Entropy-regularized penalization schemes and reflected BSDEs with singular generators

2026/02/20 by Daniel Chee, Noufel Frikha, Libo Li · 1 voice · 1 citation
Economics, Econometrics and Finance · #q-fin.MF

paper · pdf

arxiv published 2026/02/20 · arxiv updated 2026/03/03

Abstract

This paper extends our previous work to continuous-time optimal stopping, focusing on American options in an exploratory setting. Our first contribution is an entropy-regularized penalization scheme, inspired by classical penalization techniques for reflected BSDEs. It yields a smooth approximation of the stopping rule, promotes exploration, and enables gradient-based learning methods. We prove well-posedness, convergence, and illustrate numerical performance in low-dimensional examples. Our second contribution analyzes the behaviour of the scheme as the penalization parameter grows, showing that the limit solves a reflected BSDE with a logarithmically singular generator, for which we establish existence and uniqueness via a monotone limit argument.

Citations

• A Monotone Limit Approach to Entropy-Regularized American Options
• An Entropy Regularized BSDE Approach to Bermudan Options and Games
• Quadratic BSDEs with Singular Generators and Unbounded Terminal Conditions: Theory and Applications
• Well-posedness of quadratic RBSDEs and BSDEs with one-sided growth restrictions
• Exploratory Optimal Stopping: A Singular Control Formulation
• Learning to Optimally Stop Diffusion Processes, with Financial Applications
• Geometric BSDEs
• Stopping Times of Boundaries: Relaxation and Continuity
• Randomized Optimal Stopping Problem in Continuous time and Reinforcement Learning Algorithm
• Solving the optimal stopping problem with reinforcement learning: an application in financial option exercise
• Neural Optimal Stopping Boundary
• A class of quadratic reflected BSDEs with singular coefficients
• Exploratory HJB equations and their convergence
• Exploratory HJB Equations and Their Convergence
• Deep Reinforcement Learning for Optimal Stopping with Application in Financial Engineering
• Pricing and hedging American-style options with deep learning
• Neural network regression for Bermudan option pricing
• BSDEs driven by |z|²/y and applications to PDEs and decision theory
• Kriging Metamodels and Experimental Design for Bermudan Option Pricing
• Reflected BSDEs when the obstacle is not right-continuous and optimal stopping
• Optimal dual martingales, their analysis and application to new algorithms for Bermudan products
• Reflected Backward SDEs with General Jumps
• On randomized stopping
• An essay on the general theory of stochastic processes

Cited by

• A Monotone Limit Approach to Entropy-Regularized American Options

Discussions

• Daniel Chee, Noufel Frikha, Libo Li: Entropy-regularized penalization schemes for American options and reflected BSDEs with singular generators https://arxiv.org/abs/2602.18078 https://arxiv.org/pdf/2 [bsky, 0 points, 0 comments]

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