pareto最优曲面,满足投资者对不同目标的差异需求,为投资者提供合理的投资组合决策方案。

Considering that investors are often faced with both random and fuzzy uncertainty in the securities market,in this paper,we regard securities yield as a triangular fuzzy variable. We build a mean-entropy-skewness portfolio model on the basis of credibility theory to extend the research about portfolio model based on credibility theory. At the same time,an improved constrained multi-objective particle swarm optimization algorithm is proposed by improving the key operators such as constraint condition method and the pareto optimal solutions maintenance method. The feasible solution is compared with the feasible solution generated by traditional multi-objective particle swarm optimization algorithm. The results show that the solution of the improved constrained multiobjective particle swarm algorithm is superior to that generated by traditional multi-objective particle swarm optimization algorithm. The feasibility and accuracy of the algorithm is verified,and the pareto optimal surface with better distribution and approximation can be obtained in three-dimensional space to meet the demand of different target,to provide investors with a reasonable portfolio decision.