Open Approach to Bonus Malus

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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. With the obtained Long Run Distribution, a few optimal bonus scales were calculated, such as Norberg’s [1979], Borgan, Hoem’s & Norberg’s [1981], Gilde & Sundt’s [1989] and Andrade e Silva’s [1991].To compare our results, since this was the first application of the model to a Bonus Malus System, we used the Classic Model for Bonus Malus and the Open Model developed by Centeno & Andrade e Silva [2001]. The results of the Stochastic Vortices and the Open Model are highly similar and quite different from those of the Classic Model.
Original languageEnglish
Pages (from-to)41-51
Number of pages11
JournalBoletim do Instituto dos Actuários Portugueses
Publication statusPublished - 2003


  • Bonus Malus
  • Stochastic Vortices
  • Long Run Distribution
  • Optimal Bonus Scales


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