Portfolio optimization with a prescribed terminal wealth distribution. Issue 2 (1st February 2022)

• Record Type: Journal Article
• Authors: Guo, Ivan; Langrené, Nicolas; Loeper, Grégoire; Ning, Wei
• Is Part Of: Quantitative finance. Volume 22:Issue 2(2022)
• Page Start: 333
• Page End: 347
• Publication Date: 2022-02-01
• Subjects: Portfolio allocation -- Wealth distribution target -- Optimal mass transport -- HJB -- Fokker–Planck; C60 -- C61 -- G11; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2021.1967432
• Languages: English
• ISSNs: 1469-7688

Abstract

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