  Modern risk modelling approaches deal with vectors of multiple components.
The components could be, for example, returns of financial instruments or
losses within an insurance portfolio concerning different lines of business.
One of the main problems is to decide if there is any type of dependence
between the components of the vector and, if so, what type of dependence
structure should be used for accurate modelling.
  We study a class of heavy-tailed multivariate random vectors under a
non-parametric shape constraint on the tail decay rate. This class contains,
for instance, elliptical distributions whose tail is in the intermediate
heavy-tailed regime, which includes Weibull and lognormal type tails. The study
derives asymptotic approximations for tail events of random walks.
Consequently, a full large deviations principle is obtained under, essentially,
minimal assumptions. As an application, an optimisation method for a large
class of Quota Share (QS) risk sharing schemes used in insurance and finance is
obtained.
