Portfolio optimization with a prescribed terminal wealth distribution

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