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Tail probabilities of random linear functions of regularly varying random vectors

Das, Bikramjit ; Fasen-Hartmann, Vicky 1; Klüppelberg, Claudia
1 Institut für Stochastik (STOCH), Karlsruher Institut für Technologie (KIT)

Abstract:

We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in [0,∞)$^d$ under random linear transformations. This allows us to compute probabilities of a variety of tail events, which classical multivariate regularly varying models would report to be asymptotically negligible. We illustrate our findings with applications to risk assessment in financial systems and reinsurance markets under a bipartite network structure.


Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2022
Sprache Englisch
Identifikator KITopen-ID: 1000148682
Umfang 27 S.
Vorab online veröffentlicht am 26.05.2022
Nachgewiesen in Dimensions
arXiv
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