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This is the first in a series of papers in which we study an efficientapproximation scheme for solving the Hamilton-Jacobi-Bellman equation formulti-dimensional problems in stochastic control theory. The method is acombination of a WKB style asymptotic expansion of the value function, whichreduces the second order HJB partial differential equation to a hierarchy offirst order PDEs, followed by a numerical algorithm to solve the first few ofthe resulting first order PDEs. This method is applicable to stochastic systemswith a relatively large number of degrees of freedom, and does not seem tosuffer from the curse of dimensionality. Computer code implementation of themethod using modest computational resources runs essentially in real time. Weapply the method to solve a general portfolio construction problem.

Semiclassical approximation in stochastic optimal control I. Portfolio construction problem