Title: Spatial Risk Measure for Max-Stable and Max-Mixture Processes,
Abstract: 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.