In most of Europe and Asia annual automobile insurance is determined by the bonus malus system. Each policyholder is givena number (state) and the policy premium is determined as a function of this state. A policy holder's state changes from year to year in response to the number of claims made by the policy hol Suppose the number of dlaims made by a particular policyholder in any given year, is a Poisson random varia Let. s(k) be the next state of a policyholder who was in state i in the previous year and who made k claims in The following table is a simplified Bonus-Malus system having 4 states. Next state if Annual Premium State O claims 1 claim 2 claims 3 or more claims 1 200 1 3 4 250 1 3 4 4.

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