待遇预定制养老基金资产组合与缴费计划最优决策——基于随机波动率Heston模型及Legendre对偶变换法

doi:10.16381/j.cnki.issn1003-207x.2015.03.005

中国管理科学 ›› 2015, Vol. 23 ›› Issue (3): 42-46.doi: 10.16381/j.cnki.issn1003-207x.2015.03.005

待遇预定制养老基金资产组合与缴费计划最优决策——基于随机波动率Heston模型及Legendre对偶变换法

肖建武¹, 尹希明²

1. 中南林业科技大学商学院, 湖南长沙 410004;
2. 上海交通大学数学系, 上海 200240

收稿日期:2013-01-18 修回日期:2013-07-17 出版日期:2015-03-20 发布日期:2015-03-18
作者简介:肖建武(1973-),男(汉族),湖南株洲人,中南林业科技大学商学院,教授,博士,硕士生导师,研究方向:投融资管理.
基金资助:
教育部人文社会科学研究项目(10YJC790296)

The Optimal Portfolio Decision and Contribution Plan of Defined Benefit Pension Funds Based on a Heston Stochastic Volatility Model and Legendre Dual Transform Method

XIAO Jian-wu¹, YIN Xi-ming²

1. Business School, Central South University of Forestry &Technology, Hunan Changsha 410004, China;
2. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China

Received:2013-01-18 Revised:2013-07-17 Online:2015-03-20 Published:2015-03-18

摘要/Abstract

摘要： 待遇预定制养老金制度在中国应用非常广泛,缴费制定和资产配置是此类养老金管理的两大核心问题。由此,面对随机波动的现实市场,文章针对待遇预定制养老基金的资产组合管理问题,应用最优控制理论,选用对数效用函数,建立Heston随机波动率模型;在难以求解随机微分Bellman方程的情况下,应用Legendre变换,将原来问题转化为对偶问题,从而求得原问题的解析解。在理论上,进一步丰富了资产组合问题的随机最优控制模型的构建和随机微分方程的求解理论。在实践上,确定了养老金管理风险资产配置比例和缴费水平,给出了最优决策与总资产、发放待遇、净资产与风险溢价之间的数量关系,从而实现养老基金管理的最优资产配置和最低缴费水平的效用目标。

关键词: 待遇预定制养老金, 资产组合, 随机波动率, Heston模型, Legendre变换

Abstract: The defined benefit pension system applies widely in China. The portfolio and the contribution plan are the two core issues in this system. Thus, a Heston stochastic volatility control model with the logarithm utility function for the portfolio of the defined benefit pension funds is created in this paper, and a stochastic differential Bellman equation by applying optimal control theory is obtained. But this equation is very difficult to solve, so it transfers the primal problem to the dual problem and provides an analytic solution to the primal optimal problem by applying the Legendre transform and the dual theory. In theory, the paper enriches the methods of the model specification and the model solution for the stochastic volatility control model about the portfolio. In practical level, an optimal asset allocation strategy (between a risky asset and a reckless asset) and the least contribution policy, and expressions of quantity relations between the optimal decisions and the total assets, the pension benefit, the net assets and the risk premium to achieve the utility goal are found in this paper.

Key words: defined benefit pension funds, portfolio, stochastic volatility, Heston model, Legendre transform

中图分类号:

F224.11

肖建武, 尹希明. 待遇预定制养老基金资产组合与缴费计划最优决策——基于随机波动率Heston模型及Legendre对偶变换法[J]. 中国管理科学, 2015, 23(3): 42-46.

XIAO Jian-wu, YIN Xi-ming. The Optimal Portfolio Decision and Contribution Plan of Defined Benefit Pension Funds Based on a Heston Stochastic Volatility Model and Legendre Dual Transform Method[J]. Chinese Journal of Management Science, 2015, 23(3): 42-46.

参考文献

[1] 王晓军.中国养老金制度及其精算评价[M].北京:经济科学出版社,2002.

[2] Josa-Fombellida R, Rincón-Zapatero J P. Optimal asset allocation for aggregated defined benefit pension funds with stochastic interest rates [J]. European Journal of Operational Research,2010,201(1): 211-221.

[3] Boulier J F,Trussant E,Florens D. A dynamic model for pension funds management.Proceedings of the 5th AFIR International Colloquium,Brussels,September,1995.

[4] Haberman S,Butt Z,Megaloudi C.Contribution and solvency risk in a defined pension scheme[J].Insurance:Mathematics and Economics,2000,27(2):237-259.

[5] Haberman S,Vigna E.Optimal investment strategies and risk measures in defined contribution pension schemes[J].Insurance:Mathematics and Economics,2002, 31(1):35-69.

[6] 肖建武,秦成林,胡世培.待遇预定制养老基金管理的常方差弹性模型[J], 上海大学学报((自然科学版), 2004,10(6):649-653.

[7] 肖建武,秦成林.养老基金管理的常方差弹性模型及Legendre变换-对偶解法[J]. 系统工程理论与实践, 2005,25(9):49-53.

[8] Cox J. The constant elasticity of variance option pricing model [J].The Journal of Portfolio Management,1996,23:16-17.

[9] Heston S L. A closed-form solution for options with stochastic volatility with applications to bond and currency options[J].The Review of Financial Studies. 1993,6(2):327-343.

[10] 李静,周峤.Heston随机波动率模型下一类多资产期权的定价[J].系统工程学报2012,27(3):320-326.

[11] Han Jiguang, Gao Ming, Zhangc Qiang,et al. Option prices under stochastic volatility[J]. Applied Mathematics Letters, 2013,26(1): 1-4.

[12] Kim J, Kim B, Moon K S, et al. Valuation of power options under Heston's stochastic volatility model[J]. Journal of Economic Dynamics & Control,2012,36(11): 1796-1813.

[13] Li Zhongfei, Zeng Yan, Lai Yongzeng. Optimal time-consistent investment and reinsurance strategies for insurers under Heston's SV model[J]. Insurance: Mathematics and Economics,2012,51(1): 191-203.

[14] 李艳方,林祥.Heston随机方差模型下的最优投资和再保险策略[J].经济数学,2009,26(4):32-41.

[15] 林祥,杨益. Heston随机方差模型下确定缴费型养老金的最优投资[J]. 应用数学,2010,23(2):413-418.

[16] Choulli T,Hurd T R.The role of hellinger processes in mathematical finance[J].Entropy 2001, 3(3):150-161.

[17] Jonsson M,Sircar R.Optimal investment problems and volatility homogenization approximations[M]//Bourlioux A, Gander M,Sabidussi G.Modern methods in scientific computing and applications. Netherlands:Springer,2002:255-281.

[18] Xiao Jianwu, Qin Chenglin. Constant elasticity of variance model and analytical strategies for annuity contracts[J]. Applied Mathematics and Mechanics, 2006,27(11):1499-1506.

[19] Xiao Jianwu, Zhai Hong,Qin Chenglin. The constant elasticity of variance(CEV) model and Legendre transform-dual solution for annuity contracts[J]. Insurance: Mathematics and Economics, 2007,40(2):302-310.

[20] Cox J C,Huang C F.A variational problem arising in financial economics[J]. Math. Econ,1991, 20(5):465-487.

[21] Kramkov D,Schachermayer W.The asymptotic elasticity of utility functions and optimal investment in incomplete markets[J].Annals of Applied Probability 1999,9(3):904-950.

待遇预定制养老基金资产组合与缴费计划最优决策——基于随机波动率Heston模型及Legendre对偶变换法

The Optimal Portfolio Decision and Contribution Plan of Defined Benefit Pension Funds Based on a Heston Stochastic Volatility Model and Legendre Dual Transform Method

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	吴鑫育, 李心丹, 马超群. 基于期权与高频数据信息的VaR度量研究[J]. 中国管理科学, 2021, 29(8): 13-23.
[2]	朱怀念, 张成科, 曹铭. Heston模型下保险公司和再保险公司的投资与再保险博弈[J]. 中国管理科学, 2021, 29(6): 48-59.
[3]	何朝林, 涂蓓, 王鹏. 动态均值-方差资产组合的有效性:时变风险容忍度视角[J]. 中国管理科学, 2021, 29(1): 1-11.
[4]	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.
[5]	吴鑫育, 赵凯, 李心丹, 马超群. 时变风险厌恶下的期权定价——基于上证50ETF期权的实证研究[J]. 中国管理科学, 2019, 27(11): 11-22.
[6]	吴鑫育, 李心丹, 马超群. 门限已实现随机波动率模型及其实证研究[J]. 中国管理科学, 2017, 25(3): 10-19.
[7]	周艳丽, 吴洋, 葛翔宇. 一类高新技术企业专利权价值的实物期权评估方法——基于跳扩散过程和随机波动率的美式期权的建模与模拟[J]. 中国管理科学, 2016, 24(6): 19-28.
[8]	刘渝琳, 郑效晨. 基于通货膨胀和风险偏好视角的资产配置研究[J]. 中国管理科学, 2016, 24(5): 46-53.
[9]	苏治, 秦磊, 方彤. 含有图结构约束的稀疏最小方差资产组合模型[J]. 中国管理科学, 2015, 23(9): 65-70.
[10]	何朝林. 均值-方差模型具有一般不确定性下的最优资产组合选择[J]. 中国管理科学, 2015, 23(12): 63-70.
[11]	吴鑫育, 杨文昱, 马超群, 汪寿阳. 基于非仿射随机波动率模型的期权定价研究[J]. 中国管理科学, 2013, (1): 1-7.
[12]	吴鑫育, 周海林, 马超群, 汪寿阳. 基于随机贴现因子方法的权证定价研究[J]. 中国管理科学, 2012, (4): 1-7.
[13]	杨朝军, 陈浩武. 参数不确定性对投资者最优资产组合的影响：基于中国的实证[J]. 中国管理科学, 2008, 16(3): 37-43.
[14]	孟卫东, 何朝林. 基于信息更新的动态资产组合选择[J]. 中国管理科学, 2007, 15(4): 21-27.
[15]	朱微亮, 刘海龙. 稳健的动态资产组合模型研究[J]. 中国管理科学, 2007, 15(3): 19-24.