Before revision:  To do so, a model for the market dynamicsis needed. While the traditional replication or superreplication strategies find the optimal prices under the constraint that all risks are shifted to the counterparty, we weaken this assumption here by introducing risk (resp. acceptability) functionals in the stochastic optimizationframework. Moreover, we consider the associated ambiguity problem, where we replace the single probability model by a non-parametric set of models .
After revision:  To do so, a model for the underlying asset price dynamics .