  In this paper, we consider the asset-liability management under the
mean-variance criterion. The financial market consists of a risk-free bond and
a stock whose price process is modeled by a geometric Brownian motion. The
liability of the investor is uncontrollable and is modeled by another geometric
Brownian motion. We consider a specific state-dependent risk aversion which
depends on a power function of the liability. By solving a flow of FBSDEs with
bivariate state process, we obtain the equilibrium strategy among all the
open-loop controls for this time-inconsistent control problem. It shows that
the equilibrium strategy is a feedback control of the liability.
