Multivariate regular variation for additive processes and  portfolio risk management

We study the joint tail behavior of multivariate heavy-tailed additive 
processes, i.e. stochastically continuous processes with independent 
increments, and the joint tail behavior of vectors of functionals 
acting on each component of  such processes. More precisely, we assume 
that the process at some fixed time satisfies a multivariate regular 
variation condition. The tail behavior of the process is in this framework 
described by a limit measure associated with regular variation. We establish 
tail equivalence of the process at time t and its Levy measure in the sense 
of having the same multivariate regular variation limit measure.  Further we 
derive the limit measures for the vector of componentwise suprema of the 
process, the componentwise suprema of its jumps and of the componentwise 
integrals of the process. The results can be used to derive the tail behavior 
of portfolios consisting of exotic options when the logarithm of the asset 
prices assume to follow a multivariate additive process.