The project I am presenting is meant to fulfill the ideals behind a Marie Curie CIG. In fact, while it has its solid roots in the studies I have conducted so far, in my PhD thesis and during my postdoctoral research period at Bern University (CH), it also possesses all the ingredients to integrate and complement the research interests and projects of my new research “home”, TU Delft (NL).From a scientific point of view, the project represents a clear evolution of my research interests: moving from univariate shock models to the multivariate case means entering into a new exciting field of research, where just a few pioneering works are present.Imagine a system subject to random shocks of random magnitude that can make it fail. Such a situation can be visualized as a skyscraper receiving one or more earthquake shakes: the building may collapse because of one single large stroke, or because of the cumulative effect of several weaker shakes, each one partially damaging its foundations until implosion. Other examples may be a firm suffering liquidity problems, or simply a bar of metal stressed with different random loadings. Shock models are meant to study these phenomena.Most of the constructions available in the literature are univariate. This means that we often consider a single-component system subject to random shocks. Most of the times, also shocks are simply assumed to be of one single type (cumulative or extreme), even if some important exceptions are to be considered, as in the case of competing risk models.The importance of the multivariate extension is linked to the several meaningful applications that multivariate shock models may have in risk analysis, when dealing with sets of defaults and interacting risks. An electrical grid subject to voltage spikes or a financial network are good examples.My aim is to present both parametric and nonparametric models, using tools such as copulas and interacting urn models. Economic applications are expected.