  The main purpose of this paper is to analyze solutions to a fully nonlinear
parabolic equation arising from the problem of optimal portfolio construction.
We show how the problem of optimal stock to bond proportion in the management
of pension fund portfolio can be formulated in terms of the solution to the
Hamilton-Jacobi-Bellman equation. We analyze the solution from qualitative as
well as quantitative point of view. We construct useful bounds of solution
yielding estimates for the optimal value of the stock to bond proportion in the
portfolio. Furthermore we construct asymptotic expansions of a solution in
terms of a small model parameter. Finally, we perform sensitivity analysis of
the optimal solution with respect to various model parameters and compare
analytical results of this paper with the corresponding known results arising
from time-discrete dynamic stochastic optimization model.
