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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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

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

First available in Project Euclid: 15 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

regular variation spectral measure asymptotic independence risk set vague convergence


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.

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