Extremal dependence and spatial risk measures for insured losses due to extreme winds

TL;DR

This paper develops a framework to quantify and analyze the spatial risk of insured losses from extreme winds using max-stable random fields, providing insights into risk measures and diversification for insurance applications.

Contribution

It introduces a detailed study of the correlation structure of powers of Brown-Resnick fields and evaluates spatial risk measures, advancing understanding of wind risk modeling.

Findings

Spatial risk measures satisfy key axioms under realistic conditions.

Rates of spatial diversification are specified for different risk measures.

Correlation structures influence the risk assessment of wind-related losses.

Abstract

A meticulous assessment of the risk of impacts associated with extreme wind events is of great necessity for populations, civil authorities as well as the insurance industry. Using the concept of spatial risk measure and related set of axioms introduced by Koch (2017, 2019), we 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 structure of powers of the Brown-Resnick max-stable random fields and look at the influence of the power. 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 conditions which are generally satisfied for the risk of damaging extreme wind speeds. In particular, we specify the rates of spatial diversification in different cases, which is valuable for the insurance industry.