求解均值-CVaR投资组合模型的改进粒子群算法

针对粒子群算法易跳过全局极值,且只能求解连续性问题的缺点,提出离散复形法局部搜索的思想,来有效提高粒子群算法在离散型问题中的搜索性能。针对粒子群算法易陷入局部极小的缺点,引入自适应粒子迁徙操作保证粒子的多样性,有效避免陷入局部收敛。对采用CVaR度量风险、构建有交易费用和限制证券比例的均值-CVaR投资组合模型进行仿真实验,实验结果验证了算法的有效性。将改进的粒子群算法应用到求解均值-CVaR模型的投资组合问题,与其他算法相比,该方法精度更高、性能更稳定。

An improved particle swarm optimization algorithm for portfolio based on mean-CVaR model

The particle swarm optimization (PSO) has a strong capability of global search, but it easily falls into global extremum. Besides, it can only solve the continuity problems. In order to improve these problems, we present a discrete complex method of local search, which can enhance the search capability when solving discrete problems. Since the PSO is easy to fall into local minimum, we introduce the adaptive particle migration operation to ensure the diversity of particles and avoid falling into local convergence effectively. Simulation experiments adopt the CVaR risk measurement method to measure portfolio risks, and establish an optimization mean-CVaR model which contains the transaction costs and the limitation proportion of the assets. Experimental results verify the effectiveness of the algorithm. Compared with other algorithms, the improved PSO algorithm has higher precision and stability.