基于q-高斯分布的投资组合实证分析

Empirical Analysis on Portfolio Model Based on q-Gaussian

投资组合是一个复杂系统问题,选择合适的q-分布及其密度表达形式是应用中的一个重要问题。首先从含有噪声的线性随机微分方程中推导出q-高斯分布概率密度函数,其表达形式简单,参数对分布的影响非常直观;接着将q-高斯分布应用于投资组合理论的均值-方差模型和均值-VaR模型;最后结合沪市股票数据进行实证分析,结果表明两种模型在q-高斯分布假设下的实际收益均大于其在高斯分布假设下的实际收益。

q-Gaussian distribution has been widely used in interdisciplinary sciences and complex systems.In this paper,we infer density function of q-Gaussian distribution from linear stochastic differential equation with both multiplicative and additive noises.This density function form is easily-used and the influence of parameters on the distribution is more intuitive.By using q-Gaussian distribution in mean-variance and mean-VaR portfolio models with data from Shanghai Stock,a better result can be obtained under the assumption that stock returns obey q-Gaussian distribution than Gaussian distribution.