考虑随机利率和通货膨胀的连续时间资产组合选择

doi:10.16381/j.cnki.issn1003-207x.2019.02.007

中国管理科学 ›› 2019, Vol. 27 ›› Issue (2): 61-70.doi: 10.16381/j.cnki.issn1003-207x.2019.02.007

考虑随机利率和通货膨胀的连续时间资产组合选择

李爱忠¹, 汪寿阳², 彭月兰¹

1. 山西财经大学财政金融学院, 山西太原 030006;
2. 中国科学院大学经济与管理学院, 北京 100190

收稿日期:2016-10-17 修回日期:2018-05-27 出版日期:2019-02-20 发布日期:2019-04-24
通讯作者: 李爱忠(1972-),男(汉族),山西人,山西财经大学财政金融学院,讲师,博士,研究方向:数量经济、数据挖掘、金融工程与风险管理,E-mail:lazshp@sina.com. E-mail:lazshp@sina.com
基金资助:
国家自然科学基金资助项目（71171009，71031001）

Continuous-time Asset Allocation Strategy with Inflation and Stochastic Interest Rates

LI Ai-zhong¹, WANG Shou-yang², PENG Yue-lan¹

1. Faculty of Finance & Banking, Shanxi University of Finance and Economics, Taiyuan 030006, China;
2. School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, China

Received:2016-10-17 Revised:2018-05-27 Online:2019-02-20 Published:2019-04-24

摘要/Abstract

摘要： 通过随机控制技术、Bellman最优性原理和HJB方程研究了通货膨胀、随机利率和交易成本等因素影响下的连续时间投资组合选择的最优化问题，将利率假定为服从Vasicek利率模型的随机过程，应用连续时间的动态均值-方差方法得到符合实际意义的HJB方程，通过多重网格的数值逼近方法求解相应的HJB方程得到双目标优化问题的最优投资策略。用实证方法与国内证券市场上代表性指数基金进行对比研究，发现通货膨胀和利率变动以及经济环境和投资者的异质信念等因素均会对最优策略产生影响，有效前沿会随之发生变化，债券与股票之间的投资比例并不是简单维持固定比例就可以保证总资产最优，拓展了基金分离定理。考虑通货膨胀和交易成本等因素的资产组合选择模型可以实实在在为机构投资者提供客观的实践指导和科学的理论依据。

关键词: 投资组合, 多重网格, HJB方程, 连续时间, 随机控制

Abstract: The stochastic control technique, Bellman optimality principle and HJB equations are used to study the optimization of continuous-time portfolio selection under the influence of inflation, stochastic interest rate and transaction cost. The interest rate is assumed to be a stochastic process that obeys the Vasicek interest rate model, a typical HJB equation is established by applying continuous-time dynamic mean-variance approach, the optimal strategy is derived for multi-objective optimization problems with general stochastic control technique and numerical approximation algorithm for multi-grid computing. Using empirical methods to compare with representative index funds in the domestic securities market, it is found that inflation and interest rate changes, as well as economic environment and investors' heterogeneous beliefs, all influence the optimal strategy and change the effective frontier of the portfolio. The ratio between bonds and stocks does not maintain a fixed ratio to ensure that the total assets are optimal, and the fund separation theorem is expanded. The model with inflation and stochastic interest rates is more in line with the actual situation, operational and targeted. The use of nonlinear prediction methods based on support vector machines for time-varying parameter estimation is more conducive to revealing the nature of nonlinear and non-Gaussian distributions in financial markets. The portfolio selection model that considers factors such as inflation and transaction costs can provide institutional investors with a solid theoretical basis and practical guidance.

Key words: portfolio selection, multi-grid computing, HJB equation, continuous time, stochastic control

中图分类号:

F830

李爱忠, 汪寿阳, 彭月兰. 考虑随机利率和通货膨胀的连续时间资产组合选择[J]. 中国管理科学, 2019, 27(2): 61-70.

LI Ai-zhong, WANG Shou-yang, PENG Yue-lan. Continuous-time Asset Allocation Strategy with Inflation and Stochastic Interest Rates[J]. Chinese Journal of Management Science, 2019, 27(2): 61-70.

参考文献

[1] Markowitz H. Portfolio selection[J]. Journal of Finance,1952,7(1):77-91.

[2] Merton R C. Lifetime portfolio selection under uncertainty:The continuous-time case[J]. Review of Economics and Statistics 1969,51(3),247-257.

[3] Cox J, Ross S, Rubinstein M, et al. Option pricing:A simplified approach[J]. Journal of Financial Economics, 1979, 7(3):229-263.

[4] Sharpe W F, Tint L G. Liabilities-a new approach[J]. Journal of Portfolio Management,1990,16(2):5-10.

[5] Leippold M, Trojani F, Vanini P. A geometric approach to multi-period mean-variance optimization of assets and liabilities[J]. Journal of Economics Dynamics and Control,2004,28(6):1079-1113.

[6] Chiu M C, Li D. Asset and liability management under a continuous-time mean-variance optimization framework[J]. Insurance:Mathematics and Economics,2006,39(3):330-355.

[7] Papi M, Sbaraglia S. Optimal asset-liability management with constraints:A dynamic programming approach[J]. Applied Mathematics and Computation,2006,173(1):306-349.

[8] Deelstra G, Grasselli M, Koehl P F. Optimal investment strategies in a CIR framework[J].Journal of Applied Probability,2000,37(4):936-946.

[9] Xie S, Li Z, Wang S Y. Continuous-time portfolio selection with liability:Mean-variance model and stochastic LQ approach[J]. Insurance:Mathematics and Economics,2008,42(3):943-953.

[10] Grasselli M. A stability result for the HARA class with stochastic interest rates[J]. Insurance:Mathematics and Economics,2003,33(3):611-627.

[11] Korn R, Kraft H. A stochastic control approach to portfolio problems with stochastic interest rates[J].SIAM Journal of Control and optimization,2001,40(4):1250-1269.

[12] Gao Jianwei. Stochastic optimal control of DC pension funds[J]. Insurance:Mathematics and Economics, 2008,42(3):1159-1164.

[13] Boulier J F, Huang S, Taillard G. Optimal management under stochastic interest rates:The case of a protected defined contribution pension fund[J]. Insurance:Mathematics and Economics,2001,28(2):173-189.

[14] Ma Jianjing, Wu Rong. On a barrier strategy for the classical risk process with constant interest force[J].Chinese Journal of Engineering Mathematics,2009,26(6):1133-1136.

[15] Ho T S Y, Lee S B. Term structure movements and pricing interest contingent claims[J]. Journal of Finance, 1986,41(5):1011-1029.

[16] Zhou X Y, Li D. Continuous-time mean-variance portfolio selection:A stochastic LQ framework[J]. Applied Mathematics&Optimization,2000,42(1):19-33.

[17] Kim T S, Omberg E. Dynamic nonmyopic portfolio behavior[J].The Review of Financial Studies, 1996, 9(1),141-161.

[18] 项筱玲,韦维.时间最优控制的Mayer逼近[J].贵州大学学报, 2003,20(2):111-115.

[19] Potts C, Giddens T D, Yadav S B. The development and evaluation of an improved genetic algorithm based on migration and artificial selection[J]. IEEE Transactions on Systems, Man, and Cybernetics, 1994,24(1):73-86.

[20] Cairns A J G, Blake D, Dowd K. Stochastic lifestyling:Optimal dynamic asset allocation for defined contribution pension plans[J]. Journal of Economic Dynamic and Control, 2004,30(5):843-877.

[21] Lions P L, Sougarnidis P E. Differential games, optimal control and directional derivatives of viscosity solutions of Bellman's and Issac's equation[J]. Siam J Control&Optimization,1984,23(4)566-583.

[22] Sanjiv R D, Rangarajan K. An approximation algorithm for optimal consumption/investment problems[J]. International Journal of Intelligent Systems in Accounting, Finance&Management,2002,11(2):55-69.

[23] 徐林明,林志炳,李美娟,等. 基于模糊Borda法的动态组合评价方法及其应用研究[J]. 中国管理科学,2017,25(2):165-173.

[24] 张初兵,荣喜民.仿射利率模型下确定缴费型养老金的最优投资[J]. 系统工程理论与实践,2012,32(5):1048-1056.

[25] 郭文英. 基于贝叶斯学习的动态投资组合选择[J]. 中国管理科学,2017,25(8):39-45.

[26] 费为银,吕会影,余敏秀.通胀服从均值回复过程的最优消费和投资决策[J].系统工程,2014, 29(6):791-868.

[27] 卞世博,刘海龙.背景风险下DC型养老基金的最优投资策略-基于Legendre转换对偶解法[J].管理工程学报,2013, 27(3):145-149.

[28] 李斌,林彦,唐闻轩. ML-TEA:一套基于机器学习和技术分析的量化算法[J]. 系统工程理论与实践, 2017, 37(5):1089-1100.

[29] 肖进,孙海燕,刘敦虎,等. 基于GMDH混合模型的能源消费量预测研究[J].中国管理科学,2017,25(12):158-166.

[30] 龙勇,苏振宇,汪於. 基于季节调整和BP神经网络的月度负荷预测[J]. 系统工程理论与实践, 2018, 38(4):1052-1060.

考虑随机利率和通货膨胀的连续时间资产组合选择

Continuous-time Asset Allocation Strategy with Inflation and Stochastic Interest Rates

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]	金博轶, 闫庆悦, 于文广. 养老金统筹账户与个人账户最优组合策略研究[J]. 中国管理科学, 2020, 28(2): 48-57.
[2]	刘维奇, 张燕. 资产定价与劳动成本占比[J]. 中国管理科学, 2020, 28(12): 1-11.
[3]	费为银, 张繁红, 杨晓光. 通胀对高管的股权激励和工作努力策略的影响[J]. 中国管理科学, 2020, 28(11): 1-11.
[4]	金秀, 尘娜, 王佳. 安全投资转移视角下的跨行业投资组合模型及实证[J]. 中国管理科学, 2020, 28(11): 12-22.
[5]	朱鹏飞, 唐勇, 钟莉. 基于小波-高阶矩模型的投资组合策略——以国际原油市场为例[J]. 中国管理科学, 2020, 28(10): 24-35.
[6]	郭范勇, 潘和平. 基于β系数优化的动态投资组合策略研究[J]. 中国管理科学, 2019, 27(7): 1-10.
[7]	姚鸿, 王超, 何建敏, 李亮. 银行投资组合多元化与系统性风险的关系研究[J]. 中国管理科学, 2019, 27(2): 9-18.
[8]	马永红, 刘海礁, 柳清. 产业共性技术产学研协同研发策略的微分博弈研究[J]. 中国管理科学, 2019, 27(12): 197-207.
[9]	周忠宝, 任甜甜, 肖和录, 吴士健, LIU Wenbin. 基于相对财富效用的多阶段投资组合博弈模型[J]. 中国管理科学, 2019, 27(1): 34-43.
[10]	彭子衿, 徐维军. 基于股价预测的泛证券投资组合策略[J]. 中国管理科学, 2018, 26(9): 1-10.
[11]	王建建, 何枫, 吴子轩, 陈丽莉. 改进区间可接受度的证券投资组合区间二次规划模型[J]. 中国管理科学, 2018, 26(9): 11-18.
[12]	谭浩, 吴卫星. 股东为什么在解禁后会减持股票?——基于背景风险分析的股票解禁效应研究[J]. 中国管理科学, 2018, 26(7): 9-17.
[13]	凌爱凡, 陈骁阳. 嵌入GARCH波动率估计的B1ack-Litterman投资组合模型[J]. 中国管理科学, 2018, 26(6): 17-25.
[14]	刘炳越, 姬强, 范英. 黄金是否为原油的“避险天堂”?——基于组合收益及其波动视角[J]. 中国管理科学, 2018, 26(11): 1-10.
[15]	胡昌生, 程志富, 陈晶, 熊德超. 投资组合约束下分离交易可转债的定价[J]. 中国管理科学, 2017, 25(9): 11-18.