A deep learning algorithm for optimal investment strategies

TL;DR

This paper introduces a deep learning approach using the Deep Galerkin method to solve Hamilton-Jacobi-Bellman PDEs in optimal investment problems, demonstrating its effectiveness compared to traditional finite difference methods.

Contribution

It applies the Deep Galerkin method to solve complex PDEs in finance, providing a novel deep learning-based solution for the Merton problem.

Findings

Deep Galerkin method effectively solves HJB equations in investment models.

The deep learning approach outperforms finite difference methods in accuracy.

The method is adaptable to various model settings.

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.