Increases in Risk and the Optimal Deductible: ABSTRACT

Using Arrow's (1971, 1974) model of the optimal (endogenously determined) deductible, this article examines the impact of increases in risk (Rothschild-Stiglitz mean-preserving spreads and Diamond-Stiglitz mean-utility-preserving spreads) and first-order stochastic dominance shifts in the distribution function of losses on the optimal insurance contract between a risk-averse decision-maker and a risk-neutral insurer. In particular, it is found that a first-order stochastic dominance shift in the distribution of losses has generally an ambiguous impact on the deductible. This result raises some doubt about the asymmetric information (signalling) literature's identification of low (high) risk with smaller (greater) demand for insurance.