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Portfolio Management Problem with Stochastic Wage Income and Inflation-Adjusted Wealth
Department of Mathematics and Statistics, Mulungushi University, Kabwe, Zambia
Department of Mathematics and Statistics, Mulungushi University, Kabwe, Zambia
Department of Mathematics and Statistics, Mulungushi University, Kabwe, Zambia
- 1 Department of Mathematics and Statistics, Mulungushi University, Kabwe, Zambia
- 2 Department of Mathematics and Statistics, Mulungushi University, Kabwe, Zambia
- 3 Department of Mathematics and Statistics, Mulungushi University, Kabwe, Zambia
Journal of Mathematical Finance·Volume 13 (2023)·Pages 159–170·Published 12 May 2023·DOI10.4236/jmf.2023.132010
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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.
KeywordsPortfolio ManagementInflation RiskDynamic Programming PrincipleSto-chastic WageCRRA Investor
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