Robust Pricing and Hedging of American Options in Continuous Time

Battle Count: 66

Highly relevant for derivatives desks and risk management teams dealing with American-style options. The robust pricing-hedging duality provides model-independent bounds for American option prices, which is crucial for market-making, hedging, and regulatory capital calculations. The volatility constraint framework allows practitioners to incorporate market-implied information without committing to a specific model. However, the paper is purely theoretical and does not provide directly implementable trading algorithms or numerical schemes. The dynamic lift technique, while mathematically elegant, requires a fictitious market for continuous option trading that does not exist in practice.

Extremely high complexity. The paper is a pure theoretical mathematics contribution requiring deep expertise in stochastic analysis, optimal transport theory, functional analysis (Le Cam topology), and mathematical finance. The proofs involve sophisticated techniques including Azéma supermartingales, Itô-Watanabe decomposition, randomised stopping times, and semimartingale optimal transport duality. There is no algorithmic implementation or numerical procedure provided. Translating these theoretical results into practical pricing tools would require substantial additional work in numerical analysis and computational mathematics.

The paper is a self-contained theoretical mathematics paper with complete proofs. All definitions, assumptions, and theorems are explicitly stated. The proofs rely on well-established results from the literature (Karandikar 1995, Itô-Watanabe 1965, Guo-Loeper 2021). No computational experiments or numerical results are presented, so reproducibility concerns are limited to verifying the mathematical arguments. The paper is available as open access under CC BY license.