While driver telematics has gained attention for risk classification in auto insurance, scarcity of observations with telematics features has been problematic, which could be owing to either privacy concerns or favorable selection compared to the data points with traditional features.

To handle this issue, we apply a data integration technique based on calibration weights for usage-based insurance with multiple sources of data. It is shown that the proposed framework can efficiently integrate traditional data and telematics data and can also deal with possible favorable selection issues related to telematics data availability. Our findings are supported by a simulation study and empirical analysis in a synthetic telematics dataset.

We present novel cross-sectional and longitudinal claim count models for vehicle insurance built upon the combinedd actuarial neural network (CANN) framework proposed by Wüthrich and Merz. The CANN approach combines a classical actuarial model, such as a generalized linear model, with a neural network. This blending of models results in a two-component model comprising a classical regression model and a neural network part. The CANN model leverages the strengths of both components, providing a solid foundation and interpretability from the classical model while harnessing the flexibility and capacity to capture intricate relationships and interactions offered by the neural network. In our proposed models, we use well-known log-linear claim count regression models for the classical regression part and a multilayer perceptron (MLP) for the neural network part. The MLP part is used to process telematics car driving data given as a vector characterizing the driving behavior of each insured driver. In addition to the Poisson and negative binomial distributions for cross-sectional data, we propose a procedure for training our CANN model with a multivariate negative binomial specification. By doing so, we introduce a longitudinal model that accounts for the dependence between contracts from the same insured. Our results reveal that the CANN models exhibit superior performance compared to log-linear models that rely on manually engineered telematics features.

The fact that a large proportion of insurance policyholders make no claims during a one-year period highlights the importance of zero-inflated count models when analyzing the frequency of insurance claims. There is a vast literature focused on the univariate case of zero-inflated count models, while work in the area of multivariate models is considerably less advanced. Given that insurance companies write multiple lines of insurance business, where the claim counts on these lines of business are often correlated, there is a strong incentive to analyze multivariate claim count models. Motivated by the idea of Liu and Tian (Computational Statistics and Data Analysis, 83, 200–222; 2015), we develop a multivariate zero-inflated hurdle model to describe multivariate count data with extra zeros. This generalization offers more flexibility in modeling the behavior of individual claim counts while also incorporating a correlation structure between claim counts for different lines of insurance business. We develop an application of the expectation–maximization (EM) algorithm to enable the statistical inference necessary to estimate the parameters associated with our model. Our model is then applied to an automobile insurance portfolio from a major insurance company in Spain. We demonstrate that the model performance for the multivariate zero-inflated hurdle model is superior when compared to several alternatives.

Ex post moral hazard arises when the insured has an unobservable influence on the size of a loss after its occurrence. In automobile (property) insurance, ex post moral hazard could increase in the scope of the repairs and/or the value of the repairs. Both vehicle owners and auto repairers could gain from increasing the scope of repairs, while auto repairers would gain from an increase in the value of repairs. An analysis of 994 Australian road traffic crashes found that ex post moral hazard increased the value of repairs by 46.8 per cent of which 9 percentage points was explained by an increase in the scope of the repairs, which was defined as an increased from 2 to 2.4 parts per auto repair.

In this paper, a new three-parameter discrete family of distributions, the $r{\mathcal B}ell$ family, is introduced. The family is based on series expansion of the r-Bell polynomials. The proposed model generalises the classical Poisson and the recently proposed Bell and Bell–Touchard distributions. It exhibits interesting stochastic properties. Its probabilities can be computed by a recursive formula that allows us to calculate the probability function of the amount of aggregate claims in the collective risk model in terms of an integral equation. Univariate and bivariate regression models are presented. The former regression model is used to explain the number of out-of-use claims in an automobile insurance portfolio, by showing a good out-of-sample performance. The latter is used to describe the number of out-of-use and parking claims jointly. This family provides an alternative to other traditionally used distributions to describe count data such as the negative binomial and Poisson-inverse Gaussian models.

A one-parameter version of the generalised Poisson distribution provided by Consul and Jain (1973) is considered in this paper. The distribution is unimodal with a zero vertex and over-dispersed. A generalised linear model related to this distribution is also presented. Its parameters can be estimated by using a Fisher-Scoring algorithm which is equivalent to iteratively reweighted least squares. Due to its flexibility and capacity to describe highly skewed data with an excessive number of zeros, the model is suitable to be applied in insurance settings as an alternative to the negative binomial and zero-inflated model.

We put one of the predictions of adverse-selection models to the test, using data from the Danish automobile insurance market: that there is a positive correlation between claims risk and insurance coverage. We can find a statistically significant insurance coverage--risk correlation when coverage is expressed relative to the insurance premium, but not when it is expressed in monetary terms.

Modelling automobile insurance claims is a crucial component in the ratemaking procedure. This paper focuses on the probability that a policyholder reports a claim, where the classical logit link does not provide a right model. This is so because databases related with automobile claims are often unbalanced, containing more non-claims than the presence of claims. In this work an asymmetric logit model, which takes into account the large number of non-claims in the portfolio, is considered. Both, logit and asymmetric logit models from a Bayesian point of view, are used to a sample that was collected from a major automobile insurance company in Spain in 2009, resulting in a dataset of 2,000 passenger vehicle. We establish the validity of the asymmetric model in front of the conventional logit link. The use of a garage, the age of the vehicle and the duration of the client's relation with the company are all shown to be significant explanatory variables by the logit model. The asymmetric model includes, in addition, the length of time the policyholder has held a driving licence and the type of use made of the vehicle. The asymmetric model provides a better fit to the data examined.

Under certain conditions, a Bonus-Malus system can be interpreted as a Markov chain whose n-step transition probabilities converge to a limit probability distribution. In this paper, the rate of the convergence is studied by means of the eigenvalues of the transition probability matrix of the Markov chain.

The paper describes how a study group, appointed by the Belgian Professional Union of Insurance Companies, designed a new tariff structure in motor third party liability. Particular emphasis was given to the construction of a more efficient bonus–malus system.