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Sojourn times and the fragility index

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  • Falk, Michael
  • Hofmann, Martin

Abstract

We investigate the sojourn time above a high threshold of a continuous stochastic process Y=(Yt)t∈[0,1]. It turns out that the limit, as the threshold increases, of the expected sojourn time given that it is positive, exists if the copula process corresponding to Y is in the functional domain of attraction of a max-stable process. This limit coincides with the limit of the fragility index corresponding to (Yi/n)1≤i≤n as n and the threshold increase.

Suggested Citation

  • Falk, Michael & Hofmann, Martin, 2012. "Sojourn times and the fragility index," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1110-1128.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:3:p:1110-1128
    DOI: 10.1016/j.spa.2011.11.009
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    References listed on IDEAS

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    1. J.L. Geluk & L. de Haan & C.G. de Vries, 2007. "Weak & Strong Financial Fragility," Tinbergen Institute Discussion Papers 07-023/2, Tinbergen Institute.
    2. Michael Falk & Diana Tichy, 2012. "Asymptotic conditional distribution of exceedance counts: fragility index with different margins," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 1071-1085, October.
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    Cited by:

    1. Stefan Aulbach & Michael Falk & Timo Fuller, 2019. "Testing for a $$\delta $$ δ -neighborhood of a generalized Pareto copula," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 599-626, June.

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