Representable Options

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 within the continuation set associated to the American claim. This concept has interesting implications from a probabilistic, analytic and financial point of view.
 
We aim at analyzing and linking together the mathematical notions of representable American claims, embedded American payoffs (in the sense of Jourdain and Martini, 2001) and cheapest dominating European options. This process reveals a duality structure between European and American valuation problems which we deem as very promising for future research. Relying on methods from convex optimization, we make a first step towards verifying representability of certain American claims.
 
Furthermore, we will discuss a new algorithm which generates upper and lower bounds for American option prices as well as a candidate early exercise boundary. The algorithm is benchmarked against high-precision methods from the literature.