Before revision:  In addition, we show that spatial risk measures associated with several classical risk measures and induced by such cost fields satisfy (at least ) part of the previously mentioned axioms under appropriate conditions on the max-stable fields. Considering such cost fields is particularly relevant when studying the impact of extreme wind speeds on buildings and infrastructure .
After revision:  In addition, we show that spatial risk measures associated with several classical risk measures and induced by such cost fields satisfy (at least ) part of the previously mentioned axioms under conditions which are generally satisfied for the risk of damaging extreme wind speeds on buildings and infrastructure .