Optimal strategy in CIR model and modified constant elasticity of variance

This paper analyzes an optimal investment strategy problem, where the investor can invest his wealth in bonds and stocks. The bond and stock dynamics are Cox-Ingersoll-Ross (CIR) and M-CEV models, respectively. We obtain the Hamilton–Jacobi–Bellman (HJB) equation for the corresponding stochastic optimal control problems. Then, we give an explicit solution to the HJB equation and calculate the optimal strategies for a maximized power utility function. The results show that an increase in correlation, interest rate, and investor risk level augments the optimal strategy. Furthermore, the optimal strategy decreases with increased stock price and interest rate risk.