Bonus-malus system

In this paper, we compare bonus-malus systems to deductibles. Specifically, we design a system in which the policyholders in the malus zone are allowed to choose at each renewal between a premium surcharge(induced by relativities associated with the bonus-malus scale) or a deductible in case of a claim during the forthcoming year. If the deductible is selected, this induces a strong incentive to careful driving. According to signal theory, drivers opting for the deductible are expected to be better drivers(on average) than those paying the premium surcharge induced by the upward mode in the bonus-malus scale.