Optimal Investment Strategies for DC Pension Plan with Administrative Fees and Return of Premiums Clauses Under the Heston Model

doi:10.1007/s40305-023-00505-0

Journal of the Operations Research Society of China ›› 2025, Vol. 13 ›› Issue (4): 1018-1047.doi: 10.1007/s40305-023-00505-0

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Optimal Investment Strategies for DC Pension Plan with Administrative Fees and Return of Premiums Clauses Under the Heston Model

Jian Pan¹, Xiang-Ying Zhou²

1 College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, Jiangxi, China;
2 Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou 341000, Jiangxi, China

Received:2022-10-04 Revised:2023-05-31 Online:2025-12-30 Published:2025-12-19
Contact: Jian Pan E-mail:pan79610@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (No. 11761009) and the Science and Technology Project of Jiangxi Provincial Education Department (No. GJJ201403).

Abstract

Abstract: In this paper, we study an optimal investment problem for a defined contribution (DC) pension plan with two administrative fees during the accumulation phase. In our model, the pension fund member contributes a predetermined amount of money as a premium and then the pension fund administrator invests the premium in a financial market to increase the value of the accumulation, where the financial market consists of a risk-free asset and a risky asset satisfied the Heston model. Besides, to protect the rights of pension fund members who die before retirement, we introduce a return of premiums clauses and use the Abraham De Moivre model to characterize the force of mortality. With the help of actuarial theory and Taylor expansion theorem, we formalize the problem as a continuous-time portfolio optimization problem. By applying the stochastic control method and variable change techniques, we derive closed-form expressions of optimal investment strategies and corresponding value functions under the power utility function and exponential utility function. Based on the closed-form expressions, we determine the equivalent administrative charges by equating the maximum terminal certainty equivalent that can be achieved under the two types of administrative charges and find out some relationships between the two charges under the same utility function. Finally, we provide numerical experiments to analyze the effects of some parameters on the optimal investment strategy, the value function and the relationship between the two equivalent administrative charges.

Key words: DC pension plan, Administrative fees, Return of premiums clauses, Heston model, Optimal investment strategy

CLC Number:

Jian Pan, Xiang-Ying Zhou. Optimal Investment Strategies for DC Pension Plan with Administrative Fees and Return of Premiums Clauses Under the Heston Model[J]. Journal of the Operations Research Society of China, 2025, 13(4): 1018-1047.

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Optimal Investment Strategies for DC Pension Plan with Administrative Fees and Return of Premiums Clauses Under the Heston Model

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