scholarly journals Accounting for Individual Over-Dispersion in a Bonus-Malus Automobile Insurance System

1999 ◽  
Vol 29 (2) ◽  
pp. 327-337 ◽  
Author(s):  
Meng Shengwang ◽  
Yuan Wei ◽  
G.A. Whitmore
Keyword(s):  
Pareto Distribution ◽  
Negative Binomial ◽  
Poisson Model ◽  
Bayes Theorem ◽  
Third Party ◽  
Liability Insurance ◽  
Automobile Insurance ◽  
Individual Level ◽  
Insurance Portfolio ◽  
Over Dispersion

AbstractIndividual automobile insurance claims are characterized by over-dispersion relative to the Poisson model. In addition, claim propensities vary among individuals in any insurance portfolio. This paper presents a model which takes account of both characteristics. The model employs the negative-binomial distribution as the distribution for individual-level claims and a Pareto distribution as the distribution for claim propensities within the portfolio. The paper shows that the resulting model is tractable and has a number of attractive properties which make it suitable for this application. The fit of the model to actual claim numbers for automobile third party liability insurance is examined and found acceptable. Bayes theorem is then applied to this model to calculate illustrative optimal premiums under the Bonus-Malus System (BMS).

scholarly journals The Application of Bühlmann‑Straub Model with Data Correction for the Estimation of Net Premium Rates in Bonus‑Malus Systems of the Motor Third Liability Insurance

2018 ◽  
Vol 4 (336) ◽  
pp. 7-22
Author(s):  
Anna Edyta Szymańska
Keyword(s):  
Estimation Method ◽  
Third Party ◽  
Liability Insurance ◽  
New Method ◽  
Insurance Companies ◽  
Data Correction ◽  
Insurance Portfolio ◽  
Premium Rates ◽  
The Right

One of the elements used in the process of tariff calculation of premiums in motor liability insurance is a bonus‑malus system. This systems takes into account the “claims ratio” by means of increases and discounts of the base premium called net premium rates. The aim of this work is to propose an estimation method of the net premium rates in the bonus‑malus classes of the motor third‑party liability insurance portfolio of individuals. The Bühlmann‑Straub model was used for the premium estimation. In order to improve the credibility of the estimated premium rates, a data correction in the classes with premium increase was preformed. An example of the application of the new method is presented based on the data obtained from one of the insurance companies operating on the Polish market, which has reserved the right to stay anonymous.

scholarly journals Distributions You Can Count On …But What’s the Point?

Econometrics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 9 ◽  
Author(s):  
Brendan P. M. McCabe ◽  
Christopher L. Skeels
Keyword(s):  
Count Data ◽  
Negative Binomial ◽  
Broad Class ◽  
Poisson Model ◽  
Econometric Analysis ◽  
Discrete Distributions ◽  
Optimal Test ◽  
Score Tests ◽  
Optimal Tests ◽  
Over Dispersion

The Poisson regression model remains an important tool in the econometric analysis of count data. In a pioneering contribution to the econometric analysis of such models, Lung-Fei Lee presented a specification test for a Poisson model against a broad class of discrete distributions sometimes called the Katz family. Two members of this alternative class are the binomial and negative binomial distributions, which are commonly used with count data to allow for under- and over-dispersion, respectively. In this paper we explore the structure of other distributions within the class and their suitability as alternatives to the Poisson model. Potential difficulties with the Katz likelihood leads us to investigate a class of point optimal tests of the Poisson assumption against the alternative of over-dispersion in both the regression and intercept only cases. In a simulation study, we compare score tests of ‘Poisson-ness’ with various point optimal tests, based on the Katz family, and conclude that it is possible to choose a point optimal test which is better in the intercept only case, although the nuisance parameters arising in the regression case are problematic. One possible cause is poor choice of the point at which to optimize. Consequently, we explore the use of Hellinger distance to aid this choice. Ultimately we conclude that score tests remain the most practical approach to testing for over-dispersion in this context.

scholarly journals On the Validation of Claims with Excess Zeros in Liability Insurance: A Comparative Study

Risks ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 71 ◽  
Author(s):  
Marjan Qazvini
Keyword(s):  
Poisson Regression ◽  
Third Party ◽  
Liability Insurance ◽  
Insurance Pricing ◽  
Excess Zeros ◽  
Insurance Portfolio ◽  
Zip Model ◽  
Validation Set ◽  
Insurance Data ◽  
Better Than

In this study, we consider the problem of zero claims in a liability insurance portfolio and compare the predictability of three models. We use French motor third party liability (MTPL) insurance data, which has been used for a pricing game, and show that how the type of coverage and policyholders’ willingness to subscribe to insurance pricing, based on telematics data, affects their driving behaviour and hence their claims. Using our validation set, we then predict the number of zero claims. Our results show that although a zero-inflated Poisson (ZIP) model performs better than a Poisson regression, it can even be outperformed by logistic regression.

scholarly journals A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component

1989 ◽  
Vol 19 (2) ◽  
pp. 199-212 ◽  
Author(s):  
Georges Dionne ◽  
Charles Vanasse
Keyword(s):  
Negative Binomial Distribution ◽  
Negative Binomial ◽  
A Priori ◽  
Poisson Model ◽  
Random Variable ◽  
Second Step ◽  
Automobile Insurance ◽  
Binomial Model ◽  
A Posteriori ◽  
Available Information

AbstractThe objective of this paper is to provide an extension of well-known models of tarification in automobile insurance. The analysis begins by introducing a regression component in the Poisson model in order to use all available information in the estimation of the distribution. In a second step, a random variable is included in the regression component of the Poisson model and a negative binomial model with a regression component is derived. We then present our main contribution by proposing a bonus-malus system which integrates a priori and a posteriori information on an individual basis. We show how net premium tables can be derived from the model. Examples of tables are presented.

scholarly journals PROSPECTS FOR THE DEVELOPMENT OF MOTOR THIRD PARTY LIABILITY INSURANCE ON THE BULGARIAN INSURANCE MARKET

2019 ◽  
Vol 17 (Suppl.1) ◽  
pp. 480-487
Author(s):  
Tzvetelina Andreeva
Keyword(s):  
Quantitative Methods ◽  
Third Party ◽  
Liability Insurance ◽  
Insurance Market ◽  
Market Development ◽  
Local Market ◽  
Analysis And Evaluation ◽  
Insurance Portfolio ◽  
European Insurance

The aim of the report is to examine the current and important for the society issues concerning one of the most widespread insurance products - Motor Third Party Liability Insurance. The report examines the use of Motor Third Party Liability insurance on our insurance market. Specific studies have been made on the actual presence of the insurance in the local market and the motor insurance in the general insurance portfolio at European level. The problems and trends in the application and the proposed "Bonus-Malus" system are considered. Further considerations regarding the Bonus-Malus system have been made, taking into account the role of the system for fair payment of insurance premiums. The positive experience of the European insurance market is also reported. The report also focuses on other regulatory and other factors determining the market development. Quantitative methods of analysis and evaluation are used.

scholarly journals Modelling Claim Frequency in Vehicle Insurance

2016 ◽  
Vol 64 (2) ◽  
pp. 683-689
Author(s):  
Jiří Valecký
Keyword(s):  
Linear Models ◽  
Negative Binomial ◽  
Poisson Model ◽  
Binomial Model ◽  
Insurance Company ◽  
Linear Effect ◽  
New Findings ◽  
Insurance Portfolio ◽  
Systematic Component ◽  
Claim Frequency

The paper is focused on modelling claim frequency and extends the work of Kafková and Křivánková, 2014 (Kafková, S., Křivánková, L. 2014. Generalized linear models in vehicle insurance. Acta universitatis agriculturae et silviculturae mendelianae brunensis, 62(2): 383–388). We showed that overdispersion, non-linear systematic component and interacted rating factors should be considered when the claim frequency is modelled. We detected overdispersion in the Poisson model and employed the negative-binomial model to show that considering heterogeneity over insurance policies yields better fit of the model. We also analysed the linear effect of continuous rating factors and their mutual influences. We showed that non-linearity and interactions between rating factors yield the better fit of the model, as well as new findings related to the analysis of claim frequency. All empirical models were estimated on the insurance portfolio of Czech insurance company collected during the years 2004–2008.

scholarly journals Zero-inflated and over-dispersed data models: Empirical evidence from insurance claim frequencies

2018 ◽  
Vol 84 (3-4) ◽  
pp. 103-128
Author(s):  
Imen Karaa ◽  
Habib Chabchoub
Keyword(s):  
Regression Models ◽  
Claims Data ◽  
Poisson Model ◽  
Insurance Premium ◽  
Automobile Insurance ◽  
Insurance Company ◽  
Insurance Claim ◽  
Sample Data ◽  
Claim Frequency ◽  
Over Dispersion

The main objective of this paper is to model automobile claim frequency by using standard count regression and zero-inflated regression models. The use of the latter model is mainly motivated by its ability to handle the over dispersion and zero-inflation phenomenon. The sample data consist of claims data obtained from one randomly selected automobile insurance company in Tunisia for a single year, 2009, containing beginning drivers and drivers who have had a license for less than three years. Our estimation results show that many exogenous variables can explain the frequency of claims; they are not taken into account in calculating the basic insurance premium. Moreover, the ZI binomial negative regression outperforms the standard count models and the ZI Poisson model in handling zero-inflated and additional over dispersed claim count data.

scholarly journals Optimal Bonus-Malus System Design in Motor Third-Party Liability Insurance in Turkey: Negative Binomial Model

2016 ◽  
Vol 8 (8) ◽  
pp. 205 ◽  
Author(s):  
Serpil Ergün Bülbül ◽  
Kemal B. Baykal
Keyword(s):  
Financial Stability ◽  
Negative Binomial ◽  
Negative Binomial Model ◽  
Third Party ◽  
Liability Insurance ◽  
Credibility Theory ◽  
Insurance Companies ◽  
Binomial Model ◽  
Insurance Company ◽  
System Data

One of the most significant instruments used in motor third-party liability insurance rating is bonus-malus system. The aim of the bonus-malus system is to provide a fairness of the premiums paid by ensuring everyone pays a premium that corresponds exactly to their own claim frequency. A balance of total amount of bonuses and maluses is very important to maintain the financial stability of the insurance companies. In Turkey, free tariff regime in motor third-party liability insurance has been adopted since 2014. In this study, an experience rating was employed via the insured’s individual claim experience by considering the drawbacks of using mandatory bonus-malus system. Data entailing information about the claim frequencies of automobiles over a year for motor third party liability policies were obtained from an insurance company. Optimal bonus-malus rates are determined by negative binomial model by using credibility theory, Bayesian approach and the principle of expected value premium.

Cláusulas de franquicia o deducible en seguros de responsabilidad civil en el Derecho español: Naturaleza y efectos respecto de terceros perjudicados

2018 ◽  
pp. 101
Author(s):  
Rafael Lara González
Keyword(s):  
Civil Liability ◽  
Third Parties ◽  
Insurance Contract ◽  
Third Party ◽  
Liability Insurance ◽  
Legal Doctrine ◽  
Insurance Contracts ◽  
Spanish Law ◽  
Palabras Clave ◽  
Legal Nature

ResumenPese a su ubicuidad en la práctica contractual, las cláusulas de franquicia han recibido tratamiento incidental en la doctrina. La discusión sobre ellas se ha enfocado en los contratos de seguros de responsabilidad civil, y en la interpretación del artículo 76 de la Ley española de Contrato de Seguro. En este contexto se ha tratado de establecer si el asegurador puede o no oponer la cláusula de franquicia al tercero perjudicado. El presente trabajo analiza la cláusula de franquicia en la obligación principal del asegurador, su naturaleza jurídica, y examina su relación con los terceros perjudicados. La consideración principal a este respecto estará en si nos encontramos ante un seguro obligatorio o ante un seguro voluntario de responsabilidad civil. Palabras clave: Contrato de seguro; Cláusula de franquicia; Terceroperjudicado; Responsabilidad civil.AbstractDespite their ubiquity in contractual praxis, deductible clauses have received only incidental treatment in legal doctrine. Discussion on them has focused on civil liability insurance contracts, and the interpretation of article 76 of the Spanish Law of Insurance Contracts. In this context it has been attempted to establish whether the insurer can invoke the clause to oppose the injured third party's claim. This article examines the deductible clause included in the insurer's main obligation, its legal nature, and its relation to injured third parties. The main consideration in this regard will be whether the insurance contract is of a mandatory or voluntary nature.Keywords: Insurance contract; Deductible clause; Injured third party; Civil liability.

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