Portfolio Optimization with Random Liability in the Stochastic Interest Rate Environments

This paper applies dynamic programming principle and Legendre transform to study a dynamic asset allocation problem with liability process and stochastic interest rate model, where interest rate is assumed to be driven by the Ho-Lee model or the Vasicek model. By using variable change technique, we obtain the closed-form solutions to the optimal investment strategies in the quadratic utility framework. Finally, a numerical example is given to analyze the impact of market parameters on the optimal investment strategies and some economic implications are provided. The numerical results imply that the amount invested in the stocks in the liability setting is larger than that in the no-liability setting. Key–Words: the Ho-Lee model; the Vasicek model; asset and liability management(ALM); Legendre transform; optimal investment strategy;