B0315
Title: On certain notion of tail dependence of copulas
Authors: Piotr Jaworski - University of Warsaw (Poland) [presenting]
Abstract: A family of bivariate copulas $C$ such that $C(u,u)>0$, whenever $u>0$, and the tail of $C$ at $(0,0)$ is described by two functions $g$ and $h$, such that the limits $C(xu,u)/C(u,u)$ and $C(u,ux)/C(u,u)$, as $u\rightarrow 0$, exist and are equal to $g(x)$ and $h(x)$ respectively, is considered. The existence of $g$ and $h$ implies, between others, that the diagonal $\delta(u)=C(u,u)$ is regularly varying at 0. Furthermore, if $g$ and $h$ are continuous, copula $C$ can be uniformly approximated in the following way: $C(u,v)=\min(g(u/v)$, $h(v/u)) \delta(\max(u,v)) +o(\delta(\max(u,v)))$.
