Simulation of an Automobile Portfolio

In 1971 all the Belgian companies introduced in automobile third party liability a compulsory merit-rating system. From the very first years of application, it appeared that the system was not well balanced, since the average collected premium constantly decreased, when the effects of inflation were removed. In 1976, for instance, a large company distributed 315 millions B.F. in bonus discounts, and collected only 2 millions of malus increases, so that the average reduction of the premium reached 27.9 %. As this figure increases from year to year, a simulation of the portfolio of the company was performed in order to forecast the future income of this branch and to evaluate the time necessary to reach stability.Of course the simulation presents many side advantages. For instance many results on bonus-malus systems are valid only asymptotically (Lemaire [5], Loimaranta [7],Vepsalhinen [8]). If these results are to be applied, for example to compare different systems, it is necessary to verify if the evolution of the portfolio quickly converges to a "practical equilibrium ". The idea of using simulation to study the variation of an insurance premium has already been used by Bohman [1].