  We propose a long term portfolio management method which takes into account a
liability. Our approach is based on the LQG (Linear, Quadratic cost, Gaussian)
control problem framework and then the optimal portfolio strategy hedges the
liability by directly tracking a benchmark process which represents the
liability. Two numerical results using empirical data published by Japanese
organizations are served: simulations tracking an artificial liability and an
estimated liability of Japanese organization. The latter one demonstrates that
our optimal portfolio strategy can hedge his or her liability.
