A Monotone Limit Approach to Entropy-Regularized American Options

2026-02-20

AI Summary

This study addresses the pricing of American options in continuous time under entropy regularization, formulated as an optimal stopping problem. By leveraging the Doob–Meyer–Mertens decomposition of the Snell envelope and reflected backward stochastic differential equations (RBSDEs), the authors construct a fully probabilistic framework that incorporates an entropy regularization penalty to ensure monotone approximation of the value function. The proposed approach not only establishes explicit convergence rates but also introduces a policy improvement algorithm based on linear BSDEs. Under standard regularity conditions, convergence of the value function is rigorously proved, and numerical experiments on American max-call options demonstrate the algorithm’s effectiveness and stability.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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

Problem

• American options
• optimal stopping
• entropy regularization
• Snell envelope
• backward stochastic differential equations

Innovation

• entropy regularization
• reflected backward stochastic differential equations
• Snell envelope
• monotone approximation
• policy improvement algorithm