On compulsory per-claim deductibles in automobile insurance

The purposes of this paper are to analyze the theoretical characteristics of the compulsory deductible system and to verify the rationality of an increasing per-claim deductible in automobile insurance. We derive the optimal variable per-claim deductible by assuming the insurers are financially balanced and the expected utility of the insured is maximized in the absence of moral hazard. Our result suggests that a variable per-claim deductible increasing with the number of claims per year is not optimal. Instead, deductibles should be charged in a decreasing rate forming a second-best solution.