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Some asymptotic properties of bonus systems

Published online by Cambridge University Press:  29 August 2014

K. Loimaranta
K. Loimaranta*
Affiliation:
Helsinki
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In motorcar insurance—at least in Europe—is widely used a merit rating system called bonus (or malus) system, characterized among others by the fact that only the number of claims occurred does modify the premium. A great variety of different bonus systems is in use. Each country—if not each company—seems to prefer a different bonus system and there is a lack of agreement whether one of them is better than the other. Efforts to construct a theoretically optimal bonus system have not been able to change the situation. General methods to evaluate and compare different existing or proposed bonus systems are therefore wanted.

In the present paper the theory of Markow chains is used to develope formulas for some asymptotic properties of bonus systems. Quantities: efficiency of a bonus system, discrimination power of bonus rules and minimum variance bonus scale are introduced. The last of them gives an asymptotical solution for the problem to find locally “best” bonus scales for given bonus rules. Finally the Danish bonus system is used as an illustration.

We call a merit rating system bonus system if the following assumptions are valid:

i. All policies of a given risk group can be devided into a finite number of classes so that the premium of a policy for a given period depends solely on the class for that period.

ii. The actual class is uniquely defined by the class for the previous period, and the number of claims occurred (regulated) during the period.

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 6 , Issue 3 , May 1972 , pp. 233 - 245
Copyright
Copyright © International Actuarial Association 1972

References

BIBLIOGRAPHIE

[1]Bichsel, F, Erfahrungs — Tarıffıerung ın der Motorfahrzeug haft-pflıcht — Versıcherung Mıtt Vereın schweız Versıcherungsmath 64, 1964Google Scholar
[2]Buhlmann, H, Optımale Pramıenstutensysteme Mıtt Verem schweız Versıcherungsmath 64, 1964Google Scholar
[3]Delaporte, P, Quelques problèmes de statıstıques mathématıques posés par l'Assurance Automobıle et le Bonus pour non sınıstre Bull Trım ınst Actuaıres Francaıs 70, 1959 Tanfıcatıon du rısque ındıvıduel d'accıdents d'automobıles par la prıme modelee sur le rısque, ASTıN Bull III 3, 1965Google Scholar
[4]Depoıd, P, Étude de la Fréquence et de la Bonıfıcatıon pour non sınıstre dans un portefeuılle„Tous rısques modernes” Bull Trım Inst Actuaıres Francaıs 70, 1959 Applıcatıons de la statıstıque aux assurances accıdents et dommages Parıs 1967Google Scholar
[5]Decron, M, A Theoretıcal Study of the No-Claım Bonus Problem ASTıN Bull III 1, 1963Google Scholar
[6]Duboıs de Montregnaud, B, La prıme ajustable pour la tarıfıcatıon de la responsabılıté cıvıle automobıle Bull Trım Inst Actuaıres Francaıs 77, 1966Google Scholar
[7]Franckx, E, Théorıe du bonus ASTIN Bull I 1, 1960Google Scholar
[8]Fréchet, M, Méthode des fonétıons arbıtraıres Théorıe des événements en chaıne dans le cas d'un nombre fiıı d'états possıbles Parıs 1938 Essaı d'une étude des successıons de sınıstres consıdérés comme processus stochastıque Bull Trım Inst Actuaıres Francaıs 70, 1959Google Scholar
[9]Grenander, U, Some Remarks on Bonus Systems ın Automobıle Insurance Skand Aktuanetıdskrıft, 1957Google Scholar
[10]Gurtler, M, Bonus ou malus? ASTIN Bull III 1, 1963Google Scholar
[11]Lundberg, O, Une note sur des systèmes de tarıfıcatıon basés sur des modèles du type Poısson composé ASTIN Bull IV 1, 1966Google Scholar
[12]Molnar, D and Rockwell, T, Analysıs of Polıcy Movement ın a Merıt Ratıng Program an Applıcatıon of Markov Processes J Rısk ıns 33, 1966Google Scholar
[13]Pesonen, E, A Numerıcal Method of Fındıng a Suıtable Bonus Scale ASTıN Bull II 1, 1962Google Scholar
[14]Seal, M, Stochastıc Theory of a Rısk Busıness New York 1969Google Scholar
[15]Contrıbutıon a l'etude du bonus pour non sınıstre en assurance auto-mobıle ASTıN Bull I 3, 1960Google Scholar