Before revision:  Upper and lower bounds are given by asymptotic independent and fully dependent components of V in dependence of the tail index \alpha being smaller or larger than 1. Counterexamples  complete the picture.
After revision:  Upper and lower bounds are given by asymptotic independent and fully dependent components of V in dependence of the tail index \alpha being smaller or larger than 1. Counterexamples , where for non-linear aggregation functions no bounds are available, complete the picture.