An optimal investment strategy for DC pension plans with costs and the return of premium clauses under the CEV model

Xiaoyi Tang; Wei Liu; Wanyin Wu; Yijun Hu; Xiaoyi Tang; Wei Liu; Wanyin Wu; Yijun Hu

doi:10.3934/math.20241057

AIMS Mathematics

2024, Volume 9, Issue 8: 21731-21754. doi: 10.3934/math.20241057

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An optimal investment strategy for DC pension plans with costs and the return of premium clauses under the CEV model

1.
School of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, China
2.
School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China

Received: 04 April 2024 Revised: 29 May 2024 Accepted: 05 June 2024 Published: 08 July 2024
MSC : 91B16, 91B70

This paper presents a novel optimization model that explores the optimal investment strategies for DC pension plans with return of premium clauses. We have assumed that the financial market consists of a risk-free asset and a risky asset, where the price of the risky asset follows the CEV model. Under the expected utility criterion, the optimal investment strategies were derived by employing stochastic optimal control theory and the Legendre transformation method. Explicit expressions of the optimal investment strategy were provided when the utility function was specified as exponential, power, or logarithmic. Finally, numerical analysis was conducted to examine the impact of factors such as interest rate, return rate, and volatility of the risky asset on the optimal strategies.
- constant elasticity of variance model,
- defined contribution pension plan,
- return of premium clauses,
- expected utility,
- tax,
- trading fee
Citation: Xiaoyi Tang, Wei Liu, Wanyin Wu, Yijun Hu. An optimal investment strategy for DC pension plans with costs and the return of premium clauses under the CEV model[J]. AIMS Mathematics, 2024, 9(8): 21731-21754. doi: 10.3934/math.20241057

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Abstract

This paper presents a novel optimization model that explores the optimal investment strategies for DC pension plans with return of premium clauses. We have assumed that the financial market consists of a risk-free asset and a risky asset, where the price of the risky asset follows the CEV model. Under the expected utility criterion, the optimal investment strategies were derived by employing stochastic optimal control theory and the Legendre transformation method. Explicit expressions of the optimal investment strategy were provided when the utility function was specified as exponential, power, or logarithmic. Finally, numerical analysis was conducted to examine the impact of factors such as interest rate, return rate, and volatility of the risky asset on the optimal strategies.

References

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