People exercising mental accounting have an additional motive for buying insurance. They perceive a risk of having insufficient funds available to self-insure. In this way insurance protects the consumption value of the insured asset beyond the expenditure to acquire/replace it. This complements previous approaches based on probability weighting and loss aversion to explain the high profitability of warranties and an aversion toward deductibles. It helps to account for why the value of a warranty is found to be positively related to the value of the product and why there is seemingly contradictory empirical evidence on how household income affects demand for warranties. The adapted model rationalizes a strong aversion to deductibles, and explains the observed sensitivity of this aversion to the insurance context. Finally, it predicts a strong impact of how an insurer pays out benefits on the value and cost of insurance. This can explain both the evidence on strong deductible aversion for flood insurance and the lack of such evidence for long-term care insurance.