Extreme value modelling of water-related insurance claims

Abstract

snow-melt, and the number of water-related property insurance claims. Weather events which cause severe damages are of general interest, decision makers want to take efficient actions against them while the insurance companies want to set adequate premiums. The modelling is challenging since the underlying dynamics vary across geographical regions due to differences in topology, construction designs and climate. We develop new methodology to improve the existing models which fail to model high numbers of claims. The statistical framework is based on both mixture and extremal mixture modelling, with the latter being based on a discretized generalized Pareto distribution. Furthermore, we propose a temporal clustering algorithm and derive new covariates which lead to a better understanding of the association between claims and weather events. The modelling of the claims, conditional on the locally observed weather events, both fits the marginal distributions well and captures the spatial dependence between locations. Our methodology is applied to three cities across Norway to demonstrate its benefits.

Bayesian Spatial Clustering of Extremal Behavior for Hydrological Variables

“…Scheel et al (2013) showed that the upper tail of this distribution is exceptionally difficult to model for individual administrative areas (termed municipalities) in Norway. Rohrbeck et al (2018) developed an extremal regression model that shows how the largest numbers of insurance claims per weather event in a municipality can be clearly linked to extreme precipitation in that municipality, and that from such a model, marginalizing over the precipitation gives a good model for the marginal distribution of the number of claims.…”

Extreme conditional expectile estimation in heavy-tailed heteroscedastic regression models

“…A better understanding of the extremes of Y can often be achieved by inferring the conditional extremes of Y given a covariate X. Recent examples include the analysis of high healthcare costs in [49] and large insurance claims in [41]. We focus on the case when Y given X is heavy-tailed (i.e.…”

Inference for extreme earthquake magnitudes accounting for a time-varying measurement process

“…Coles and Pericchi (2003) demonstrated in a hydrological context the benefits of using the encompassing generalised Pareto model to properly represent uncertainty in the tail shape. Secondly, the exponential distribution does not account for rounding of the data, resulting in biased parameter estimates (Marzocchi et al, 2019;Rohrbeck et al, 2018). Failing to acknowledge this rounding can therefore also cause bias in threshold selection.…”