A Monotone Limit Approach to Entropy-Regularized American Options

Daniel Chee, Noufel Frikha () and Libo Li ()
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Daniel Chee: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Noufel Frikha: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, UP1 - Université Paris 1 Panthéon-Sorbonne
Libo Li: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia

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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: American option; Optimal stopping; Entropy regularization; Policy improvement algorithm (search for similar items in EconPapers)
Date: 2026-02-20
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