Theoretical framework for the pricing of contingent claims in the presence of model uncertainty

The aim of this work is to evaluate the cheapest superreplication price of a general (possibly path-dependent) European contingent claim in a context where the model is uncertain. This setting is a generalization of the uncertain volatility model (UVM) introduced in by Avellaneda. Levy and Paras. The uncertainty is specified by a family of martingale probability measures which may not be dominated. we obtain a partial characterization result and a full characterization which extends Avellaneda. Levy and Paras results in the UVM case.