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JOINT OPTIMIZATION OF TRANSITION RULES AND THE PREMIUM SCALE IN A BONUS-MALUS SYSTEM

Published online by Cambridge University Press:  11 September 2020

Kolos Csaba Ágoston  and
Márton Gyetvai
Kolos Csaba Ágoston
Affiliation:
Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest, H-1093, Fővám tér 8., Budapest, Hungary, E-Mail: kolos.agoston@uni-corvinus.hu
Márton Gyetvai*
Affiliation:
Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest, H-1093, Fővám tér 8., Budapest, Hungary, Institute of Economics, Centre for Economic and Regional Studies, H-1097, Tóth Kálmán u. 4., Budapest, Hungary, E-Mail: gyetvai.marton@krtk.mta.hu
*
E-Mail: gyetvai.marton@krtk.mta.hu
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Abstract

Bonus-malus systems (BMSs) are widely used in actuarial sciences. These systems are applied by insurance companies to distinguish the policyholders by their risks. The most known application of BMS is in automobile third-party liability insurance. In BMS, there are several classes, and the premium of a policyholder depends on the class he/she is assigned to. The classification of policyholders over the periods of the insurance depends on the transition rules. In general, optimization of these systems involves the calculation of an appropriate premium scale considering the number of classes and transition rules as external parameters. Usually, the stationary distribution is used in the optimization process. In this article, we present a mixed integer linear programming (MILP) formulation for determining the premium scale and the transition rules. We present two versions of the model, one with the calculation of stationary probabilities and another with the consideration of multiple periods of the insurance. Furthermore, numerical examples will also be given to demonstrate that the MILP technique is suitable for handling existing BMSs.

Keywords

Adverse selectionbonus-malus systeminteger programmingC44C61D82D86G22
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 3 , September 2020 , pp. 743 - 776
Copyright
© 2020 by Astin Bulletin. All rights reserved

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