Analysis of bonus systems in motor insurance
A continuous time Markov Chain model is proposed for the analysis of bonus systems in motor insurance which as a particular merit takes explicitly into account the effect of cancellation of policies. Most analysis of bonus systems treat these as "closed" systems while in reality they are very "open" systems with a considerable change of the portfolio within one year. Relating to Danish experiences there is a yearly number of cancellations (excluding lapses i.e. failure to renew) corresponding to 15-20% of the portfolios and a level of new business of approximately the same size making the real changes of the portfolios rather small.