Expected utility provides simple, testable properties of the optimum behaviour that should be displayed by risk-averse individuals in risky decisions. Simultaneously, given the existence of paradoxes under the expected utility paradigm, expected utility can only be regarded as an approximation of actual behaviour. A more realistic model is needed. This is particularly true when treating attitudes toward small probability events: the standard situation for insurable risks. This book examines whether the existing results in insurance economics are robust to more general models of behaviour under risk.