基于通胀和劳动收入的最优消费投资问题研究

Study on optimal consumption-portfolio problem based on labor income and inflation

在消费篮子价格完全可观察下,考虑通胀与劳动收入对投资者最优消费投资的影响.首先,将投资者的生命周期分为就业阶段和退休阶段,分别建立两个阶段对应的随机控制数学模型;其次,利用随机控制方法推导出相应的HJB方程,并在CRRA(常相对风险厌恶)效用的情形下,获得最优化问题值函数显式解;最后,在给定参数的条件下进行数值模拟,分析了通胀因素对投资者的消费投资策略的影响.

This paper considers the impact of inflation and labor income on optimal consumption and portfolio of an investor in the case of fully observed consumption basket price.Firstly,the life cycle of the in- vestor is divided into two phases of retirement and employment, and then the corresponding stochastic control mathematical models are set up.Secondly,by using the method of stochastic control, the HJB e- quation is derived,an explicit expression of the valued function of the optimization problem is obtained in the case of constant relative risk aversion （CRRA） utility. Finally, the effect of inflation on an investor ＇s optimal consumption and portfolio strategy is analyzed by numerical simulation with given parameters.