多期证券投资组合问题的区间多目标规划求解方法

Interval multi-objective programming methods for solving multi-period portfolio selection problems

投资组合问题主要研究如何将有限的资金合理地分配到不同的金融资产中,以实现收益最大化与风险最小化之间的均衡.然而,证券市场往往具有很强的不确定性,投资者对于证券的期望收益率和风险损失率难以用精确数值描述,区间规划则是处理这类不确定性问题的有力工具.鉴于此,首先基于区间多目标规划建立一个以预期收益率、风险损失率和流动性为目标函数的多期投资组合选择模型;然后通过设计一个定向变异算子,改进基于偏好多面体的交互式遗传算法,并将上述算法的运算机制与所建模型的多期特性相结合以求解模型;最后在不确定交互进化优化系统上进行实证分析.实验结果表明,所提出算法能够根据投资者的不同需要得到相应最满意的多期资产组合.

Portfolio selection problems mainly address how to rationally allocate limited funds to different financial assets to balance maximal returns and minimal risks.However,it is difficult for investors to describe the expected return rate and the risk loss rate of securities via crisp numbers due to the big uncertainties in the security market.Interval programming is a powerful tool to deal with these uncertain problems.In this paper,a multi-period portfolio selection model,which takes the expected return rate,risk loss rate of securities and liquidity as objective functions,is first constructed based on interval multi-objective programming.Then,a directional mutation operator is developed to modify the interactive genetic algorithm based on preference polyhedron whose operator mechanism combines with multi-period characteristics of the constructed model to tackle the model.Finally,empirical analysis is conducted on an uncertain interactive evolutionary optimization system.Experimental results demonstrate that the proposed algorithm can find the most satisfied multi-period portfolios corresponding to an investor’s different demands.