通货膨胀下的α-鲁棒最优投资策略研究  

α-Robust Optimal Investment Strategy Under Inflation

作　　者：陈雅婷[1] 刘海燕[1] 陈密[1,2,3] Chen Yating;Liu Haiyan;Chen Mi(School of Mathematics and Statistics,Fujian Normal University,Fuzhou 350117;Key Laboratory of Analytical Mathematics and Applications(Ministry of Education),Fuzhou 350117;Fujian Provincial Key Laboratory of Statistics and Artificial Intelligence,Fuzhou 350117)

机构地区：[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

出　　处：《数学物理学报（A辑）》2024年第6期1617-1629,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(11701087);福建省自然科学基金(2023J01537,2023J01538)

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α-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.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 theα-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.

关 键 词：通货膨胀 指数债券 通胀折现 α -鲁棒均值方差准则 CEV 模型 

分 类 号：O211.6[理学—概率论与数理统计]