通货膨胀下的$\alpha$-鲁棒最优投资策略研究

数学物理学报 ›› 2024, Vol. 44 ›› Issue (6): 1617-1629.

通货膨胀下的$\alpha$-鲁棒最优投资策略研究

陈雅婷¹(),刘海燕¹(),陈密^1,^2,^3,^*()

¹福建师范大学数学与统计学院福州 350117
²分析数学及应用教育部重点实验室福州 350117
³统计学与人工智能福建省高校重点实验室福州 350117

收稿日期:2024-01-19 修回日期:2024-05-06 出版日期:2024-12-26 发布日期:2024-11-22
通讯作者: ^*陈密, Email: chenmi0610@163.com
作者简介:陈雅婷, Email: 895707632@qq.com;|刘海燕, Email: rain6397@163.com
基金资助:
国家自然科学基金(11701087);福建省自然科学基金(2023J01537);福建省自然科学基金(2023J01538)

$\alpha$-Robust Optimal Investment Strategy Under Inflation

Chen Yating¹(),Liu Haiyan¹(),Chen Mi^1,^2,^3,^*()

¹School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117
²Key Laboratory of Analytical Mathematics and Applications $($Ministry of Education$)$, Fuzhou 350117
³Fujian Provincial Key Laboratory of Statistics and Artificial Intelligence, Fuzhou 350117

Received:2024-01-19 Revised:2024-05-06 Online:2024-12-26 Published:2024-11-22
Supported by:
NSFC(11701087);NSF of Fujian Province(2023J01537);NSF of Fujian Province(2023J01538)

摘要/Abstract

摘要：

该文主要研究通货膨胀下具有模型不确定性的最优投资问题. 假定金融市场上存在无风险资产、风险资产以及用于对冲通胀风险的通货膨胀指数债券可投资, 其中风险资产价格服从 CEV 模型, 而后利用价格指数水平折现各类资产价格呈现其真实价格, 运用 $\alpha$-maxmin 均值方差效用函数建立投资模型, 并通过求解 HJB 方程获得均衡投资策略与值函数的显式解. 最后结合数值仿真分析了参数变动下的最优投资策略变化趋势.

关键词: 通货膨胀, 指数债券, 通胀折现, $\alpha$-鲁棒均值方差准则, CEV 模型

Abstract:

This paper focuses on the optimal investment problem with model uncertainty under inflation. It is assumed that there are risk-free assets, risky assets and inflation-indexed bonds used to hedge inflation risk in the financial market, in which the price of risky assets obeys the CEV model, and then the price index level is used to discount the price of each type of asset to present its true price, and the investment model is built by applying the $\alpha$-maxmin mean-variance utility function and the equilibrium investment strategy and value function are obtained by solving the HJB equation. Finally, the trend of optimal investment strategies under parameter variations is analyzed by numerical simulation.

Key words: Inflation, Index bonds, Inflation discounting, $\alpha$-robust mean-variance criterion, CEV model

中图分类号:

O211.6

陈雅婷, 刘海燕, 陈密. 通货膨胀下的$\alpha$-鲁棒最优投资策略研究[J]. 数学物理学报, 2024, 44(6): 1617-1629.

Chen Yating, Liu Haiyan, Chen Mi. $\alpha$-Robust Optimal Investment Strategy Under Inflation[J]. Acta mathematica scientia,Series A, 2024, 44(6): 1617-1629.

图/表 5

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