A vague multidimensional dependency structure: conditional versus unconditional fuzzy copula models

Ambiguity refers to a fogginess inducing some lack of precision in variables, parameters or magnitudes in models whose aim is to represent real phenomena or better that are strictly linked to the human feelings and beliefs. It has recently become an usual model assumption in several stream of literature. Here we focus on multivariate models affected by ambiguity and provide a rigorous modellization of the main ingredients causing a multidimensional fuzzification. We introduce a conditional fuzzified model, where a certain level of uncertainty affects the set of univariate margins individually taken and also an unconditional model where the ambiguity involves the dependency structure as well. Both these models, i.e. the conditional and the unconditional fuzzy copula model, are compared and their convergence is discussed. Finally a pricing application of these multidimensional fuzzy models, based on Sugeno measures, is proposed.