Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2025, Vol. 42 ›› Issue (1): 97-113.

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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).

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

CLC Number: