Comparing two Bonus-Malus Systems in a m-continuous years

A solution of moving between two Bonus-Malus systems is considered in this paper. Also it will be shown that a Bonus-Malus system how sensible to change level, claim count distribution and year of Bonus-Malus system in a m-continuous years. In this way, it will be shown which level of Bonus-Malus system1 is most suitable for policyholder wanting to move to Bonus-Malus system2 with exact level. In the new conclusion, roll of Bonus-Malus system will be more sensible. Others calculated suitable level just for one year when a Bonus-Malus systems get steady-state, but in the new approach, situation of m continues years are considered. Also the new approach will be obtained for Poisson-gamma, inflated Poisson-gamma, binomial-gamma and inflated binomial-gamma distribution under mean square error loss by using credibility.