The defined contribution pension plan after retirement under the criterion of a revised loss considering the economic situation

Zongqi Sun; Peng Yang; Jing Wu; Yunpeng Fan; Zongqi Sun; Peng Yang; Jing Wu; Yunpeng Fan

doi:10.3934/math.2024229

AIMS Mathematics

2024, Volume 9, Issue 2: 4749-4761. doi: 10.3934/math.2024229

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Research article

The defined contribution pension plan after retirement under the criterion of a revised loss considering the economic situation

1.
School of Computer Science, Xijing University, Xi'an, Shaanxi 710123, China
2.
School of Statistics, Xi'an University of Finance and Economics, Xi'an, Shaanxi 710048, China
3.
Department of Mathematics, Xian Siyuan University, Xi'an, Shaanxi 710038, China

Received: 28 December 2023 Revised: 15 January 2024 Accepted: 15 January 2024 Published: 22 January 2024
MSC : 91B05, 91G05

Considering the economic situation, we investigate the optimal asset allocation of defined contribution pension funds with random payouts after retirement under a modified criterion of quadratic loss. The HJB equation is derived adhering to the dynamic programming principle, and the time-consistent optimal investment strategy is designed based on the calculus theory. Finally, under two different risk attitudes, namely surplus preference and risk aversion, the impact of key parameters on the optimal investment strategy and the function of minimum loss at the initial moment is compared and analyzed, the economic significance is demonstrated, and the rationality of the model is verified.
- criterion of modified quadratic loss,
- penalty coefficient,
- risk investment,
- value function,
- HJB equation,
- time-consistent investment strategy
Citation: Zongqi Sun, Peng Yang, Jing Wu, Yunpeng Fan. The defined contribution pension plan after retirement under the criterion of a revised loss considering the economic situation[J]. AIMS Mathematics, 2024, 9(2): 4749-4761. doi: 10.3934/math.2024229

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Abstract

Considering the economic situation, we investigate the optimal asset allocation of defined contribution pension funds with random payouts after retirement under a modified criterion of quadratic loss. The HJB equation is derived adhering to the dynamic programming principle, and the time-consistent optimal investment strategy is designed based on the calculus theory. Finally, under two different risk attitudes, namely surplus preference and risk aversion, the impact of key parameters on the optimal investment strategy and the function of minimum loss at the initial moment is compared and analyzed, the economic significance is demonstrated, and the rationality of the model is verified.

References

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