A Continous-Time Optimal Investment and Consumption Strategy for Commercial Banks under the Hamilton-Jacob-Bellman Optimization Technique with Bounded Interest Rates

Abstract

The CIR model is used to model interest rates in this project, which analyses an investment and consumption problem under bounded interest rate conditions. Our goal is to determine the optimal investment and consumption strategy to maximize predicted utility of consumption and terminal wealth. To begin, we build the HJB equation for the value function using the dynamic programming approach, and then complete our analysis using the logarithm utility. Second, by conjecturing the shape of a solution and solving partial differential equations, we build closedform solutions to the optimal investment and consumption strategies. Finally, we present a numerical example that demonstrates how market variables influence the best investment and consumption strategy.