Hostname: page-component-5c6d5d7d68-sv6ng Total loading time: 0 Render date: 2024-08-10T07:51:24.274Z Has data issue: false hasContentIssue false
  • English
  • Français

Bonus-malus Systems as Markov Set-chains

Published online by Cambridge University Press:  17 April 2015

Małgorzata Niemiec
Małgorzata Niemiec*
Affiliation:
Warsaw School of Economics, Institute of Econometrics, Al. Niepodległości 164, 02-554 Warsaw, Poland, Tel: +48 601 371 611, Fax: +48 22 564 86 17, E-mail: malgorzata.niemiec@sgh.waw.pl
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The objective of this paper is to present an analysis of a bonus-malus system (BMS) within the framework of the theory of ergodic Markov set-chains. It is shown that this type of Markov chains enables the evaluation of BMS, even in steady-state, under the assumption that transition probabilities change in a definite range. We introduce a model that allows the determination of the consequences of changes in the claim frequency of a policyholder. In a numerical example we examine the BMS employed by one of the Polish insurance companies.

Keywords

Markov set-chainbonus-malus systemclaim frequency
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 37 , Issue 1 , May 2007 , pp. 53 - 65
Copyright
Copyright © ASTIN Bulletin 2007

References

Hartfiel, D.J. (1991) Component bounds for Markov set-chain limiting sets. Journal of Statistical Computation and Simulation 38, 15–24.CrossRefGoogle Scholar
Hartfiel, D.J. (1998) Markov Set-Chains. Springer, New York.CrossRefGoogle Scholar
Hartfiel, D.J. and Seneta, E. (1994) On the Theory of Markov-Set Chains. Advances in Applied Probability 26, 947–964.CrossRefGoogle Scholar
Lemaire, J. (1995) Bonus-Malus Systems in Automobile Insurance. Kluwer Academic Publishers, Boston.CrossRefGoogle Scholar