We call a given American option representable if there exists a European claim which dominates the American payoff at any time and such that the values of the two options coincide in the continuation region of the American option. This concept has interesting implications from a probabilistic, analytic, financial, and numeric point of view. Relying on methods from (Math. Finance 24 (2014) 156–172; Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001) 1–17; Ann. Appl. Probab. 12 (2002) 196–223) and convex duality, we make a first step towards verifying representability of American options.
The authors thank Josef Teichmann for fruitful discussions and for bringing the papers [7, 8] to their attention. Thanks are also due to an anonymous referee for his/her very useful comments.
"Are American options European after all?." Ann. Appl. Probab. 32 (2) 853 - 892, April 2022. https://doi.org/10.1214/21-AAP1698