Paper: arXiv 2602.18062

Authors: Daniel Chee, Noufel Frikha, Libo Li

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

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using BSDEs and Snell envelope decompositions to analyze entropy-regularized American option stopping. While mathematically sophisticated with solid convergence proofs and policy iteration theory, it lacks empirical backtesting and offers only minimal numerical experiments in a stylized setup.

Research Flowchart

  flowchart TD
    A["<b>Research Goal:</b> Probabilistic framework & monotone approximation for Entropy-Regularized American Options"] --> B["<b>Inputs & Tools:</b> Snell envelope, Doob-Meyer-Mertens decomposition & Reflected BSDEs"]
    
    B --> C["<b>Entropy-Regularized Penalization:</b> Construct monotone approximation of value function"]
    
    C --> D["<b>Theoretical Analysis:</b> Establish explicit convergence rates under regularity assumptions"]
    
    C --> E["<b>Policy Improvement Algorithm:</b> Iterative scheme based on linear BSDEs"]
    
    E --> F["<b>Numerical Validation:</b> Test algorithm performance on American-style max call option"]
    
    D & F --> G["<b>Key Outcomes:</b> Fully probabilistic foundation, proven convergence, and efficient pricing algorithm"]