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The conventional wisdom since Yaari (1965) is that households without a bequest motive should fully annuitize their investments. Numerous frictions do not break this sharp result. We modify the Yaari framework by allowing a household's mortality risk itself to be stochastic due to health shocks. A lifetime annuity still helps to hedge longevity risk. But the annuity's remaining present value is correlated with medical costs, such as those for nursing home care, thereby reducing annuity demand, even without ad-hoc liquidity constraints. We find that most households should not hold a positive level of annuities, and many should hold negative amounts. (JEL D14, D82, G23, I12, J14, J26)
