Optimal Portfolio Management in a CIR Framework

The optimal portfolio problem for a bank account, single risky stock and a rolling horizon bond is developed. The stochastic short-term interest rate with the Cox-Ingersoll-Ross (CIR) dynamics affects the prices of the stock and rolling horizon bond. The investment objective is maximizing expected CRRA utility of terminal wealth. The problem has been solved by the stochastic dynamic programming principle and the completion of squares technique. The closed-form optimal trading strategy is obtained. A numerical example illustrating the results is presented.