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Title: Multivariate credibility in bonus-malus systems distinguishing between different types of claims
Authors: Gómez Déniz, Emilio 
Calderín Ojeda,Enrique 
UNESCO Clasification: 5302 Econometría
Keywords: Bayesian
Bonus-Malus System
Claim Number
Claim Size
Conjugate Distribution
Issue Date: 2018
Project: Nuevos Desarrollos en Métodos Cuantitativos Bayesianos. Aplicaciónes en Evaluación Económica de Tratamientos Mediante Meta-Análisis y Medición de Riesgos Con Datos Actuariales 
Aportaciones A la Toma de Decisiones Bayesianas Óptimas: Aplicaciones Al Coste-Efectividad Con Datos Clínicos y Al Análisis de Riestos Con Datos Acturiales. 
Journal: Risks 
Abstract: In the classical bonus-malus system the premium assigned to each policyholder is based only on the number of claims made without having into account the claims size. Thus, a policyholder who has declared a claim that results in a relatively small loss is penalised to the same extent as one who has declared a more expensive claim. Of course, this is seen unfair by many policyholders. In this paper, we study the factors that affect the number of claims in car insurance by using a trivariate discrete distribution. This approach allows us to discern between three types of claims depending wether the claims are above, between or below certain thresholds. Therefore, this model implements the two fundamental random variables in this scenario, the number of claims as well as the amount associated with them. In addition, we introduce a trivariate prior distribution conjugated with this discrete distribution that produce credibility bonus-malus premiums that satisfy appropriate traditional transition rules. A practical example based on real data is shown to examine the differences with respect to the premiums obtained under the traditional system of tarification.
ISSN: 2227-9091
DOI: 10.3390/risks6020034
Source: Risks [ISSN 2227-9091], v. 6(2), 34
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