  This paper deals with the problem of quantifying the impact of model
misspecification when computing general expected values of interest. The
methodology that we propose is applicable in great generality, in particular,
we provide examples involving path dependent expectations of stochastic
processes. Our approach consists in computing bounds for the expectation of
interest regardless of the probability measure used, as long as the measure
lies within a prescribed tolerance measured in terms of a flexible class of
distances from a suitable baseline model. These distances, based on optimal
transportation between probability measures, include Wasserstein's distances as
particular cases. The proposed methodology is well-suited for risk analysis, as
we demonstrate with a number of applications. We also discuss how to estimate
the tolerance region non-parametrically using Skorokhod-type embeddings in some
of these applications.
