  This is the first in a series of papers in which we study an efficient
approximation scheme for solving the Hamilton-Jacobi-Bellman equation for
multi-dimensional problems in stochastic control theory. The method is a
combination of a WKB style asymptotic expansion of the value function, which
reduces the second order HJB partial differential equation to a hierarchy of
first order PDEs, followed by a numerical algorithm to solve the first few of
the resulting first order PDEs. This method is applicable to stochastic systems
with a relatively large number of degrees of freedom, and does not seem to
suffer from the curse of dimensionality. Computer code implementation of the
method using modest computational resources runs essentially in real time. We
apply the method to solve a general portfolio construction problem.
