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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (2): 266-278.doi: 10.3969/j.issn.1005-3085.2024.02.005

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基于通胀和股票误定价带保费退还条款的DC型养老金最优投资策略

殷艳红,  夏登峰,  费为银,  郭宇超   

  1. 安徽工程大学数理与金融学院，芜湖 241000
  • 收稿日期:2021-08-08 接受日期:2022-08-01 出版日期:2024-04-15 发布日期:2024-06-15
  • 通讯作者: 费为银 E-mail: wyfei@ahpu.edu.cn
  • 基金资助:
    国家自然科学基金 (71873002; 62273003; 72271003).

Optimal Investment Strategy of DC Pension Fund with Premium Refund under Inflation and Mispricing

YIN Yanhong,  XIA Dengfeng,  FEI Weiyin,  GUO Yuchao   

  1. School of Mathematics-Physics and Finance, Anhui Polytechnic University, Wuhu 241000
  • Received:2021-08-08 Accepted:2022-08-01 Online:2024-04-15 Published:2024-06-15
  • Contact: W. Fei. E-mail address: wyfei@ahpu.edu.cn}
  • Supported by:
    The National Natural Science Foundation of China (71873002; 62273003; 72271003).

摘要：

研究了在通胀环境和保费退还条款下，缴费确定型 (Defined Contribution, DC) 养老金管理者考虑在无风险资产和带有误定价股票间寻求最优配置以达到终端真实财富预期效用最大化。首先，在通胀环境下，利用随机分析得到养老金管理者的真实财富过程。其次，利用随机控制理论建立了关于养老金管理者值函数满足的 HJB (Hamilton-Jacobi-Bellman) 方程，针对 CRRA (Constant Relateve Risk Aversion) 效用函数求解 HJB 方程，并找出了解析解。最后，通过数值模拟，从经济学角度分析了通胀波动率、误定价系数、风险厌恶系数以及保费退还等参数对养老金管理者投资策略的影响，并给出相应的经济学解释。

关键词: 误定价, 通胀, 养老金, 保费退还, 随机控制

Abstract:

In this article, we consider the optimal investment problem for a defined contribution (DC) pension plan under the inflation environment and the premium refund clause. We assume that the pension funds are allowed to invest in a risk-free asset and a risky asset with mispricing, for the aim of maximizing the expected utility of the terminal real wealth. Firstly, under the inflation environment, the dynamic equation of the real wealth procession is obtained by using the stochastic Calculus. Secondly, stochastic control theory is used to establish the HJB equation of the real value function of fund manager with the CRRA utility function. Moreover, the analytical solutions of the HJB equation are found. Finally, the impact of inflation volatility, mispricing, risk aversion and premium refund on the optimal strategies are given by numerical simulations. The explain of the economic implications of our theoretical results also be presented.

Key words: mispricing, inflation, pension investment, premium refund, stochastic control

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