Portfolio optimization with a prescribed terminal wealth distribution

TL;DR

This paper introduces a novel approach to portfolio optimization by prescribing the terminal wealth distribution using optimal mass transport, solved via dual formulation and numerical methods, with extensions to include consumption during investment.

Contribution

It develops a new framework combining optimal mass transport with financial portfolio optimization, including a dual formulation and numerical algorithms for prescribed terminal distributions.

Findings

Successfully reaches various prescribed terminal distributions

Demonstrates the effectiveness of the gradient descent algorithm

Extends the model to include consumption during investment

Abstract

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.