带随机工资的目标收益养老金计划的鲁棒最优投资和收益支付调整策略

doi:10.15960/j.cnki.issn.1007-6093.2025.01.011

运筹学学报（中英文） ›› 2025, Vol. 29 ›› Issue (1): 127-141.doi: 10.15960/j.cnki.issn.1007-6093.2025.01.011

带随机工资的目标收益养老金计划的鲁棒最优投资和收益支付调整策略

张欣茹¹, 马世霞¹^,*(), 张雨萌¹, 慕蕊¹

1. 河北工业大学理学院, 天津 300401

收稿日期:2021-07-21 出版日期:2025-03-15 发布日期:2025-03-08
通讯作者: 马世霞 E-mail:mashixia1@163.com
基金资助:
国家自然科学基金(12071107)

Robust optimal investment and benefit payment adjustment strategy for target benefit pension plans with stochastic salary

Xinru ZHANG¹, Shixia MA¹^,*(), Yumeng ZHANG¹, Rui MU¹

1. School of Science, Hebei University of Technology, Tianjin 300401, China

Received:2021-07-21 Online:2025-03-15 Published:2025-03-08
Contact: Shixia MA E-mail:mashixia1@163.com

摘要/Abstract

摘要：

本文在目标收益计划(TBPs)下考虑了具有违约风险和模型不确定性的最优投资和收益支付问题。养老金可以投资到无风险资产, 价格服从Heston模型的股票和违约债券。特别地, TBPs成员的工资是随机的。利用随机最优控制方法, 分别推导出了违约后和违约前的鲁棒最优策略和相应的值函数。此外, 还考虑了模糊中性情况下的最优策略。最后给出数值分析来说明参数对最优策略的影响, 从而为养老金管理者提供了有效的决策依据。

关键词: 目标收益养老金计划, 随机工资, 模糊厌恶, 违约风险, Hamilton-Jacobi-Bellman方程

Abstract:

This paper considers the optimal investment and benefit payment problem with default risk and model uncertainty under target benefit plans~(TBPs). The pension funds can be invested in a risk-free asset, a stock whose price process follows Heston model and a defaultable bond. In particular, the salary of TBPs members is stochastic. Using the stochastic optimal control approach, we derive the robust optimal strategies as well as the corresponding value functions in the post-default and pre-default, respectively. Besides, we also consider the optimal strategies for the non-ambiguity case. Finally, numerical analysis is provided to illustrate the effects of parameters on the optimal strategies, which provides an effective decision-making basis for pension managers.

Key words: target benefit pension plans, stochastic salary, ambiguity aversion, default risk, Hamilton-Jacobi-Bellman equation

中图分类号:

O211

张欣茹, 马世霞, 张雨萌, 慕蕊. 带随机工资的目标收益养老金计划的鲁棒最优投资和收益支付调整策略[J]. 运筹学学报（中英文）, 2025, 29(1): 127-141.

Xinru ZHANG, Shixia MA, Yumeng ZHANG, Rui MU. Robust optimal investment and benefit payment adjustment strategy for target benefit pension plans with stochastic salary[J]. Operations Research Transactions, 2025, 29(1): 127-141.

图/表 5

参考文献 21

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带随机工资的目标收益养老金计划的鲁棒最优投资和收益支付调整策略

Robust optimal investment and benefit payment adjustment strategy for target benefit pension plans with stochastic salary

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