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arXiv · 1706.08244

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

Ahmed Manaf·Véronique Maume-Deschamps·Pierre Ribereau·Céline Vial
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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.

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Ahmed Manaf, Véronique Maume-Deschamps, Pierre Ribereau, Céline Vial. 2017-06-26. Spatial Risk Measure for Max-Stable and Max-Mixture Processes. https://arxiv.org/abs/1706.08244

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