Abstract

The tail behavior of sums of heavy-tailed (regularly varying) random vectors is known to follow the so-called principle of ‘one large jump’. We establish that, in fact, a more general principle may hold. Assuming that the random vectors are multivariate regularly varying on various subcones of the positive quadrant, first we show that their aggregates are also multivariate regularly varying on these subcones. This allows us to approximate certain tail probabilities which are rendered asymptotically negligible under classical regular variation, despite the ‘one large jump’ asymptotics. We also discover that depending on the structure of the tail event of concern, the tail behavior of the aggregates may be characterized by more than a single large jump. We discuss extensions of the result to multivariate Lévy processes. The results are used to compute asymptotic behaviour of ruin probabilities in the context of insurance portfolios. Based on joint work with: Vicky Fasen-Hartmann