Abstract : In this thesis, I try to introduce a framework for Mathematical Finance problems taking into account Model Uncertainty. This uncertainty will be specified by a family of probability martingals which is not supposed dominated, meaning all probabilities are not absolutely continuous with respect to a reference probability.
First part deals with the definition of the framework and its properties. Second part is about the problem of utility maximization using duality within this framework. In third and fourth parts I introduce and study risk measures and their properties in this framework. Eventually I define a dynamic risk measure in this context.