Optimal Stopping with Trees: The Details

TL;DR

This paper compares neural network and CART-tree methods for high-dimensional optimal stopping problems, highlighting interpretability benefits of trees and analyzing their performance on benchmark examples.

Contribution

It introduces a CART-tree based algorithm for optimal stopping, offering more interpretability than neural networks, and evaluates its performance on benchmark problems.

Findings

CART-trees provide interpretable stopping rules.

Neural networks and trees have different strengths in high-dimensional problems.

Bermudan max-call may not be ideal as a benchmark for high-dimensional stopping.

Abstract

The purpose of this paper is two-fold, first, to review a recent method introduced by S. Becker, P. Cheridito, and P. Jentzen, for solving high-dimensional optimal stopping problems using deep Neural Networks, second, to propose an alternative algorithm replacing Neural Networks by CART-trees which allow for more interpretation of the estimated stopping rules. We in particular compare the performance of the two algorithms with respect to the Bermudan max-call benchmark example concluding that the Bermudan max-call may not be suitable to serve as a benchmark example for high-dimensional optimal stopping problems. We also show how our algorithm can be used to plot stopping boundaries.