  This paper concerns the numerical solution of the finite-horizon Optimal
Investment problem with transaction costs under Potential Utility. The problem
is initially posed in terms of an evolutive HJB equation with gradient
constraints. In Finite-Horizon Optimal Investment with Transaction Costs: A
Parabolic Double Obstacle Problem, Day-Yi, the problem is reformulated as a
non-linear parabolic double obstacle problem posed in one spatial variable and
defined in an unbounded domain where several explicit properties and formulas
are obtained. The restatement of the problem in polar coordinates allows to
pose the problem in one spatial variable in a finite domain, avoiding some of
the technical difficulties of the numerical solution of the previous statement
of the problem. If high precision is required, the spectral numerical method
proposed becomes more efficient than simpler methods as finite differences for
example.
