Paper: arXiv 2602.18078

Authors: Daniel Chee, Noufel Frikha, Libo Li

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents rigorous mathematical foundations for entropy-regularized reflected BSDEs with singular generators and proves clear convergence bounds. However, as a purely theoretical mathematical finance paper, it lacks comprehensive empirical backtesting or real-world dataset validation beyond low-dimensional toy examples.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve American Option Optimal Stopping via Exploratory/RL Framework] --> B[Inputs: Continuous-Time Market Model & Entropy Regularization Parameter]
    B --> C[Methodology 1: Formulate Entropy-Regularized Penalization Scheme]
    C --> D[Computational Process: Apply Gradient-Based Learning & Perform Numerical Experiments]
    B --> E[Methodology 2: Analyze Limit as Penalization Parameter Grows]
    
    D --> F[Outcome 1: Smooth Stopping Approximations & Efficient Low-Dim RL Performance]
    E --> G[Outcome 2: Proof of Existence/Uniqueness for Reflected BSDE with Log-Singular Generator]