Abstract
Summary The introduction of a bonus-malus premium system in automobile insurance induces the insured drivers to defray the cost of the cheap claims themselves, in order to avoid any future increase in premiums. We analyse this “hunger for bonus” and use a dynamic programming algorithm to determine the optimal behaviour of Scandinavian, Swiss and German drivers, as a function of two parameters: the claim frequency and the discount factor. We then define an efficiency concept for a bonus-malus system and study the influence of the hunger for bonus on this notion.
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