A Monotone Limit Approach to Entropy-Regularized American Options
Abstract
Recent advances in continuous-time optimal stopping have been driven by entropy-regularized formulations of randomized stopping problems, with most existing approaches relying on partial differential equation methods. In this paper, we propose a fully probabilistic framework based on the Doob-Meyer-Mertens decomposition of the Snell envelope and its representation through reflected backward stochastic differential equations. We introduce an entropy-regularized penalization scheme yielding a monotone approximation of the value function and establish explicit convergence rates under suitable regularity assumptions. In addition, we develop a policy improvement algorithm based on linear backward stochastic differential equations and illustrate its performance through a simple numerical experiment for an American-style max call option
Keywords
Cite
@article{arxiv.2602.18062,
title = {A Monotone Limit Approach to Entropy-Regularized American Options},
author = {Daniel Chee and Noufel Frikha and Libo Li},
journal= {arXiv preprint arXiv:2602.18062},
year = {2026}
}