Assessing hail risk for property insurers with a dependent marked point process

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.