Background Risk, Demand for Insurance, and Choquet Expected Utility Preferences

This article deals with demand for insurance with a background risk in a nonprobabilized uncertainty framework, where preferences are represented by a nonadditive model of decision making. The Choquet expected utility model that we use generalizes expected utility and allows for a separation of the attitude towards uncertainty and the attitude towards wealth. When the insurable and the background risk are comonotone, the impact of the background risk on the demand for insurance is related to the attitude towards wealth. In contrast, when the two risks are anticomonotone, the attitude towards uncertainty is determinant. In this case, some of the resulting behaviors cannot be explained by the standard expected utility model.