Robust Pricing and Hedging of American Options in Continuous Time

Paper: arXiv 2510.05463

Authors: Ivan Guo, Jan Obłój

Abstract

We consider the robust pricing and hedging of American options in a continuous time setting. We assume asset prices are continuous semimartingales, but we allow for general model uncertainty specification via adapted closed convex constraints on the volatility. We prove the robust pricing-hedging duality. When European options with given prices are available for static trading, we show that duality holds against richer models where these options are traded dynamically. Our proofs rely on probabilistic treatment of randomised stopping times and suitable measure decoupling, and on optimal transport duality. In addition, similarly to the approach of Aksamit et al. (2019) in discrete time, we identify American options with European options on an enlarged space.

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework for robust pricing and hedging of American options in continuous time using optimal transport duality and measure decoupling. However, it is purely theoretical with no empirical backtesting, code, or real-market data analysis.

Research Flowchart

  flowchart TD
    A[Goal: Robust Pricing & Hedging of American Options under Model Uncertainty] --> B[Inputs: Continuous Semimartingales & Volatility Constraints]
    B --> C[Method: Enlarged Space Mapping & Randomised Stopping Times]
    C --> D[Method: Measure Decoupling & Optimal Transport Duality]
    D --> E[Outcome: Robust Pricing-Hedging Duality Proved]
    E --> F[Outcome: Duality Extended to Dynamic Trading of Static European Options]