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Bonus-Malus Systems with Two Component Mixture Models Arising from Different Parametric Families

Tzougas, G and Vrontos, S and Frangos, N (2018) 'Bonus-Malus Systems with Two Component Mixture Models Arising from Different Parametric Families.' North American Actuarial Journal. ISSN 1092-0277

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Abstract

Two component mixture distributions defined so that the component distributions do not necessarily arise from the same parametric family are employed for the construction of Optimal Bonus-malus Systems (BMS) with frequency and severity components. The proposed modelling framework is used for the first time in actuarial literature research and includes an abundance of alternative model choices to be considered by insurance companies when deciding on their Bonus-Malus pricing strategies. Furthermore, we advance one step further by assuming that all the parameters and mixing probabilities of the two component mixture distributions are modelled in terms of covariates, extending our previous work in Tzougas, Vrontos and Frangos (2014). Applying Bayes theorem we derive optimal BMS either by updating the posterior probability of the policyholders' classes of risk or by updating the posterior mean and the posterior variance. The resulting tailor-made premiums are calculated via the expected value and variance principles and are compared to those based only on the a posteriori criteria. The use of the variance principle in a Bonus-Malus ratemaking scheme in a way that takes into consideration both the number and the costs of claims based on both the a priori and the a posterior classification criteria has not yet been proposed and can alter the resulting premiums significantly, providing the actuary with useful alternative tariff structures.

Item Type: Article
Uncontrolled Keywords: Optimal BMS; Claim frequency; Claim severity; Two component mixture regression models for location, scale, shape and prior probabilities; Expected value premium calculation principle; Variance premium calculation principle
Subjects: H Social Sciences > HA Statistics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Spyridon Vrontos
Date Deposited: 07 Jun 2017 08:02
Last Modified: 27 Feb 2018 13:15
URI: http://repository.essex.ac.uk/id/eprint/19775

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