Optimal insurance without expected utility: The dual theory and the linearity of insurance contracts

Abstract

Models of the insurance markets and institutions are routinely based on expected utility. Since EU is being challenged by an increasing number of decision models, we examine whether EU-based models are robust in their predictions. To do so, we rework some basic models of optimal insurance contracts and equilibrium using the “dual” theory to EU of Yaari. When there is a single, insurable source of risk, dual theory permits only corner solutions if the contract itself is linear. This contrasts sharply with EU. Nonlinearity, and thereby the possibility of interior solutions, is introduced in two ways. First, the contract itself is nonlinear, i.e., a deductible insurance policy. Or second, the decision maker is subject to some background risk such as uninsurable risky assets or default of the insurer. When decision problems are subject to nonlinearity, the predictions on optimal insurance are more similar to, though not identical with, those generated with EU.