In this paper we treat an individual's health as a continuous variable, in contrast to the traditional literature on income insurance, where it is assumed that the individual is either able or unable to work. A continuous treatment of an individual's health sheds new light on the role of income insurance and makes it possible to capture a number of real-world phenomena that are not easily captured in the traditional, dichotomous models. In particular, we show that moral hazard is not necessarily outright fraud, but a gradual adjustment of the willingness to work, depending on preferences and the conditions stated in the insurance contract. Further, the model can easily encompass phenomena such as administrative rejection of claims, and it clarifies the conditions for the desirability of insurance in the first place.