Heston模型下DC型养老金等价管理费用问题研究

doi:10.16381/j.cnki.issn1003-207x.2019.12.002

中国管理科学 ›› 2019, Vol. 27 ›› Issue (12): 11-21.doi: 10.16381/j.cnki.issn1003-207x.2019.12.002

Heston模型下DC型养老金等价管理费用问题研究

李方超¹, 张成科², 朱怀念²

1. 广东工业大学管理学院, 广东广州 510520;
2. 广东工业大学经济与贸易学院, 广东广州 510520

收稿日期:2018-05-28 修回日期:2018-09-19 出版日期:2019-12-20 发布日期:2019-12-30
通讯作者: 朱怀念(1985-),男(汉族),安徽蚌埠人,广东工业大学经济与贸易学院副教授,博士,研究方向:动态博弈理论及应用、保险精算等,E-mail:zhuhuainian@gdut.edu.cn. E-mail:zhuhuainian@gdut.edu.cn
基金资助:
国家自然科学基金资助项目（71571053）；广东省自然科学基金资助项目（2016A030313701，2018A030313687）；广东工业大学研究生创新项目（50010102）

Equivalent Administrative Charges of the DC Pension Plan under the Heston Model

LI Fang-chao¹, ZHANG Cheng-ke², ZHU Huai-nian²

1. School of Management, Guangdong University of Technology, Guangzhou 510520, China;
2. School of Economics & Commence, Guangdong University of Technology, Guangzhou 510520, China

Received:2018-05-28 Revised:2018-09-19 Online:2019-12-20 Published:2019-12-30

摘要/Abstract

摘要： 本文针对DC型养老金收费管理问题展开了系统研究，假定风险资产服从Heston模型，养老金管理者按资产财富比例和工资比例两种方式收取管理费用，试图在这两种方式中找到一个平衡点（等价管理费用）。运用随机最优控制理论得到了CARA和CRRA两种效用准则下等价管理费用的解析表达，从表达式中发现等价管理费用只与无风险利率、积累时间以及按工资比例收费的代表参数有关，而积累时间与参保人年龄有很强的相关性。最后，通过数值算例分析了参保人年龄对等价管理费用的影响以及等价管理费用对财富过程的影响，研究结果显示：在CARA效用下，等价管理费用随参保人年龄严格递增，而在CRRA效用下相反；无论在CARA效用还是CRRA效用下，等价管理费用对养老金账户财富都有正负两方面的影响。

关键词: DC型养老金, Heston模型, 效用函数, 等价管理费用

Abstract: During the periods of DC pensioninvestment and management, pension managers need to charge some administrative charges, which has a significant impact on the terminal wealth of individual pension accounts. At present, there are mainly two ways of charging administrative charges:charge onbalance and charge on flow, and how to get accurate administrative charges is very urgent for the pension investment and management. The Heston model is used to describe the price process of the risky asset in financial markets; and a balance (equivalent administrative charges)in these two charge ways is found. By using stochastic optimal control theory, the explicit solutions of the equivalent administrative charges are given under the cases of CARA utility and CRRA utility, respectively.From the explicit solutions, it is found that the equivalent administrative charges are only related to the risk-free interest rate, the length of the accumulation period and the representative parameters in the way of charge on flow, and the length of the accumulation period have a strong correlation with age. Finally, a numerical example is given to analyze the impact of age on the equivalent administrative charges and the impact of equivalent administrative charges on the process of wealth. The results show that:under the case of CARA utility, the equivalent administrative charges is strictly increasing in age, and under CRRA utility instead; under the case of CARA utility and the CRRA utility, the equivalent administrative charges has both positive and negative effects on the wealth of the pension account.The main conclusions of this paper will improve the research on DC pension investment and management, enrich the research on pension administrative charges, and provide reference for pension managers to make precise investment.

Key words: DC pension, Heston model, utility function, equivalent administrative charges

中图分类号:

F830.59

李方超, 张成科, 朱怀念. Heston模型下DC型养老金等价管理费用问题研究[J]. 中国管理科学, 2019, 27(12): 11-21.

LI Fang-chao, ZHANG Cheng-ke, ZHU Huai-nian. Equivalent Administrative Charges of the DC Pension Plan under the Heston Model[J]. Chinese Journal of Management Science, 2019, 27(12): 11-21.

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Heston模型下DC型养老金等价管理费用问题研究

Equivalent Administrative Charges of the DC Pension Plan under the Heston Model

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