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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 ›› 2025, Vol. 42 ›› Issue (1): 97-113.

• • 上一篇    下一篇

随机利率与通胀风险下带有最低担保的均值–方差养老金计划

寇梦柯,  常  浩   

  1. 天津工业大学数学科学学院，天津 300387
  • 收稿日期:2022-05-29 接受日期:2022-09-29 出版日期:2025-02-15 发布日期:2025-04-15
  • 通讯作者: 常浩 E-mail: ch8683897@126.com
  • 基金资助:
    国家社会科学基金(21FJYB042).

Dynamic Mean-variance DC Pension Planning with a Minimum Guarantee under Stochastic Interest Rate and Inflation Environments

KOU Mengke,  CHANG Hao   

  1. School of Mathematical Sciences, Tiangong University, Tianjin 300387
  • Received:2022-05-29 Accepted:2022-09-29 Online:2025-02-15 Published:2025-04-15
  • Contact: H. Chang. E-mail address: ch8683897@126.com
  • Supported by:
    The National Social Science Foundation of China (21FJYB042).

摘要：

研究了在利率风险和通胀风险环境下带有最低担保的均值–方差养老金计划问题。在缴费确定型养老金计划中，其中缴费率是预先确定的，养老金的给付取决于养老金积累阶段的缴费和投资收益，而且投资风险完全由养老金成员承担。因此，实现养老金的精准投资以及提高养老金的给付效率，对于缓解当前的养老压力具有重要意义。假设利率模型由Cox-Ingersoll-Ross利率模型描述，为了维持养老金成员退休后的生活水平，养老金计划的终端财富收益应超过最低担保。应用拉格朗日对偶定理和随机动态规划原理，求解扩展的Hamilton-Jacobi-Bellman方程，得到有效策略和有效前沿的显式表达式。结果表明：利率风险、通胀风险和工资风险环境下的资本市场线在均值–标准差平面内仍然是一条直线。

关键词: DC型养老金计划, 利率风险, 通胀风险, 最低担保, 均值–方差模型, 随机动态规划原理

Abstract:

In a defined contribution (DC) pension plan, the contribution rate is determined in advance and the pension payment depends on the contribution and investment return during the pension accumulation stage, and the investment risk is borne by the pension members themselves. In this situation, to realize the precise investment in pension funds and to improve the payment efficiency of pension funds has great theoretical and practical significance for relieving the current pension pressure. The interest rate model is described by the Cox-Ingersoll-Ross (CIR) dynamics. In addition, in order to keep the living standard of members, the terminal value of the pension plan should exceed a guarantee which serves as an annuity after retirement. By applying the principle of Lagrangian duality theorem and stochastic dynamic programming, the extended Hamilton-Jacobi-Bellman (HJB) equation is solved, we obtain the mean-variance efficient strategy and the efficient frontier explicitly. The result shows that the capital market line in the environment of the interest rate risk, the inflation risk and the salary risk is still a straight line in the mean-standard deviation plane.

Key words: DC pension plans, interest rate risk, inflation risk, minimum guarantee, mean-variance model, stochastic dynamic programming

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