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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Aggregating regularly varying vectors: phenomena o
 f a few large jumps - Bikramjit Das (Singapore Uni
 versity of Technology and Design)
DTSTART;TZID=Europe/London:20240424T151500
DTEND;TZID=Europe/London:20240424T160000
UID:TALK214219AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/214219
DESCRIPTION:The tail behavior of sums of heavy-tailed (regular
 ly varying) random vectors is known to follow the 
 so-called principle of &lsquo\;one large jump&rsqu
 o\;. We establish that\, in fact\, a more general 
 principle may hold. Assuming that the random vecto
 rs are multivariate regularly varying on various s
 ubcones of the positive quadrant\, first we show t
 hat their aggregates are also multivariate regular
 ly varying on these subcones. This allows us to ap
 proximate certain tail probabilities which are ren
 dered asymptotically negligible under classical re
 gular variation\, despite the &lsquo\;one large ju
 mp&rsquo\; asymptotics. We also discover that depe
 nding on the structure of the tail event of concer
 n\, the tail behavior of the aggregates may be cha
 racterized by more than a single large jump. We di
 scuss extensions of the result to multivariate L&e
 acute\;vy processes. The results are used to compu
 te asymptotic behaviour of ruin probabilities in t
 he context of insurance portfolios.\nBased on join
 t work with: Vicky Fasen-Hartmann
LOCATION:External
CONTACT:
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