Deep optimal stopping

TL;DR

This paper introduces a deep learning approach for optimal stopping problems that learns stopping rules from simulations, demonstrating high accuracy and efficiency in complex financial and stochastic scenarios.

Contribution

It presents a novel deep learning method for directly learning optimal stopping rules from Monte Carlo samples, applicable to high-dimensional problems.

Findings

Accurately prices Bermudan max-call options in high dimensions.

Effectively prices callable multi barrier reverse convertibles.

Successfully stops fractional Brownian motion with high precision.

Abstract

In this paper we develop a deep learning method for optimal stopping problems which directly learns the optimal stopping rule from Monte Carlo samples. As such, it is broadly applicable in situations where the underlying randomness can efficiently be simulated. We test the approach on three problems: the pricing of a Bermudan max-call option, the pricing of a callable multi barrier reverse convertible and the problem of optimally stopping a fractional Brownian motion. In all three cases it produces very accurate results in high-dimensional situations with short computing times.