基于遗传算法的高阶矩投资组合模型研究

The Higher Moment Portfolio Model Based on Genetic Algorithm

金融资产收益数据普遍具有非对称和尖峰厚尾的分布,传统的马克维茨投资组合模型仅仅考虑了均值和方差的约束,这在确定投资组合时是不充分的.考虑了三阶矩偏度和四阶矩峰度对投资组合的影响,假定交易费用为V-型函数,建立了均值-方差-偏度-峰度投资组合模型,鉴于多目标优化求解的复杂性,编写遗传算法程序求解这一高阶矩投资组合,最后给出了一个数值算例.

The data of financial assets gains generally have asymmetric distribution and a fat tail, the traditional Markowitz portfolio model only considers the constraints of mean and variance, which is not sufficient in the deter- mination of the portfolio. Considering the impact of third-order moments skewness and the four order moment kurtosis on portfolio, assuming that the transaction costs are the V-type function, we established a mean-variance- skewness-kurtosis portfolio model. Then we used the genetic algorithm to solve the higher moment portfolio model and give a numerical example at the final.