  This paper studies a portfolio allocation problem, where the goal is to
prescribe the wealth distribution at the final time. We study this problem with
the tools of optimal mass transport. We provide a dual formulation which we
solve by a gradient descent algorithm. This involves solving an associated HJB
and Fokker--Planck equation by a finite difference method. Numerical examples
for various prescribed terminal distributions are given, showing that we can
successfully reach attainable targets. We next consider adding consumption
during the investment process, to take into account distribution that either
not attainable, or sub-optimal.
