Superhedging of American options on an incomplete market with discrete time and finite horizon

We establish an existence criterion for the decomposition that generalizes a wellknown uniform Doob decomposition to a set of equivalent probability measures. Based on this criterion, we obtain necessary and sufficient existence conditions for a minimal superhedging (with respect to any measure out of the set of equivalent measures) American option portfolio on an incomplete frictionless market with a finite number of risky assets, discrete time, and finite horizon. We give a sample construction of such a portfolio for an American option with an arbitrary bounded dynamical contingent claim on an incomplete market with one risky asset.

Presented by the member of Editorial Board: A. I. Kibzun