基于状态相依风险厌恶的最优动态协整配对交易策略  

Optimal dynamic cointegrated pairs trading strategies with state-dependent risk aversion

作　　者：邓辛凝 毕秀春 张曙光[1] DENG Xinning;BI Xiuchun;ZHANG Shuguang(Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China)

机构地区：[1]中国科学技术大学管理学院统计与金融系,安徽合肥230026

出　　处：《中国科学技术大学学报》2019年第8期655-667,共13页JUSTC

基　　金：国家自然科学基金(11401556,11471304)资助。

摘　　要：协整配对交易试图在协整资产偏离平衡时获取收益.在常风险厌恶的均值-方差模型中,最优动态协整配对交易策略显示,配置在风险资产上的额度仅与时间有关而与财富总额无关,这不符合常理.研究了在状态相依风险厌恶的均值-方差模型下协整资产的最优分配问题,并通过求解广义HJB方程得到最优配置策略的一个代数形式.策略显示,最优配置额度不仅与时间有关,还依赖于现有财富总额,并且策略能保证财富总额始终为正.因而从经济学的意义来看,相比于常风险厌恶下的最优策略,本文策略更加合理.数值例子表明,本文策略在资产分配方面表现得更加稳定,并且配置额度随着时间增加有增加的趋势,与常风险厌恶下的最优策略正好相反.此外,还分析了协整系数矩阵和均值回复速度对策略的影响,并对其加以解释.Cointegrated pairs trading attempts to make profits when cointegrated assets depart from their equilibrium.For the mean-variance model with constant risk aversion,the optimal dynamic cointegrated pairs trading strategy shows that the allocation amounts on risky assets depend only on time but not on wealth,which goes against common sense.The optimal allocation of cointegration assets under the mean-variance model with state-dependent risk aversion was studied,and an algebraic form of the optimal strategy was obtained by solving an extended HJB equation.The strategy shows that the optimal allocation amounts depend not only on time but also on current wealth,and the strategy makes sure that the total assets remain positive all the time.Thus our strategy is more economically reasonable compared to those under constant risk aversion.The numerical example implies that our strategy behaves more steadily in terms of asset allocation,and there is an increasing trend in the allocation amounts as time goes by,a in contrast to the strategy under constant risk aversion.In addition,the influence of cointegration coefficients matrix and mean-reverting speed on the strategy was studied and explained.

关 键 词：协整 动态协整配对交易 均值方差投资选择 时间不一致性 

分 类 号：O29[理学—应用数学] F224.7[理学—数学]