Assessing Hail Risk for Property Insurers with a Dependent Marked Point Process

Abstract

Hail risk is among the most challenging perils to insure and property damage due to hailstones has been on the top of the list of annual claims for most non‐life insurers. In this article, we present a simple yet flexible statistical model for insurers to assess and manage hail risks from two aspects: analysing the insurance claims arrival pattern upon occurrence of a hailstorm and quantifying the subsequent financial impact of the hailstorm. We formulate the problem using a marked point process where the reporting of insurance claims due to a hailstorm is treated as recurrent events and the claim amounts are viewed as associated marks. Three complications are addressed in model building: the unobserved heterogeneity in claim arrival, the dependence between the event time and the mark and the complex distribution in claim amount. Using a unique data that combine the exposure data from a major US insurer and the radar data from a third‐party vendor, we show the proposed method help improve predictive analytics for post‐hailstorm claims volume, arrival rate and severity, and thus claim management decisions for the insurer.

Multi-State Modelling of Customer Churn

“…Third, the assumption that all policyholders are independent is not only questionable in our application but also in studies of personal homeowners and automobiles where things being insured that is, houses and cars, are close to one another, sharing common environmental hazards such as hail, windstorm, and so forth. Some research has been being done to accommodate these dependencies, such as the spatial autocorrelation approach (Brechmann and Czado, 2014) and the more recent marked point process approach (Shi et al, 2022). Both of these, among others, may serve as valuable reference points for relaxing such assumption in future developments of multi-state customer churn modelling.…”

Ratemaking in a changing environment

“…We could allow dependence by incorporating unobservable policy-specific random effects or by using copula modeling. For example, Shi et al (2016Shi et al ( , 2022 and Frees et al (2021) accommodate the dependence of the multilevel structure of claims using copula modeling, and Okine et al (2022) use random effects to capture the association between the size of claims and time to settlement. However, we note that Frees et al (2016) verify that dependence modeling has little influence on the claim scores under the frequency-severity model approach.…”