Deep Learning for the Multiple Optimal Stopping Problem
This addresses a complex problem in quantitative finance and decision theory, providing a scalable solution for high-dimensional multiple exercise cases.
The paper tackles the multiple optimal stopping problem in high dimensions by developing a deep learning framework that combines the Dynamic Programming Principle with neural network approximation of the value function. Numerical experiments on high-dimensional American basket options and nonlinear utility maximization show the method is efficient and scalable.
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.