A study on optimal consumption and portfolio with labour income under inflation

Abstract

This paper studies the problem of optimal consumption and portfolio with labour income under inflation. The purpose of investor is to maximize the expected utility of personal terminal real wealth. Firstly, the life cycle of the investor is divided into two phases of retirement and employment, and a stochastic optimal control model for the optimal consumption and portfolio problem with labour income is established under inflation. Secondly, with the method of stochastic control, the HJB equation of the optimal consumption and portfolio under inflation is built, and then an explicit expression of the valued function of the optimization problem in the case of hyperbolic absolute risk aversion (HARA) utility is obtained. Finally, through the numerical simulation under the condition of given parameters, the economic analysis of the results is provided.