常弹性方差模型下含资本利得税的最优投资策略
PDF下载 (202)李千妍,王 伟.常弹性方差模型下含资本利得税的最优投资策略[J].宁波大学学报(理工版),2023,36(4):104-111.DOI:10.20098/j.cnki.1001-5132.2023.0235
LI Qianyan,WANG Wei.Optimal investment strategies with capital gains tax under constant elasticity of variance model[J].Journal of Ningbo University(Natural Science & Engineering Edition),2023,36(4):104-111.DOI:10.20098/j.cnki.1001-5132.2023.0235
| Title: | Optimal investment strategies with capital gains tax under constant elasticity of variance model |
| 作者: | 李千妍, 王 伟 |
| Author(s): | LI Qianyan, WANG Wei |
| 关键词: | 资本利得税; 常弹性方差; 动态规划; 最优投资 |
| Keywords: | capital gains tax; constant elasticity of variance; dynamic programming; optimal investment |
| 分类号: | O211.9 |
| DOI: | 10.20098/j.cnki.1001-5132.2023.0235 |
| 文献标识码: | A |
| 摘要: | 研究风险资产价格动态满足常弹性方差模型且考虑资本利得税情形下的最优投资问题. 假定金融市场中有无风险债券和风险资产两种可投资资产, 风险资产的价格动态满足常弹性方差模型且这两种资产的收益都将被征收不同税率的税收. 基于最大化终端财富期望效用的目标, 利用随机动态规划原理建立相应的Hamilton-Jacobi-Bellman (HJB)方程, 通过求解HJB方程并利用一阶最优条件, 分别得到幂效用和指数效用下最优投资策略的解析解, 最后给出数值结果和经济学解释. |
| Abstract: | The optimal investment problem with capital gains tax under the constant elastic variance model is studied in this article. Furthermore, it is assumed that there are two kinds of investable assets in the financial market: a risk-free bond and a risk asset. The price dynamics of risk asset is assumed to satisfy the constant elastic variance model and the income of these two assets will be taxed at different tax rates. Based on the goal of maximizing the expected utility of terminal wealth, the corresponding Hamilton-Jacobi-Bellman (HJB) equation is established using the principle of stochastic dynamic programming. By solving the HJB equation and using the first-order optimal conditions, the analytical solutions of the optimal investment strategies under power utility and exponential utility are obtained respectively. Finally, the numerical results and economic explanations are given in this article. |
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| 备注/Memo: | 收稿日期: 2023－02－22. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/基金项目: 教育部人文社科基金（18YJC910012）.第一作者: 李千妍（1998－）, 女, 安徽宣城人, 在读硕士研究生, 主要研究方向: 应用概率. E-mail: 2111071019@nbu.edu.cn*通信作者: 王伟（1982－）, 男, 安徽安庆人, 教授, 主要研究方向: 应用概率. E-mail: wangwei2@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
