基于加权效用和VaR-PI约束下DC型养老金计划的最优资产配置

doi:10.15960/j.cnki.issn.1007-6093.2023.01.005

运筹学学报 ›› 2023, Vol. 27 ›› Issue (1): 70-86.doi: 10.15960/j.cnki.issn.1007-6093.2023.01.005

基于加权效用和VaR-PI约束下DC型养老金计划的最优资产配置

董迎辉¹^,*(), 魏思媛¹, 殷子涵¹

1. 苏州科技大学数学科学学院, 江苏苏州 215009

收稿日期:2021-01-11 出版日期:2023-03-15 发布日期:2023-03-16
通讯作者: 董迎辉 E-mail:dongyinghui1030@163.com
作者简介:董迎辉, E-mail: dongyinghui1030@163.com
基金资助:
国家自然科学基金(12071335);教育部人文社会科学基金(20YJAZH025)

Optimal investment of DC pension plan under a weighted utility and VaR-PI constraint

Yinghui DONG¹^,*(), Siyuan WEI¹, Zihan YIN¹

1. College of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, Jiangsu, China

Received:2021-01-11 Online:2023-03-15 Published:2023-03-16
Contact: Yinghui DONG E-mail:dongyinghui1030@163.com

摘要/Abstract

摘要：

本文从养老金计划参与人和基金经理的双重视角出发, 以最大化双方加权的期望效用为目标, 研究了在最低保障和VaR约束下, DC养老金计划的最优资产配置问题。假设养老金计划参与人和基金经理均是损失厌恶的, 分别用两个S型的效用函数来刻画双方的损失厌恶行为。VaR约束和加权的效用函数使得本文所研究的优化问题成为一个复杂的非凹效用最大化问题。利用拉格朗日对偶理论和凹化方法求得了最优财富和最优投资组合的封闭解。数值结论表明当更为看重养老金计划参与人的利益时, 基金经理会采取更为激进的投资策略, VaR约束可以改进对DC养老金计划的风险管理。

关键词: VaR约束, DC养老金计划, 损失厌恶, 加权效用

Abstract:

From the dual perspective of the DC pension plan members and the manager, we investigate the asset allocation of a DC pension plan under a VaR-PI constraint by maximizing a weighted utility of the two parties. Assuming that the DC pension plan members and the manager are loss averse and we use two S-shaped utility functions to demonstrate the loss aversion behavior. The VaR constraint and a weighed utility lead to a complex, nonconcave utility maximization problem. We apply the Lagrange duality theory and the concavification technique to derive the optimal wealth and the optimal portfolio processes. Numerical results show that the manager shall take a much riskier portfolio strategy when the benefits of the DC pension plan members are paid much more attention. The VaR constraint can improve the risk management of the DC pension plan.

Key words: VaR constraint, DC pension plan, loss aversion, weighted utility

中图分类号:

董迎辉, 魏思媛, 殷子涵. 基于加权效用和VaR-PI约束下DC型养老金计划的最优资产配置[J]. 运筹学学报, 2023, 27(1): 70-86.

Yinghui DONG, Siyuan WEI, Zihan YIN. Optimal investment of DC pension plan under a weighted utility and VaR-PI constraint[J]. Operations Research Transactions, 2023, 27(1): 70-86.

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参考文献 16

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$ (G, \theta) $	$ (50, 90) $	$ (50, 80) $	$ (50, 70) $	$ (40, 70) $	$ (30, 70) $
$ \pi^{, \beta^}(0)(a=0.5) $	14.55	11.69	8.35	10.04	11.64
$ \pi^{, \beta^}(0)(a=1) $	17.57	15.58	12.93	14.33	15.52
$ \pi^{, \beta^, 0.05}(a=0.5) $	12.94	10.41	8.32	9.29	10.42
$ \pi^{, \beta^, 0.05}(a=1) $	16.83	14.59	12.46	13.30	14.26

$ (G, \theta) $	$ (50, 90) $	$ (50, 80) $	$ (50, 70) $	$ (40, 70) $	$ (30, 70) $
$ E(X^{\pi^, \beta^}(T)) $	108.6	105.03	101.84	103.17	104.81
$ \sigma(X^{\pi^, \beta^}(T)) $	39.86	33.63	29.30	30.80	33.28
$ P(X^{\pi^, \beta^}(T)=L) $	0.14	0.10	0.06	0.08	0.1
$ P(X^{\pi^, \beta^}(T)>L) $	0.85	0.90	0.94	0.92	0.9

$ (G, \theta) $	$ (50, 90) $	$ (50, 80) $	$ (50, 70) $	$ (40, 70) $	$ (30, 70) $
$ E(X^{\pi^, \beta^, 0.05}(T)) $	102.85	99.62	97.62	99.24	99.73
$ \sigma(X^{\pi^, \beta^, 0.0.05}(T)) $	28.06	22.90	21.76	23.15	23.59
$ P(X^{\pi^{, \beta^, 0.05}}(T)=L) $	0.05	0.05	0.05	0.05	0.05
$ P(X^{\pi^{, \beta^, 0.05}}(T)>L) $	0.95	0.95	0.95	0.95	0.95

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[2]	伊博, 李仲飞, 曾燕. 基于动态VaR约束与随机波动率模型的最优投资策略[J]. 运筹学学报, 2012, 16(2): 77-90.
[3]	米辉, 张曙光. 不完全市场下考虑损失厌恶的连续时间投资组合选择[J]. 运筹学学报, 2012, 16(1): 1-12.

基于加权效用和VaR-PI约束下DC型养老金计划的最优资产配置

Optimal investment of DC pension plan under a weighted utility and VaR-PI constraint

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