TITLE:
Portfolio Management Problem with Stochastic Wage Income and Inflation-Adjusted Wealth
AUTHORS:
Stanley Jere, George Mukupa, Edwin Moyo
KEYWORDS:
Portfolio Management, Inflation Risk, Dynamic Programming Principle, Sto-chastic Wage, CRRA Investor
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.13 No.2,
May
23,
2023
ABSTRACT: In this paper, the portfolio management problem with stochastic wage income and inflation risk for CRRA investors is solved. In real life, investors experience stochastic wage income and inflation risk. This could be due to events such as COVID-19, fiscal policy, financial policy adjustments, and climate change. We consider an agent who invests in the financial market with one risk-free security (e.g. a money market account or bond) and one risky security (e.g. a stock or stock index). Our goal is to choose the optimal controls that maximize the objective function in order to obtain the value function. By applying Dynamic Programming Principle, we determine the HJB PDE. Solving the HJB PDE, we establish the value function and optimal controls.