The selection of a deductible level in insurance is governed by the willingness to limit the risk borne by risk-averse agents at an acceptable cost, given the deadweight insurance loading. We examine the demand for insurance in a simple lifecycle model with a liquidity constraint and no serial correlation in the insurable risk. This allows for consumers to follow a time-diversification (self-insurance) strategy by accumulating buffer stock wealth. We conclude that insurance would only be demanded for catastrophic risks, or by people that are currently liquidity constrained. The added value of the insurance sector is thus surprisingly low in such an economy.