基于Heston模型时间一致的资产负债管理鲁棒策略

doi:10.16381/j.cnki.issn1003-207x.2019.1991

中国管理科学 ›› 2021, Vol. 29 ›› Issue (10): 47-57.doi: 10.16381/j.cnki.issn1003-207x.2019.1991

• 论文 • 上一篇

基于Heston模型时间一致的资产负债管理鲁棒策略

杨璐¹，张成科²，朱怀念²，李方超¹

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:2019-12-01 修回日期:2020-04-03 出版日期:2021-10-20 发布日期:2021-10-21
通讯作者: 张成科(1964-)，男(瑶族)，广西贺州人，广东工业大学经济与贸易学院,教授，博士生导师，研究方向：博弈理论及其应用、金融工程，Email：zhangck@gdut.edu.cn. E-mail:zhangck@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(2018A030313687)

Ambiguity Aversion and Time-consistent Optimal Investment for Asset-liability Management under the Heston Model

YANG Lu¹, ZHANG Chengke², ZHU Huainian², LI Fangchao¹

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

Received:2019-12-01 Revised:2020-04-03 Online:2021-10-20 Published:2021-10-21

摘要/Abstract

摘要： 本文在非完备市场框架下，研究了时间一致的鲁棒最优投资组合选择问题。首先，假设金融市场由无风险资产和风险资产构成，其中风险资产的价格过程服从Heston随机波动率模型，且投资者面临一个不可控的外生负债。其次，应用随机最优控制理论，给出并证明了验证定理，建立了相应的拓展Hamilton-Jacobi-Bellman(HJB)方程组，通过求解拓展的HJB方程组，得到了鲁棒均衡投资策略和值函数的显式解。最后，通过数值模拟，给出了模型参数变动对均衡投资策略和效用改善的影响。结果表明：(1) 当风险资产的价格和其波动的相关系数大于零时，股票方差的波动越大，越不利于投资。否则反之。(2) 当风险资产的价格和其波动的相关系数越大时，风险资产的风险就越大，投资者会采取保守的投资策略，减少投资。(3) 负债的波动率变大，投资者会面临更大的负债风险，为了对冲风险，投资者会增加风险资产的投资。(4) 当投资者考虑模型不确定的影响时，采用鲁棒投资策略能显著提高投资者的效用水平。

关键词: 时间一致, 鲁棒策略, 资产负债, 投资组合

Abstract: This paper focuses on an asset-liability management problem for an investor who can invest in a risk-free asset and a risky asset whose price process is described by the Heston model, while the liability process is described by a Brownian motion with drift. The objective of the Ambiguity-Averse Investor (AAI) is to find a robust optimal investment strategy under the mean-variance criterion. By applying stochastic control theory, a verification theorem is provided and proved and the corresponding extended HJB equation is established. Furthermore, the robust equilibrium investment strategy and the corresponding equilibrium value function are derived by solving the extended HJB equation. Finally, numerical examples are also provided to illustrate how the optimal robust investment strategy changes and utility improvement when some model parameters vary. Our main findings are: (1) when the correlation coefficient between the price of risky assets and its variance is non-negative number, the bigger the fluctuation of stock variance, the more disadvantageous investment. (2) when the correlation coefficient between the price of risky assets and its variance greater, the risk of risky assets is greater, and investors will adopt a conservative investment strategy. (3) when investors have more debt, they hedge their bets by investing in riskier assets. (4) ignoring model uncertainty leads to significant utility loss for the AAI. These result analyses reveal some interesting phenomena and provide useful guidance for optimal investment of asset-liability management in reality.

Key words: time-consistent, robust strategy, asset-liability, portfolio

中图分类号:

F224
F840

杨璐，张成科，朱怀念，李方超. 基于Heston模型时间一致的资产负债管理鲁棒策略[J]. 中国管理科学, 2021, 29(10): 47-57.

YANG Lu, ZHANG Chengke, ZHU Huainian, LI Fangchao. Ambiguity Aversion and Time-consistent Optimal Investment for Asset-liability Management under the Heston Model[J]. Chinese Journal of Management Science, 2021, 29(10): 47-57.

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基于Heston模型时间一致的资产负债管理鲁棒策略

Ambiguity Aversion and Time-consistent Optimal Investment for Asset-liability Management under the Heston Model

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