The Measures of Accuracy of Claim Frequency Credibility Predictor

Nowadays, the sustainability risks and opportunities start to affect strongly insurance companies in regard to the resulting additional variability of future values of variables taken into account in the decision processes. This is important especially in the era of sustainable non-life insurance promoting, among others, the use of ecological car engines or ecological systems of building heating. The fundamental issue in non-life insurance is to predict future claims (e.g., the aggregate value of claims or the number of claims for a single policy) in a heterogeneous portfolio of policies taking account of claim experience. For this purpose, the so-called credibility theory is used, which was initiated by the fundamental Bühlmann model modified to the Bühlmann–Straub model. Several modifications of the model have been proposed in the literature. One of them is the development of the relationship between the credibility models and statistical mixed models (e.g., linear mixed models) for longitudinal data. The article proposes the use of the parametric bootstrap algorithm to estimate measures of accuracy of the credibility predictor of the number of claims for a single policy taking into account new risk factors resulting from the emergence of green technologies on the considered market. The predictor is obtained for the model which belongs to the class of Generalised Linear Mixed Models (GLMMs) and which is a generalization of the Bülmann–Straub model. Additionally, the possibility of predicting the number of claims and the problem of the assessment of the prediction accuracy are presented based on a policy characterized by new green risk factor (hybrid motorcycle engine) not previously present in the portfolio. The paper presents the proposed methodology in a case study using real insurance data from the Polish market.

Modelling Claim Frequency in Insurance Using Count Models

Background: In modelling claim frequency in actuary science, a major challenge is the number of zero claims associated with datasets. Aim: This study compares six count regression models on motorcycle insurance data. Methodology: The Akaike Information Criteria (AIC) and the Bayesian Information Criterion (BIC) were used for selecting best models. Results: Result of analysis showed that the Zero-Inflated Poisson (ZIP) with no regressors for the zero component gives the best predictive ability for the data with the least BIC while the classical Negative Binomial model gives the best result for explanatory purpose with the least AIC.

Boosting Poisson regression models with telematics car driving data

With the emergence of telematics car driving data, insurance companies have started to boost classical actuarial regression models for claim frequency prediction with telematics car driving information. In this paper, we propose two data-driven neural network approaches that process telematics car driving data to complement classical actuarial pricing with a driving behavior risk factor from telematics data. Our neural networks simultaneously accommodate feature engineering and regression modeling which allows us to integrate telematics car driving data in a one-step approach into the claim frequency regression models. We conclude from our numerical analysis that both classical actuarial risk factors and telematics car driving data are necessary to receive the best predictive models. This emphasizes that these two sources of information interact and complement each other.

Discrete-Time Risk Models with Claim Correlated Premiums in a Markovian Environment

In this paper we consider a discrete-time risk model, which allows the premium to be adjusted according to claims experience. This model is inspired by the well-known bonus-malus system in the non-life insurance industry. Two strategies of adjusting periodic premiums are considered: aggregate claims or claim frequency. Recursive formulae are derived to compute the finite-time ruin probabilities, and Lundberg-type upper bounds are also derived to evaluate the ultimate-time ruin probabilities. In addition, we extend the risk model by considering an external Markovian environment in which the claims distributions are governed by an external Markov process so that the periodic premium adjustments vary when the external environment state changes. We then study the joint distribution of premium level and environment state at ruin given ruin occurs. Two numerical examples are provided at the end of this paper to illustrate the impact of the initial external environment state, the initial premium level and the initial surplus on the ruin probability.

Bivariate Mixed Poisson and Normal Generalised Linear Models with Sarmanov Dependence—An Application to Model Claim Frequency and Optimal Transformed Average Severity

The aim of this paper is to introduce dependence between the claim frequency and the average severity of a policyholder or of an insurance portfolio using a bivariate Sarmanov distribution, that allows to join variables of different types and with different distributions, thus being a good candidate for modeling the dependence between the two previously mentioned random variables. To model the claim frequency, a generalized linear model based on a mixed Poisson distribution -like for example, the Negative Binomial (NB), usually works. However, finding a distribution for the claim severity is not that easy. In practice, the Lognormal distribution fits well in many cases. Since the natural logarithm of a Lognormal variable is Normal distributed, this relation is generalised using the Box-Cox transformation to model the average claim severity. Therefore, we propose a bivariate Sarmanov model having as marginals a Negative Binomial and a Normal Generalized Linear Models (GLMs), also depending on the parameters of the Box-Cox transformation. We apply this model to the analysis of the frequency-severity bivariate distribution associated to a pay-as-you-drive motor insurance portfolio with explanatory telematic variables.

IMPLEMENTASI METODE BAYES PADA PENGHITUNGAN PREMI ASURANSI KENDARAAN BERMOTOR

One type of general insurance is motor vehicle insurance. Premium pricing of general insurance can be calculated by some methods. In this study, Bayes method will be used. The distribution of claim frequency is Poisson distribution and the distribution of claim severity is Exponential distribution. The premium is calculated by multiplying the expectation of claim frequency and the expectation of claim severity. Based on the historical data analysis using the Bayes method, the highest pure premium of motor vehicle insurance in Indonesia is Hino brand and the lowest pure premium is Honda brand. The result of this premium pricing can be used as a reference for the insurance companies to manage their motor vehicle insurance reserves.

The Impact of Medical Malpractice Reforms

This article evaluates the effects of medical malpractice reform on claiming, malpractice premiums, physician supply, and defensive medicine. We conclude that damage caps materially reduce claim frequency, payouts per claim, and total payouts. The effects of damage caps on malpractice premiums, physician supply, and defensive medicine are more modest. It is difficult to quantify the impact of reforms other than damage caps—partly because reforms are typically adopted as a package deal, and partly because of the limitations of the available data. We close by identifying three areas that would benefit from more research.