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has been cited by the following article:

• 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.