This article deals with demand for insurance under non-probabilized uncertainty: the available information allows only to locate the loss probability into a given interval. In this context, we apply a model, generalizing expected utility which involves, besides the standard utility function, a pessimism-optimism index representing the agent's attitude towards ambiguity. In this context, choices empirically observed, but impossible to explain with the vNM model, are enlightened: when the insurance premium is fair, risk averse agents can choose not to buy insurance, while with loaded premium, there are agents who buy full coverage. Choices of this type appear with both linear and non-linear contracts.
Keywords. demand for insurance, coinsurance, deductibles, ambiguity, imprecise probabilities
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