On the evaluation of the asymptotic fairness of bonus-malus systems

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dc.contributor.authorHeras Martínez, Antonio José
dc.contributor.authorVilar Zanón, José Luis
dc.contributor.authorGil Fana, José Antonio
dc.date.accessioned2023-06-21T01:43:37Z
dc.date.available2023-06-21T01:43:37Z
dc.date.issued2001
dc.description.abstractIn this paper we try to evaluate the asymptotic fairness of bonus-malus systems, assuming the simplest case when there is no hunger for bonus.The asymptotic fairness has to be understood as the bonus-malus systemability in assessing the individual risks in the long run (see Lemaire[1995] p.xvi). Firstly we de…ne the asymptotic fairness of a bonus-malussystem following an expression that can be found in Lemaire [1985] p.168. Secondly, we de…ne a measure of the global asymptotic fairness considering the structure function of the risk group. Finally we try to calculate, for each set of transition rules and a given structure function,the scale of premiums that brings the global asymptotic fairness closest to the ideal situation where each insured pays in the long run a premium corresponding to its own claim frequency. This is possible thanks to the application of a multiobjective optimization technique named Goal Programing. We give an example illustrating the fact that the ideal case could be fairly well approached.
dc.description.departmentDecanato
dc.description.facultyFac. de Ciencias Económicas y Empresariales
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/6754
dc.identifier.citationDE PRIL, N. [1978]: The E¢ciency of a Bonus-Malus System. ASTIN Bulletin, no10, 59-72. KEMENY, J.G. and SNELL, J.L. [1976]: Finite Markov Chains. Springer-Verlag. KLUGMAN, S.A. and PANJER, H.H. andWILLMOT, G.E. [1998]: Loss Models. From Data to Decisions. Wiley series in Probability and Statistics. LEMAIRE, J. [1985]: Automobile Insurance. Actuarial Models. Kluwer-Nijho¤ Publishing. LEMAIRE, J. [1995]: Bonus-Malus Systems in Automobile Insurance. Kluwer Academic Publishers. LEMAIRE, J. [1998]: Bonus-Malus System: the European and Asian Approach to Merit-Rating. North American Actuarial Journal. Volume 2, Number 1. LOIMARANTA, K. [1972]: Some Asymptotic Properties of Bonus Systems. ASTIN Bulletin, 6, 233-245. NORBERG, R. [1976]: A Credibility Theory for Automobile Bonus Systems. Scandinavian Actuarial Journal, 92-107. PESONEN, M. [1963]: A Numerical Method of Finding a Suitable Bonus Scale. ASTIN Bulletin 2, 102-108. ROMERO, C. [1991]: Handbook of Critical Issues in Goal Programming. Pergamon Press, Oxford. ROMERO, C. [1993]: Teoría de la Decisión Multicriterio: Conceptos, Técnicas y Aplicaciones. Alianza Universidad Textos, Madrid. VILAR, J.L. [2000]: Arithmetization of Distributions and Linear Goal Programming. Insurance: Mathematics and Economics 27, 113-122.
dc.identifier.doib19081017
dc.identifier.issn2255-5471
dc.identifier.relatedurlhttp://www.ucm.es/centros/webs/fccee/
dc.identifier.relatedurlhttps://economicasyempresariales.ucm.es/working-papers-ccee
dc.identifier.urihttps://hdl.handle.net/20.500.14352/64429
dc.issue.number32
dc.language.isoeng
dc.page.total38
dc.publication.placeMadrid
dc.publisherFacultad de Ciencias Económicas y Empresariales, Universidad Complutense de Madrid
dc.relation.ispartofseriesDocumentos de Trabajo de la Facultad de Ciencias Económicas y Empresariales
dc.rightsAtribución-NoComercial-CompartirIgual 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttps://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.subject.keywordBonus-malus system
dc.subject.keywordAsymptotic fairness
dc.subject.keywordGoal Programming
dc.subject.keywordSimplex method.
dc.subject.ucmDinero
dc.subject.unesco5304.06 Dinero y Operaciones Bancarias
dc.titleOn the evaluation of the asymptotic fairness of bonus-malus systems
dc.typetechnical report
dc.volume.number2001
dspace.entity.typePublication
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relation.isAuthorOfPublication3115ae81-6ff7-43dd-a41f-e6ea35178c9f
relation.isAuthorOfPublication5a503bdf-bc23-4af1-9e54-92b62228786b
relation.isAuthorOfPublication.latestForDiscovery047e514e-3517-4265-8bb2-dba00d57d167
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