Risk Transformations, Deductibles, and Policy Limits

Rothschild and Stiglitz (1970, 1971) pioneered the study of how an increase in risk affects the demand for a risky asset. Gollier (1995) first identified a necessary and sufficient condition for unambiguous comparative statics for demand under transformations of the asset's probability distribution function. In this article, the authors examine the necessary and sufficient conditions for unambiguous comparative statics for insurance demand for coverage deductibles and policy limits, when the loss variable undergoes certain classes of transformations. The authors show that, if a transformation is both mean-preserving above (below) the optimal deductible (policy limit), and probability-preserving above (below) the optimal deductible (policy limit), then the necessary and sufficient condition is given by first-order stochastic dominance below (above) the optimal point.