Characteristics of hail hazard in South Africa based on satellite detection of convective storms

Accurate estimates of hail risk to fixed and mobile assets such as crops, infrastructure and vehicles are required for both insurance pricing and preventive measures. Here we present an event catalog to describe hail hazard in South Africa guided by 14 years of geostationary satellite observations of convective storms. Overshooting cloud tops have been detected, grouped and tracked to describe the spatio-temporal extent of potential hail events. It is found that hail events concentrate mainly in the southeast of the country, along the Highveld and the eastern slopes. Events are most frequent from mid-November through February and peak in the afternoon, between 13 and 17 UTC. Multivariate stochastic modeling of event properties yields an event catalog spanning 25 000 years, aiming to estimate, in combination with vulnerability and exposure data, hail damage for return periods of 200 years.

Premium for implicit deposit insurance within Russian state banks

Deposit insurance system (DIS) exists for 17 years in Russia. The major deposit market share belongs to state banks. Ordinary depositors may perceive the status of the bank state ownership to reflect additional deposit safety, even in the excess of the DIS limits. Such a situation is called an “implicit deposit insurance” in the literature. By offering a sort of implicit deposit insurance services state banks might underprice the deposits in excess of DIS limits compared to the private banks. We utilize data from the open sources to measure the scale of the implicit deposit insurance pricing in Russian state banks. We have revealed that Russian state banks pay extra premium all other things being equal. More specifically, the premium is larger in the smallest and the largest state banks, than in the medium-sized ones. Thus, we claim that the implicit insurance premium has a U-shaped form for Russian state banks depending on their asset size. However, Russian state banks underprice all deposits all other things being equal. Additionally, we find out that IRB banks in Russia are more prone to set up higher deposit rates when they take on more risks, than non-IRB banks.

Concordance Probability for Insurance Pricing Models

The concordance probability, also called the C-index, is a popular measure to capture the discriminatory ability of a predictive model. In this article, the definition of this measure is adapted to the specific needs of the frequency and severity model, typically used during the technical pricing of a non-life insurance product. For the frequency model, the need of two different groups is tackled by defining three new types of the concordance probability. Secondly, these adapted definitions deal with the concept of exposure, which is the duration of a policy or insurance contract. Frequency data typically have a large sample size and therefore we present two fast and accurate estimation procedures for big data. Their good performance is illustrated on two real-life datasets. Upon these examples, we also estimate the concordance probability developed for severity models.

DISCRIMINATION-FREE INSURANCE PRICING

We consider the following question: given information on individual policyholder characteristics, how can we ensure that insurance prices do not discriminate with respect to protected characteristics, such as gender? We address the issues of direct and indirect discrimination, the latter resulting from implicit learning of protected characteristics from nonprotected ones. We provide rigorous mathematical definitions for direct and indirect discrimination, and we introduce a simple formula for discrimination-free pricing, that avoids both direct and indirect discrimination. Our formula works in any statistical model. We demonstrate its application on a health insurance example, using a state-of-the-art generalized linear model and a neural network regression model. An important conclusion is that discrimination-free pricing in general requires collection of policyholders’ discriminatory characteristics, posing potential challenges in relation to policyholder’s privacy concerns.

Contributions from Spatial Models to Non-Life Insurance Pricing: An Empirical Application to Water Damage Risk

This paper explores the application of spatial models to non-life insurance data focused on the multi-risk home insurance branch. In the pricing modelling and rating process, spatial information should be considered by actuaries and insurance managers because frequencies and claim sizes may vary by region and the premium should be different considering this rating variable. In addition, it is relevant to examine the spatial dependence due to the fact that the frequency of claims in neighbouring regions is often expected to be more closely related than those in regions far from each other. In this paper, a comparison between spatial models, such as spatial autoregressive models (SAR), the spatial error model (SEM), and the spatial Durbin model (SDM), and a non-spatial model has been developed. The data used for this analysis are for a home insurance portfolio located in Spain, from which we have selected peril of water coverage.