A two-dimensional random vector in the domain of attraction of an extreme value distribution G is said to be asymptotically independent (i.e. in the tail) if G is the product of its marginal distribution functions. Ledford and Tawn (1996) discussed a form of residual dependence in this case. In this paper we give a characterization of this phenomenon (see also Ramos and Ledford (2009)), and offer extensions to higher-dimensional spaces and stochastic processes. Systemic risk in the banking system is treated in a similar framework.

Asymptotic independence, Extreme residual dependence, Spectral measure
dx.doi.org/10.1239/aap/1300198520, hdl.handle.net/1765/25626
Advances in Applied Probability
Erasmus MC: University Medical Center Rotterdam

de Haan, L.F.M, & Zhou, C. (2011). Extreme residual dependence for random vectors and processes. Advances in Applied Probability, 43(1), 217–242. doi:10.1239/aap/1300198520