Spatial risk measures for max-stable and max-mixture processes. Issue 7 (2nd October 2020) - Ahmed, M.; Maume-Deschamps, V.; Ribereau, P.; Vial, C.
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].