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.
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
.
DOI: 10.1007/s40305-023-00505-0
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