CAJ | 학술논문

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。
투자조합시일개복잡계통문제，선택합괄적q-분포급기밀도표체형식시응용중적일개중요문제。수선종함유조성적선성수궤미분방정중추도출q-고사분포개솔밀도함수，기표체형식간단，삼수대분포적영향비상직관；접착장q-고사분포응용우투자조합이론적균치-방차모형화균치-VaR모형；최후결합호시고표수거진행실증분석，결과표명량충모형재q-고사분포가설하적실제수익균대우기재고사분포가설하적실제수익。
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 .