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Advancing annuity demand theory, we present sufficient conditions for the optimality of full annuitization under market completeness which are substantially less restrictive than those used by Menahem E. Yaari (1965). We examine demand with market incompleteness, finding that positive annuitization remains optimal widely, but complete annuitization does not. How uninsured medical expenses affect demand for illiquid annuities depends critically on the timing of the risk. A new set of calculations with optimal consumption trajectories very different from available annuity income streams still shows a preference for considerable annuitization, suggesting that limited annuity purchases are plausibly due to psychological or behavioral biases.

numerous seminar participants for helpful comments and discussions. We are especially grateful to Jim Robinson for generously sharing his data on long-term care utilization and for helpful discussions, and to Norma Coe for exceptional research assistance. We also thank Qian Deng and Chiao-Wen Lin for programming assistance.

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