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STATISTICAL APPROACH FOR OPEN BONUS MALUS

Published online by Cambridge University Press:  18 October 2013

Gracinda Rita Guerreiro ,
João Tiago Mexia  and
Maria de Fátima Miguens
Gracinda Rita Guerreiro*
Affiliation:
Departamento de Matemática, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa Campus de Caparica, 2829-516 Caparica, Portugal & CMA/FCT/UNL
João Tiago Mexia
Affiliation:
Departamento de Matemática, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa Campus de Caparica, 2829-516 Caparica, Portugal & CMA/FCT/UNL E-Mail: jtm@fct.unl.pt
Maria de Fátima Miguens
Affiliation:
Departamento de Matemática, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa Campus de Caparica, 2829-516 Caparica, Portugal & CMA/FCT/UNL E-Mail: jtm@fct.unl.pt
*
E-Mail: grg@fct.unl.pt
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Abstract

In this paper, following an open portfolio approach, we show how to estimate a Bonus-malus system evolution.

Considering a model for the number of new annual policies, we obtain ML estimators, asymptotic distributions and confidence regions for the expected number of new policies entering the portfolio in each year, as well as for the expected number and proportion of insureds in each bonus class, by year of enrollment. Confidence regions for the distribution of policyholders result in confidence regions for optimal bonus scales.

Our treatment is illustrated by an example with numerical results.

Keywords

Bonus-malus systemsopen portfoliostochastic vorticesMarkov chainslimit distributionstatistical inference
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 44 , Issue 1 , January 2014 , pp. 63 - 83
Copyright
Copyright © ASTIN Bulletin 2013 

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