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Living on the Multidimensional Edge: Seeking Hidden Risks Using Regular Variation

Part of: Nonparametric inference Stochastic processes Limit theorems

Published online by Cambridge University Press:  04 January 2016

Bikramjit Das ,
Abhimanyu Mitra  and
Sidney Resnick
Bikramjit Das*
Affiliation:
ETH Zürich
Abhimanyu Mitra*
Affiliation:
Cornell University
Sidney Resnick*
Affiliation:
Cornell University
*
∗ Postal address: RiskLab, Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland. Email address: bikram@math.ethz.ch
∗∗ Postal address: School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, USA.
∗∗ Postal address: School of Operations Research and Information Engineering, Cornell University, Ithaca, NY 14853, USA.
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Abstract

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Multivariate regular variation plays a role in assessing tail risk in diverse applications such as finance, telecommunications, insurance, and environmental science. The classical theory, being based on an asymptotic model, sometimes leads to inaccurate and useless estimates of probabilities of joint tail regions. This problem can be partly ameliorated by using hidden regular variation (see Resnick (2002) and Mitra and Resnick (2011)). We offer a more flexible definition of hidden regular variation that provides improved risk estimates for a larger class of tail risk regions.

Keywords

regular variationspectral measureasymptotic independencerisk setvague convergence

MSC classification

Primary: 60F99: None of the above, but in this section 62G32: Statistics of extreme values; tail inference
Secondary: 60G70: Extreme value theory; extremal processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 45 , Issue 1 , March 2013 , pp. 139 - 163
Copyright
© Applied Probability Trust 

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