We present a dynamic pay-how-you-drive pricing scheme for motor insurance using telematics signals. More specifically, our approach allows the insurer to apply penalties to a baseline premium on the occurrence of events such as hard acceleration or braking. In addition, we incorporate a bonus-malus system (BMS) adapted for telematics data, providing a credibility component based on past telematics signals to the claim frequency predictions. We purposefully consider a weekly setting for our ratemaking approach to benefit from the signal’s high-frequency rate and to encourage safe driving via dynamic premium corrections. Moreover, we provide a detailed structure that allows our model to benefit from historical records and detailed telematics data collected weekly through an onboard device. We showcase our results numerically in a case study using data from an insurance company.

This paper is concerned with presenting the Exponential-Lognormal (ELN) regression model as a competitive alternative to the Pareto, or Exponential-Inverse Gamma, regression model that has been used in a wide range of areas, including insurance ratemaking. This is the first time that the ELN regression model is used in a statistical or actuarial context. The main contribution of the study is that we illustrate how maximum likelihood estimation of the ELN regression model, which does not have a density in closed form, can be accomplished relatively easily via an Expectation-Maximisation type algorithm. A real data application based on motor insurance data is examined in order to emphasise the versatility of the proposed algorithm. Finally, assuming that the number of claims is distributed according to the classic Negative Binomial and Poisson-Inverse Gaussian regression models, both the a priori and a posteriori, or Bonus–Malus, premium rates resulting from the ELN regression model are calculated via the net premium principle and compared to those determined by the Pareto regression model that has been traditionally used for modelling claim sizes.

In insurance underwriting, misrepresentation represents the type of insurance fraud when an applicant purposely makes a false statement on a risk factor that may lower his or her cost of insurance. Under the insurance ratemaking context, we propose to use the expectation-maximization (EM) algorithm to perform maximum likelihood estimation of the regression effects and the prevalence of misrepresentation for the misrepresentation model proposed by Xia and Gustafson [(2016) The Canadian Journal of Statistics, 44, 198–218]. For applying the EM algorithm, the unobserved status of misrepresentation is treated as a latent variable in the complete-data likelihood function. We derive the iterative formulas for the EM algorithm and obtain the analytical form of the Fisher information matrix for frequentist inference on the parameters of interest for lognormal losses. We implement the algorithm and demonstrate that valid inference can be obtained on the risk effect despite the unobserved status of misrepresentation. Applying the proposed algorithm, we perform a loss severity analysis with the Medical Expenditure Panel Survey data. The analysis reveals not only the potential impact misrepresentation may have on the risk effect but also statistical evidence on the presence of misrepresentation in the self-reported insurance status.

While Bayesian methods have attracted considerable interest in actuarial science, they are yet to be embraced in large-scaled insurance predictive modeling applications, due to inefficiencies of Bayesian estimation procedures. The paper presents an efficient method that parallelizes Bayesian computation using distributed computing on Apache Spark across a cluster of computers. The distributed algorithm dramatically boosts the speed of Bayesian computation and expands the scope of applicability of Bayesian methods in insurance modeling. The empirical analysis applies a Bayesian hierarchical Tweedie model to a big data of 13 million insurance claim records. The distributed algorithm achieves as much as 65 times performance gain over the non-parallel method in this application. The analysis demonstrates that Bayesian methods can be of great value to large-scaled insurance predictive modeling.

We start by describing how, in some cases, we can use variance-related premium principles in ratemaking, when the claim numbers and individual claim amounts are independent. We use quasi-likelihood generalized linear models, under the assumption that the variance function is a power function of the mean of the underlying random variable. We extend this approach to the cases where the claim numbers are correlated. Some alternatives to deal with dependent risks are presented, taking explicitly into account overdispersion. We present regression models covering the bivariate Poisson, the generalized bivariate negative binomial and the bivariate Poisson–Laguerre polynomial, which nest the bivariate negative binomial. We apply these models to a portfolio of the Portuguese insurance company Tranquilidade and compare the results obtained.

The General Insurance Premium Rating Issues Working Party (GRIP) was established by the General Insurance Board of the Faculty and Institute of Actuaries in 2005 to review actuarial involvement in premium rating issues, pricing being one of the key areas in which actuaries work.

GRIP published a full report in January 2007, which is available at www.actuaries.org.uk/grip. This short paper summarises the recommendations of that full report. Further background, discussion and the rationale for these recommendations are set out in more detail in the full report.