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Living on the multi-dimensional edge: seeking hidden risks using regular variation

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  • Bikramjit Das
  • Abhimanyu Mitra
  • Sidney Resnick

Abstract

Multivariate regular variation plays a role 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 [Resnick, 2002, Mitra and Resnick, 2010]. We offer a more flexible definition of hidden regular variation that provides improved risk estimates for a larger class of risk tail regions.

Suggested Citation

  • Bikramjit Das & Abhimanyu Mitra & Sidney Resnick, 2011. "Living on the multi-dimensional edge: seeking hidden risks using regular variation," Papers 1108.5560, arXiv.org.
  • Handle: RePEc:arx:papers:1108.5560
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    File URL: http://arxiv.org/pdf/1108.5560
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    References listed on IDEAS

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    1. Gourieroux, Christian & Jasiak, Joann, 2006. "Multivariate Jacobi process with application to smooth transitions," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 475-505.
    2. Robert Fernholz & Ioannis Karatzas, 2005. "Relative arbitrage in volatility-stabilized markets," Annals of Finance, Springer, vol. 1(2), pages 149-177, November.
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