Optimal portfolio strategies in a Vasicek Framework

The optimal portfolio problem for a riskless asset and (n+1) risky stocks is developed. The stochastic short-term interest rate with Vasicek dynamics affects the prices of the stocks. The investment objective is maximizing expected CRRA utility of the difference between the terminal wealth and the stochastic benchmark with the constraint: the terminal wealth is more than the stochastic benchmark. The problem has been solved by the martingale approach. The closed-form optimal trading strategies are obtained. A numerical example illustrating the results is presented.