Spatial risk measures for max-stable and max-mixture processes. Issue 7 (2nd October 2020)

• Record Type: Journal Article
• Authors: Ahmed, M.; Maume-Deschamps, V.; Ribereau, P.; Vial, C.
• Is Part Of: Stochastics. Volume 92:Issue 7(2020)
• Page Start: 1005
• Page End: 1020
• Publication Date: 2020-10-02
• Subjects: Risk measures -- spatial dependence -- max-stable process -- max-mixture process -- extreme value theory; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2019.1687703
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : In this paper, we consider isotropic and stationary max-stable, inverse max-stable and max-mixture processes X = ( X ( s ) ) s ∈ R 2 and the damage process D X ν = | X | ν with 0 < ν < 1 / 2 . We study the quantitative behaviour of a risk measure which is the variance of the average of D X ν over a region A ⊂ R 2 . This kind of risk measure has already been introduced and studied for some max-stable processes in Koch [ Spatial risk measures and applications to max-stable processes, Extremes 20(3) (2017), pp. 635–670].