Heston模型下基于期权投资的鲁棒最优控制  

Robust optimal control for derivative-based investment under the Heston model

作　　者：杨璐 朱怀念[1] 张成科[1] Yang Lu;Zhu Huainian;Zhang Chengke(School of Economics&Commerce,Guangdong University of Technology,Guangzhou 510520,China;School of Management,Guangdong University of Technology,Guangzhou 510520,China)

机构地区：[1]广东工业大学经济与贸易学院,广东广州510520 [2]广东工业大学管理学院,广东广州510520

出　　处：《系统工程学报》2021年第2期157-170,共14页Journal of Systems Engineering

基　　金：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);教育部人文社会科学研究青年资助基金项目(18YJC790003);广东大学生科技创新培育专项资金资助项目(pdjha0151)。

摘　　要：针对Heston随机波动率模型下的鲁棒最优投资问题,构建了带期权投资的资产负债管理模型.投资者的目标是最大化终端时刻净财富的幂效用,利用随机最优控制方法,分别获得了带期权投资以及无期权投资两种情形下鲁棒最优投资策略、最坏概率测度及值函数的解析表达式,通过数值模拟发现考虑模型的鲁棒性以及进行期权投资能够改进投资者的效用.With regard to the robust optimal investment problem for an ambiguity-averse investor(AAI)with stochastic volatility,an asset-liability management model with derivative-based investment is constructed.The objective of investors is to maximize the power utility of net wealth at the end of time.The paper derives the explicit expressions for the robust optimal investment strategy,the worst-case scenario and the corresponding value function with and without derivative investment respectively by means of using stochastic optimal control method.The result of the numerical simulation shows that the established model and its algorithm are feasible and effective.Considering the robustness of the model and derivative trading the model can improve the utility of the investor.

关 键 词：Heston模型 模糊风险厌恶 期权 鲁棒最优投资策略 

分 类 号：F224.9[经济管理—国民经济]