BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Aggregating regularly varying vectors: phenomena of a few large ju mps - Bikramjit Das (Singapore University of Technology and Design) DTSTART:20240424T141500Z DTEND:20240424T150000Z UID:TALK214195@talks.cam.ac.uk DESCRIPTION:The tail behavior of sums of heavy-tailed (regularly varying) random vectors is known to follow the so-called principle of &lsquo\;one l arge jump&rsquo\;. We establish that\, in fact\, a more general principle may hold. Assuming that the random vectors are multivariate regularly vary ing on various subcones of the positive quadrant\, first we show that thei r aggregates are also multivariate regularly varying on these subcones. Th is allows us to approximate certain tail probabilities which are rendered asymptotically negligible under classical regular variation\, despite the &lsquo\;one large jump&rsquo\; asymptotics. We also discover that dependin g 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 disc uss extensions of the result to multivariate Lé\;vy processes. The r esults are used to compute asymptotic behaviour of ruin probabilities in t he context of insurance portfolios.\nBased on joint work with: Vicky Fasen -Hartmann LOCATION:External END:VEVENT END:VCALENDAR