基于Stein-Stein波动率和动态VaR约束下DC型养老基金的最优投资策略

doi:10.15960/j.cnki.issn.1007-6093.2019.02.004

运筹学学报 ›› 2019, Vol. 23 ›› Issue (2): 44-56.doi: 10.15960/j.cnki.issn.1007-6093.2019.02.004

基于Stein-Stein波动率和动态VaR约束下DC型养老基金的最优投资策略

孙景云^1,*, 田丽娜², 陈峥³

1. 兰州财经大学统计学院, 兰州 730020;
2. 兰州城市学院数学学院, 兰州 730070;
3. 中山大学管理学院, 广州 510275

收稿日期:2017-05-22 出版日期:2019-06-15 发布日期:2019-06-15
通讯作者: 孙景云 E-mail:sunjy13@lzu.edu.cn
基金资助:
国家自然科学基金（No.71701084）

Optimal investment strategy for the DC pension fund with Stein-Stein volatility and dynamic VaR constraint

SUN Jingyun^1,*, TIAN Lina², CHEN Zheng³

1. School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730020, China;
2. School of Mathematics, Lanzhou City University, Lanzhou 730070, China;
3. Business School, Sun Yat-sen University, Guangzhou 510275, China

Received:2017-05-22 Online:2019-06-15 Published:2019-06-15

摘要/Abstract

摘要： 研究了确定缴费型养老基金在退休前累积阶段的最优资产配置问题.假设养老基金管理者将养老基金投资于由一个无风险资产和一个价格过程满足Stein-Stein随机波动率模型的风险资产所构成的金融市场.利用随机最优控制方法，以最大化退休时刻养老基金账户相对财富的期望效用为目标，分别获得了无约束情形和受动态VaR（Value at Risk）约束情形下该养老基金的最优投资策略，并获得相应最优值函数的解析表达形式.最后通过数值算例对相关理论结果进行数值验证并考察了最优投资策略关于相关参数的敏感性.

关键词: DC型养老基金, Stein-Stein波动率, Hamilton-Jacobi-Bellman方程, VaR约束

Abstract: In this paper, we consider the optimal asset allocation problem for the defined contribution pension plan on the phase of accumulation before retirement. We assume that the pension fund can be invested into a financial market consisting of a risk-free asset and a risky asset who's price process satisfies Stein-Stein stochastic volatility model. By using the method of stochastic optimal control, we obtain the optimal investment strategy of the pension fund without or with dynamic value at risk constraint aiming to maximize the expected utility of relative wealth at retirement time, and derive the corresponding analytic expression of the optimal value function. Finally, a numerical example is provided to verify the related theoretical results and the sensitivity of the optimal investment strategy on some parameters is analyzed.

Key words: DC pension fund, Stein-Stein volatility, Hamilton-Jacobi-Bellman equation, VaR constraint

中图分类号:

F830.59
F224

孙景云, 田丽娜, 陈峥. 基于Stein-Stein波动率和动态VaR约束下DC型养老基金的最优投资策略[J]. 运筹学学报, 2019, 23(2): 44-56.

SUN Jingyun, TIAN Lina, CHEN Zheng. Optimal investment strategy for the DC pension fund with Stein-Stein volatility and dynamic VaR constraint[J]. Operations Research Transactions, 2019, 23(2): 44-56.

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基于Stein-Stein波动率和动态VaR约束下DC型养老基金的最优投资策略

Optimal investment strategy for the DC pension fund with Stein-Stein volatility and dynamic VaR constraint

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