Sojourn times and the fragility index

Michael Falk and Martin Hofmann

Stochastic Processes and their Applications, 2012, vol. 122, issue 3, 1110-1128

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.

Keywords: Sojourn time; Fragility index; Max-stable process; Functional domain of attraction; Copula process; Generalized Pareto process; Expected shortfall; Sojourn time distribution; Excursion time (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:122:y:2012:i:3:p:1110-1128

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DOI: 10.1016/j.spa.2011.11.009

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