STATISTICAL APPROACH FOR OPEN BONUS MALUS

In this paper, following an open portfolio approach, we show how to estimate a Bonus-malus system evolution. Considering a model for the number of new annual policies, we obtain ML estimators, asymptotic distributions and confidence regions for the expected number of new policies entering the portfolio in each year, as well as for the expected number and proportion of insureds in each bonus class, by year of enrollment. Confidence regions for the distribution of policyholders result in confidence regions for optimal bonus scales. Our treatment is illustrated by an example with numerical results.