Deep Learning for the Multiple Optimal Stopping Problem

2025-12-28

AI Summary

High-dimensional multiple optimal stopping problems suffer from the curse of dimensionality, rendering conventional policy-search methods intractable. Method: This paper proposes a value-function approximation framework that rigorously integrates dynamic programming principles with deep neural networks, explicitly modeling the multi-stage stopping-value surface. It introduces the first end-to-end differentiable neural architecture grounded in discrete-time dynamic programming, accompanied by theoretical analysis of both training error (in discrete time) and discretization error (relative to the underlying continuous-time process). Results: Evaluated on high-dimensional American basket option pricing and nonlinear utility maximization via Monte Carlo simulation, the method achieves superior computational efficiency and dimensional scalability compared to policy-gradient approaches. Its complexity grows markedly more slowly with dimension, while retaining theoretical interpretability and strong empirical performance.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Deep Neural Architectures and Foundation Models

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Develops a deep learning framework for high-dimensional multiple optimal stopping problems
• Combines Dynamic Programming with neural networks to approximate the value function
• Provides an efficient and scalable method for complex recursive financial decisions

Innovation

• Combines Dynamic Programming with neural network approximation
• Explicitly learns value surface unlike policy-search methods
• Efficient scalable method for high-dimensional multiple stopping problems