On the Optimality of Deductibles with Heterogeneous Beliefs

Abstract

This article attempts to extend Arrow's theorem of the deductible to the case of belief heterogeneity, which allows the insured and the insurer to have different beliefs about the distribution of the underlying loss. Like Huberman et al. (1983), we preclude ex post moral hazard by asking both parties in the insurance contract to pay more for a larger realization of the loss. It is shown that, ceteris paribus, full insurance above a constant deductible is always optimal for any chosen utility function of a risk averse insured if and only if the insurer appears more optimistic about the conditional loss given non-zero loss than the insured in the sense of monotone hazard rate order. We derive the optimal deductible level explicitly, and then examine how it is affected by the changes of the insured's risk aversion, the insurance price and the degree of belief heterogeneity.