Spatial risk measure for Gaussian processes

Manaf Ahmed (1, 2) , Véronique Maume-Deschamps (1, 2) , Pierre Ribereau (1, 2) , Céline Vial (3, 1, 2)

1 ICJ - Institut Camille Jordan
2 PSPM - Probabilités, statistique, physique mathématique
3 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis

In this paper, we study the quantitative behavior of a spatial risk measure corresponding to a damage function and a region, taking into account the spatial dependence of the underlying process. This kind of risk measure has already been introduced and studied for some max-stable processes in [Koch2015]. In this paper, we consider isotropic Gaussian processes and the excess damage function over a threshold. We performed a simulation study and a real data study.

Mots clés: Risk measures; Gaussian processes; Spatial dependence

Domaines: Statistiques [math.ST]; Probabilités [math.PR]

Manaf Ahmed, Véronique Maume-Deschamps, Pierre Ribereau, Céline Vial. Spatial risk measure for Gaussian processes. Annales de l'ISUP, 2019, 63 (1), pp.3-21. ⟨hal-01421078v2⟩