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**Optimal control of DC pension plan management under two incentive schemes.**
*(English)*
Zbl 1411.91285

Summary: Since the late 1990s, a performance fee arrangement has been approved as a managerial incentive in direction contribution (DC) pension plan management to motivate managers. However, the fact that managers may take undue risk for the larger performance fees and thus reduce members’ utility has been a subject of debate. As such, this study investigates the optimal risk-taking policies of DC pension fund managers under both the single management fee scheme and a mixed scheme with a lower management fee, as well as an additional performance fee. The analytical solutions are derived by using the duality method and concavification techniques in a singular optimization problem. The results show the complex risk-taking structures of fund managers and recognize the win-win situation of implementing performance-based incentives in DC pension plan management. Under the setting of geometric Brownian motion asset price dynamics and constant relative risk aversion utility, the optimal risk investment proportion shows a peak-valley pattern under the mixed scheme. Further, the manager gambles for gain when fund wealth is low and time to maturity is short. As opposed to the existing literature, this study found that the risk-taking policy is more conservative when fund wealth is relatively large. Furthermore, the utilities of the manager and members could both be improved by appropriately choosing the performance fee rate.

### MSC:

91B30 | Risk theory, insurance (MSC2010) |

49N90 | Applications of optimal control and differential games |

### Keywords:

direction contribution pension plan management; optimal control; optimal risk-taking policies
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\textit{L. He} et al., N. Am. Actuar. J. 23, No. 1, 120--141 (2019; Zbl 1411.91285)

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