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Tail probabilities of random linear functions of regularly varying random vectors

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  • Bikramjit Das
  • Vicky Fasen-Hartmann
  • Claudia Kluppelberg

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 $[0,\infty)^d$ 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.

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  • Bikramjit Das & Vicky Fasen-Hartmann & Claudia Kluppelberg, 2019. "Tail probabilities of random linear functions of regularly varying random vectors," Papers 1904.06824, arXiv.org, revised Jun 2020.
    • Handle: RePEc:arx:papers:1904.06824
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    References listed on IDEAS

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    1. Basrak, Bojan & Davis, Richard A. & Mikosch, Thomas, 2002. "Regular variation of GARCH processes," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 95-115, May.
    2. Oliver Kley & Claudia Klüppelberg & Gesine Reinert, 2016. "Risk in a Large Claims Insurance Market with Bipartite Graph Structure," Operations Research, INFORMS, vol. 64(5), pages 1159-1176, October.
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