Portfolio Optimization With a Prescribed Terminal Wealth Distribution
21 Pages Posted: 16 Nov 2020
Date Written: September 28, 2020
Abstract
This paper studies a portfolio allocation problem, where the goal is to prescribe the wealth distribution at 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.
Keywords: portfolio allocation, optimal mass transport, HJB, Fokker–Planck, gradient descent
JEL Classification: C61
Suggested Citation: Suggested Citation