Spatial risk measures and applications to max-stable processes

TL;DR

This paper introduces a new framework for spatial risk measures that account for environmental damages over regions, focusing on max-stable processes and their implications for insurance and risk management.

Contribution

It develops a novel concept of spatial risk measure with axioms capturing spatial diversification, and provides theoretical models based on max-stable processes for environmental extremes.

Findings

Proposed a new set of axioms for spatial risk measures.

Constructed models based on max-stable processes exceeding thresholds.

Analyzed implications for insurance and environmental risk assessment.

Abstract

The risk of extreme environmental events is of great importance for both the authorities and the insurance industry. This paper concerns risk measures in a spatial setting, in order to introduce the spatial features of damages stemming from environmental events into the measure of the risk. We develop a new concept of spatial risk measure, based on the spatially aggregated loss over the region of interest, and propose an adapted set of axioms for these spatial risk measures. These axioms quantify the sensitivity of the risk measure with respect to the space and are especially linked to spatial diversification. The proposed model for the cost underlying our definition of spatial risk measure involves applying a damage function to the environmental variable considered. We build and theoretically study concrete examples of spatial risk measures based on the indicator function of max-stable processes exceeding a given threshold. Some interpretations in terms of insurance are provided.