变系数模型CVaR约束下最优投资组合选择——基于非广延统计理论

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摘要：

考虑到经济变量随时间的变化而变化,设想资产的收益和协方差矩阵为时间的函数是合理的.一些实证结果表明,风险资产的收益分布呈现出厚尾特征.因此,应用Tsallis分布来驱动风险资产收益的变化,可以更好地捕捉厚尾这一特征.基于非广延统计理论,在CVaR约束下,提出了连续时间最优投资组合选择问题.针对模型中的时变系数,采用局部常数拟合的方法.首先,在非广延统计理论下,构造了风险资产的价格过程.然后,利用随机动态规划方法得到了HJB方程.在对数效用函数下,利用拉格朗日乘子法,得到了对数效用函数下具有CVaR约束的最优投资组合策略,并通过实证分析展示了所得结论的拟合效果.

Considering that economic variables vary over time,it is reasonable to assume that the returns and covariance matrices of assets are time-varying functions.Moreover,several empirical resalts show that the distributions of returns for risky assets have appeared the characteristics of fat tails.Therefore,we apply Tsallis distribution to driving the returns of risky assets,which can capture this characteristics of fat tails better.In this paper,we propose continuous-time optimal portfolio selection problem with CVaR constraint under non-extensive statistical mechanics.According to the time-varying coefficient in the model,the local constant fitting method is adopted.We first construct the price process of risky asset under non-extensive statistical mechanics.Then,the HJB equation is obtained by using the stochastic dynamic programming method.Furthermore,we propose the optimal portfolio strategy with CVaR constraint under the logarithmic utility function by Lagrange multiplier techniques.Empirical analysis is discussed to show the fitting effect of the obtained conclusions.

作者：

王继霞赫梦钰

Wang Jixia;He Mengyu(College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China)

机构地区：

betway官方app 数学与信息科学学院

出处：

《betway官方app 学报：自然科学版》 CAS 北大核心 2022年第1期59-66,共8页

Journal of Henan Normal University(Natural Science Edition)

基金：

国家自然科学基金(11971154)。

关键词：

非广延统计理论投资组合选择 CVAR约束时变模型 HJB方程