Deep Learning for the Multiple Optimal Stopping Problem

TL;DR

This paper introduces a deep learning framework that effectively solves high-dimensional multiple optimal stopping problems by combining dynamic programming with neural network approximation, demonstrating efficiency on financial and utility maximization tasks.

Contribution

The paper presents a novel neural network-based approach for high-dimensional multiple optimal stopping problems, explicitly learning the value surface and analyzing errors in both discrete and continuous settings.

Findings

Efficiently solves high-dimensional American basket options.

Scalable method for nonlinear utility maximization.

Provides error analysis for neural network training and discretization.

Abstract

This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex recursive dependencies that remain challenging. We address this by combining the Dynamic Programming Principle with neural network approximation of the value function. Unlike policy-search methods, our algorithm explicitly learns the value surface. We first consider the discrete-time problem and analyze neural network training error. We then turn to continuous problems and analyze the additional error due to the discretization of the underlying stochastic processes. Numerical experiments on high-dimensional American basket options and nonlinear utility maximization demonstrate that our method provides an efficient and scalable method for the multiple optimal stopping problem.