Utility portfolio optimization with liability and multiple risky assets under the extended CIR model

This paper studies an asset and liability management problem with extended Cox-Ingersoll-Ross (CIR) interest rate, where the financial market is composed of one risk-free asset and multiple risky assets and one zero-coupon bond. We assume that risk-free interest rate is driven by extended CIR interest rate model, while liability is modeled by Brownian motion with drift and is generally correlated with stock price. Firstly, we use stochastic optimal control theory to obtain Hamilton-Jacobi-Bellman (HJB) equation for the value function and choose power utility and exponential utility for our analysis. Secondly, we obtain the closed-form solutions to the optimal investment strategies by applying variable change technique. Finally, a numerical example is presented to analyze the dynamic behavior of the optimal investment strategy and provide some economic implications for our results. Key–Words: CIR interest rate model; liability process; dynamic portfolio selection; stochastic optimal control; optimal investment strategy;