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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 (3): 455-472.doi: 10.3969/j.issn.1005-3085.2025.03.005doi: 32411.14.1005-3085.2025.03.005

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通胀风险下带有保费返还条款的TBP养老金最优控制策略

陈  娅,   刘  伟   

  1. 新疆大学数学与系统科学学院，乌鲁木齐  830017
  • 收稿日期:2022-09-02 接受日期:2023-08-21 出版日期:2025-06-15 发布日期:2025-06-15
  • 通讯作者: 刘伟 E-mail: liuwei.math@xju.edu.cn
  • 基金资助:
    新疆维吾尔自治区自然科学基金 (2024D01C39).

Optimal Control Strategy for TBP Pension with Premium Refund Clauses under Inflation Risk

CHEN Ya,   LIU Wei   

  1. School of Mathematics and System Sciences, Xinjiang University, Urumqi 830017
  • Received:2022-09-02 Accepted:2023-08-21 Online:2025-06-15 Published:2025-06-15
  • Contact: W. Liu. E-mail address: liuwei.math@xju.edu.cn
  • Supported by:
    The Natural Science Foundation of Xinjiang Uygur Autonomous Region (2024D01C39).

摘要：

研究了通胀风险下目标收益养老金计划的最优控制策略。为了保障在累积阶段死亡的养老金成员的权益，在计划中引入保费返还条款。养老基金管理者可以将资金投资于无风险资产，通胀指数债券和股票组成的金融市场。以收益给付和养老基金终端财富的预期效用最大为优化目标，求解最优投资策略和收益给付策略，其中效用函数采用Cobb-Douglas效用函数。运用动态规划方法，通过求解相应的Hamilton-Jacobi-Bellman (HJB) 方程，得到了最优策略以及值函数的显式表达式。最后，通过数值分析讨论了重要参数对最优收益给付和养老基金财富的影响。

关键词: 目标收益养老金计划, 通胀风险, 保费返还条款, Cobb-Douglas效用函数

Abstract:

This paper explores optimal control strategies for target benefit pension plans in the presence of inflation risk. It proposes a premium refund clause to protect members who pass away during the accumulation phase. The pension fund can invest in a risk-free asset, an inflation-indexed bond, and a stock. By maximizing the expected utility of benefits and final wealth using the Cobb-Douglas utility function, the optimal investment and benefits strategies are determined through Hamilton-Jacobi-Bellman (HJB) equations. Numerical analyses examine the influence of important parameters on benefit payment and fund wealth.

Key words: target benefit pension plans, inflation risk, premium refund clause, Cobb-Douglas utility function

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