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Bonus–Malus systems with Weibull distributed claim severities

Published online by Cambridge University Press:  19 May 2014

Weihong Ni ,
Corina Constantinescu  and
Athanasios A. Pantelous
Weihong Ni
Affiliation:
Department of Mathematical Sciences, Institute for Actuarial and Financial Mathematics, University of Liverpool, UK
Corina Constantinescu
Affiliation:
Department of Mathematical Sciences, Institute for Actuarial and Financial Mathematics, University of Liverpool, UK
Athanasios A. Pantelous*
Affiliation:
Department of Mathematical Sciences, Institute for Actuarial and Financial Mathematics, University of Liverpool, UK; Institute for Risk and Uncertainty, University of Liverpool, UK
*
*Correspondence to: Athanasios A. Pantelous, Department of Mathematical Sciences, Institute for Actuarial and Financial Mathematics, University of Liverpool, UK. E-mail: A.Pantelous@liverpool.ac.uk
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Abstract

One of the pricing strategies for Bonus–Malus (BM) systems relies on the decomposition of the claims’ randomness into one part accounting for claims’ frequency and the other part for claims’ severity. By mixing an exponential with a Lévy distribution, we focus on modelling the claim severity component as a Weibull distribution. For a Negative Binomial number of claims, we employ the Bayesian approach to derive the BM premiums for Weibull severities. We then conclude by comparing our explicit formulas and numerical results with those for Pareto severities that were introduced by Frangos & Vrontos.

Keywords

Bonus–Malus SystemsWeibull DistributionBayesian Estimator
Type
Papers
Information
Annals of Actuarial Science , Volume 8 , Issue 2 , September 2014 , pp. 217 - 233
Copyright
© Institute and Faculty of Actuaries 2014 

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