Geodesic
An alternative approach to bonus malus
Discussiones Mathematicae. Probability and Statistics, Tome 24 (2004) no. 2, pp. 197-213

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Under the assumptions of an open portfolio, i.e., considering that a policyholder can transfer his policy to another insurance company and the continuous arrival of new policyholders into a portfolio which can be placed into any of the bonus classes and not only in the "starting class", we developed a model (Stochastic Vortices Model) to estimate the Long Run Distribution for a Bonus Malus System. These hypothesis render the model quite representative of the reality.
Keywords: bonus malus, stochastic vortices, long run distribution, optimal bonus scales 
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Guerreiro, Gracinda; Mexia, João. An alternative approach to bonus malus. Discussiones Mathematicae. Probability and Statistics, Tome 24 (2004) no. 2, pp. 197-213. http://geodesic.mathdoc.fr/item/DMPS_2004_24_2_a2/