Robust Hedging of American Options via Aggregated Snell Envelopes

Paper: arXiv 2506.14553

Authors: Marco Rodrigues

Abstract

We construct an aggregator for a family of Snell envelopes in a nondominated framework. We apply this construction to establish a robust hedging duality, along with the existence of a minimal hedging strategy, in a general semi-martingale setting for American-style options. Our results encompass continuous processes, or processes with jumps and non-vanishing diffusion. A key application is to financial market models, where uncertainty is quantified through the semi-martingale characteristics.

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a highly sophisticated theoretical framework for robust superhedging of American options under Knightian uncertainty using semi-martingale processes and aggregated Snell envelopes. However, it is entirely theoretical with no empirical backtesting, numerical simulations, or real-world data validation.

Research Flowchart

  flowchart TD
    A[Goal: Robust Hedging of American Options under Model Uncertainty] --> B[Inputs: Financial Semi-martingale Characteristics & Nondominated Framework]
    B --> C[Construct Aggregator for Family of Snell Envelopes]
    C --> D[Analyze Continuous & Jump-Diffusion Semi-martingale Processes]
    D --> E[Establish Robust Hedging Duality Theorem]
    E --> F[Outcome: Minimal Hedging Strategy for American-Style Options]