一类部分信息下带有劳动力收入的最优投资消费问题  

Optimal portfolio and consumption selection problem with labor income under partial information

作　　者：张盼盼 王光臣[1] ZHANG Pan-pan;WANG Guang-chen(School of Control Science and Engineering,Shandong University,Jinan Shandong 250061,China)

机构地区：[1]山东大学控制科学与工程学院,山东济南250061

出　　处：《控制理论与应用》2021年第11期1835-1844,共10页Control Theory & Applications

基　　金：国家自然科学基金项目(61821004,61925306,11831010);山东省自然科学基金项目(ZR2019ZD42,ZR2020ZD24)资助。

摘　　要：最优投资消费问题属于一类典型的随机最优控制问题.劳动力收入可通过影响期望效用从而影响投资消费策略的制定.本文首次在股票收益率和劳动力收入均为不可观测过程情形下,研究了一类部分信息下的最优投资消费问题.首先综合运用Kalman滤波和非线性滤波,得到了Zakai方程的显式解,将部分信息下的随机最优控制问题转化为完备信息下的随机最优控制问题.其次通过求解HJB方程以及证明验证定理,得到了该类最优投资消费问题的最优策略以及值函数的显式表达.最后采用真实市场数据进行仿真,对比经典完备信息模型与本文部分信息模型所得最优策略的差异,验证了本文所得最优策略在有效利用市场信息方面的优越性.Optimal portfolio and consumption selection problem is a typical stochastic optimal control problem.Labor income can influence portfolio and consumption strategies by affecting expected utility.For the first time,this paper studies a type of optimal portfolio and consumption selection problem under partial information,where both stock’s return rate and labor income are unobservable processes.Firstly,by virtue of Kalman filtering and nonlinear filtering,an explicit solution of Zakai equation is obtained,which transforms the stochastic optimal control problem under partial information into one under complete information.Secondly,optimal strategy and value function of this kind of optimal portfolio and consumption selection problem are explicitly obtained by solving HJB equation and proving verification theorem.Finally,real market data is used for simulation,and differences between the optimal strategy of the classic complete information model and the partial information case of this paper are shown,which verifies the superiority of the optimal strategy obtained in this paper in effectively using market information.

关 键 词：最优投资组合与消费选择 自融资策略 随机控制 KALMAN滤波 Zakai方程 HJB方程 

分 类 号：F014.5[经济管理—政治经济学]