Dynamic mean-variance portfolio selection with liability and stochastic interest rate

This paper is concerned with an asset and liability management problem in a continuous-time mean-variance framework, in which interest rate is driven by the Vasicek model and liability process is governed by Brownian motion with drift. Moreover, interest rate and liability dynamics are generally correlated with stock price dynamics. The objective of the investor is to minimize the variance of terminal net wealth for a given terminal expected net wealth. The explicit solutions of the efficient strategy and the efficient frontier are obtained by applying stochastic dynamic programming principle and Lagrange duality theorem. A numerical example is given to illustrate the results obtained.