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): 139-158.

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Optimal Asset Allocation and Life Annuity Payment Strategy under Cobb-Douglas Utility and Epstein-Zin Recursive Utility

WANG Suxin1,  RONG Ximin2,  ZHAO Hui2   

  1. 1. School of Finance, Tianjin University of Finance and Economics, Tianjin 300222
    2. School of Mathematics, Tianjin University, Tianjin 300072
  • Received:2022-05-11 Accepted:2022-09-29 Online:2025-02-15 Published:2025-04-15
  • Supported by:
    The National Natural Science Foundation of China (11901427; 12171360; 11771329; 12371475; 11871052); the Natural Science Foundation of Tianjin City (20JCYBJC01160); the Outstanding Young Teachers Support Program of Tianjin University of Finance and Economics.

Abstract:

Life annuity plays an important role in the withdrawal phase of pensions, and it can help people deal with longevity risks effectively. This paper considers a stochastic model for a life annuity plan in continuous time, where the initial value of the individual annuity \mbox{account} is determined in advance, while the annuity payments depend on the financial situation of the account. The annuity fund is allowed to invest in a risk-free asset and a risky asset. The fund manager can adjust the annuity payment level and charge management fees to ensure the stable operation of the plan. In the objective function, we aim to maximize the utility of the weighted product of the annuity payment adjustment and the management fee, which is taken in the form of Cobb-Douglas utility. By applying dynamic programming approach, we establish the corresponding Hamilton-Jacobi-Bellman equation and derive the optimal strategies and the value function explicitly. Furthermore, the Epstein-Zin recursive utility is considered as an extension and we find the elasticity of intertemporal substitution has a positive effect on the annuity payment adjustment and the management fee. Numerical examples are presented to illustrate the sensitivity of the optimal strategies to model parameters, and the corresponding economic explanations are given, which demonstrate that this annuity plan is sustainable and can provide stable annuity payment for participants.

Key words: life annuity, Cobb-Douglas utility, Epstein-Zin recursive utility, dynamic programming, optimal investment

CLC Number: