2015 Volume 2015 Pages 112-117
We study the long term portfolio which is able to track a liability. The portfolio optimization problem is defined as the stochastic optimal control problem and the performance criterion is the lower mean square error between the liability and our wealth. We impose constraints for the portfolio weights and obtain the optimal portfolio strategy numerically by solving the Hamilton-Jacobi-Bellman equation applying the quadratic approximation scheme. The numerical simulations using the empirical data provided by Japanese organizations are run under the two types of constraints: the no-short-selling constraint; the upper bound constraint for the portfolio weights. The former demonstrates that the liability tracking ability of our optimal portfolio strategy does not drop if we restrict the short selling. The latter implies the imbalance between the growth rate of the liability and the profitability of the assets.