Dynamic portfolio selection with liability and stochastic interest rates in the utility framework

This paper is concerned with a continuous–time dynamic portfolio selection problem with liability process in the stochastic interest rate settings, where interest rate dynamics is supposed to be governed by the Ho–Lee model and the Vasicek model respectively, while liability dynamics is driven by Brownian motion with drift. Moreover, we assume that interest rate dynamics and liability dynamics are all generally correlated with stock prices. We use dynamic programming principle to investigate the optimal investment strategies in the power utility and exponential utility cases and obtain the closed–form solutions in explicit form. Finally, a numerical example is provided to illustrate how market parameters affect the optimal investment strategy respectively.