Before revision:  Koch (2017, 2018) introduced a concept of spatial risk measure and a related set of axioms which are well-suited to analyse and quantify the risk due to events having a spatial extent, precisely such as natural disasters. In this paper, we first carry out a detailed study of the correlation (and covariance) structure of powers of the Smith and Brown-Resnick max-stable random fields  .
After revision:  Koch (2017, 2018) introduced a concept of spatial risk measure and a related set of axioms which are well-suited to analyse and quantify the risk of losses due to extreme wind speeds. The insured cost due to wind events is proportional to the wind speed at a power ranging typically between 2 and 12. Hence we first perform a detailed study of the correlation (and covariance) structure of powers of the Smith and Brown-Resnick max-stable random fields .