Advances in Applied Probability

Living on the multidimensional edge: seeking hidden risks using regular variation

Bikramjit Das, Abhimanyu Mitra, and Sidney Resnick

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Abstract

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.

Article information

Source
Adv. in Appl. Probab., Volume 45, Number 1 (2013), 139-163.

Dates
First available in Project Euclid: 15 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aap/1363354106

Digital Object Identifier
doi:10.1239/aap/1363354106

Mathematical Reviews number (MathSciNet)
MR3077544

Zentralblatt MATH identifier
1276.60041

Subjects
Primary: 60F99: None of the above, but in this section 62G32: Statistics of extreme values; tail inference
Secondary: 60G70: Extreme value theory; extremal processes

Keywords
regular variation spectral measure asymptotic independence risk set vague convergence

Citation

Das, Bikramjit; Mitra, Abhimanyu; Resnick, Sidney. Living on the multidimensional edge: seeking hidden risks using regular variation. Adv. in Appl. Probab. 45 (2013), no. 1, 139--163. doi:10.1239/aap/1363354106. https://projecteuclid.org/euclid.aap/1363354106


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