基于引力搜索和粒子群混合优化算法的证券投资组合问题研究

A Hybrid Algorithm Based on Gravitational Search and Particle Swarm for the Portfolio Optimization Problem

本文研究考虑交易成本的投资组合模型,分别以风险价值(VAR)和夏普比率(SR)作为投资组合的风险评价指标和效益评价指标。为有效求解此模型,本文在引力搜索和粒子群算法的基础上提出了一种混合优化算法(IN-GSA-PSO),将粒子群算法的群体最佳位置和个体最佳位置与引力搜索算法的加速度算子有机结合,使混合优化算法充分发挥单一算法的开采能力和探索能力。通过对算法相关参数的合理设置,算法能够达到全局搜索和局部搜索的平衡,快速收敛到模型的最优解。本文选取上证50股2014年下半年126个交易日的数据,运用Matlab软件进行仿真实验,实验结果显示,考虑交易成本的投资组合模型可使投资者得到更高的收益率。研究同时表明,基于PSO和GSA的混合算法在求解投资组合模型时比单一算法具有更好的性能,能够得到满意的优化结果。

This research focuses on the portfolio optimization model considering transaction costs. Value-at-Risk （VAR）and Sharpe-Ratio（SR）are used respectively as the risk evaluation index and efficiency evaluation index for a portfolio. To solve the problem effectively, a hybrid optimization algorithm named IN-GSA-PSO is proposed by combining the Gravitational Search Algorithm （ GSA ） and the Particle Swarm Optimization （ PSO ） algorithm. The ＂global best＂ and ＂personal best＂ positions in PSO are integrated with the ＂ acceleration＂ mechanism in GSA to determine the search direction. As a result, the hybrid algorithm is able to fully utilize the exploration and exploitation abilities of each individual algorithm. With fine-tuned parameters, the hybrid algorithm can achieve an effective balance between global search and local search and thus converges fast to high-quality solu- tions. We adopt the data of 50 stocks in the Shanghai index during 126 trading days in the second half of 2014 for simulation experiments using Matlab software. Experimental results show that the portfolio model considering transaction costs can guarantee higher yields for the investors. Computational results also suggest that the hybrid algorithm based on PSO and GSA outperforms individual algorithms when solving the portfolio optimization problem, leading to more satisfactory solutions.