A deep learning algorithm for optimal investment strategies

2021/01/29 by Daeyung Gim, Gim, Daeyung, Hyungbin Park +1
Economics, Econometrics and Finance · Engineering · #FOS: Economics and business #Fluid Dynamics and Turbulent Flows #Mathematical Finance (q-fin.MF) #Portfolio Management (q-fin.PM) #Reservoir Engineering and Simulation Methods #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2101.12387

openalex publication_date 2021/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper treats the Merton problem how to invest in safe assets and risky assets to maximize an investor's utility, given by investment opportunities modeled by a d-dimensional state process. The problem is represented by a partial differential equation with optimizing term: the Hamilton-Jacobi-Bellman equation. The main purpose of this paper is to solve partial differential equations derived from the Hamilton-Jacobi-Bellman equations with a deep learning algorithm: the Deep Galerkin method, first suggested by Sirignano and Spiliopoulos (2018). We then apply the algorithm to get the solution of the PDE based on some model settings and compare with the one from the finite difference method.

Citations

• Neural-network methods for boundary value problems with irregular boundaries

Related

• Solving Nonlinear and High-Dimensional Partial Differential Equations via Deep Learning
• Neural networks-based algorithms for stochastic control and PDEs in finance
• Extensions of the Deep Galerkin Method
• Deep Learning Methods for S Shaped Utility Maximisation with a Random Reference Point
• Differential learning methods for solving fully nonlinear PDEs