Corrado De Vecchi
University of Verona
Room: M3 3127
Hidden dependence and aggregate tail risk
In this talk, we introduce the notion of hidden dependence for random vectors, which is built on the concepts of risk concentration and common tail events developed in Wang and Zitikis (2021). We then study the role of hidden dependence in risk aggregation problems for arbitrary non-decreasing aggregation functions and tail risk measures. In particular, we show that, starting from a tail event 𝐴 of the aggregate loss for an arbitrary random vector 𝑌 , one can construct a random vector with hidden dependence that dominates 𝑌 on the tail event 𝐴. We then focus on the case in which model uncertainty is described by small perturbations of the distribution of a random vector with respect to a suitable probability distance without changing the marginals. We show that these perturbations of the reference distribution are compatible with hidden dependence and thus lead to the same worst-case risk bounds as in the unconstrained case for arbitrary 𝛾-tail risk measures with a suitable level 𝛾. Joint work with Max Nendel.