  In this article, we provide a numerical method based on fitted finite volume
method to approximate the Hamilton-Jacobi-Bellman (HJB) equation coming from
stochastic optimal control problems. The computational challenge is due to the
nature of the HJB equation, which may be a second-order degenerated partial
differential equation coupled with optimization. In the work, we discretize the
HJB equation using the fitted finite volume method and show that matrix
resulting from spatial discretization is an M-matrix. The optimization problem
is solved at every time step using iterative method. Numerical results are
presented to show the robustness of the fitted finite volume numerical method
comparing to the standard finite difference method.
