Increases in Risk and the Optimal Deductible

Arrow's (1971, 1974) model of the optimal (endogenously determined) deductible is used to analyze the impact of increased riskiness of loss on the optimal insurance contract between a risk-averse decision maker and a risk-neutral insurer. The impact of Rothschild-Stiglitz (1971) mean-preserving spreads, Diamond-Stiglitz (1974) mean-utility-preserving spreads, and a shift in loss distribution in the sense of first-order stochastic dominance are examined. In each case, the comparative statics effects of increases in risk are shown to be related to the degree of risk aversion of the insured agent. 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.