Title: Spatial risk measures induced by powers of max-stable random fields,
Abstract: A meticulous assessment of the risk of extreme environmental events is of
great necessity for populations, civil authorities as well as the
insurance/reinsurance industry. 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. Then, using the latter results, we
thoroughly investigate spatial risk measures associated with variance and
induced by powers of max-stable random fields. 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.