Bonus-malus Systems as Markov Set-chains

Małgorzata Niemiec

ASTIN Bulletin, 2007, vol. 37, issue 1, 53-65

Abstract: 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.

Date: 2007
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