Spatial Risk Measure for Max-Stable and Max-Mixture Processes

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

1 ICJ - Institut Camille Jordan
2 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis

In this paper, we consider isotropic and stationary max-stable, inverse max-stable and max-mixture processes $X=(X(s))_{s\in\bR^2}$ and the damage function $\cD_X^{\nu}= |X|^\nu$ with $0<\nu<1/2$. We study the quantitative behavior of a risk measure which is the variance of the average of $\cD_X^{\nu}$ over a region $\mathcal{A}\subset \bR^2$.} This kind of risk measure has already been introduced and studied for \vero{some} max-stable processes in \cite{koch2015spatial}. %\textcolor{red}{In this study, we generalised this risk measure to be applicable for several models: asymptotic dependence represented by max-stable, asymptotic independence represented by inverse max-stable and mixing between of them.} We evaluated the proposed risk measure by a simulation study.

Mots clés: max-mixture processes; spatial risk measures

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

Manaf Ahmed, Véronique Maume-Deschamps, Pierre Ribereau, Céline Vial. Spatial Risk Measure for Max-Stable and Max-Mixture Processes. 2017. ⟨hal-01546570v1⟩