This paper considers the question of why the annuity market is thin. A model is presented in which consumers have the option of purchasing annuities before discovering their survival probability; they can then recontract the initial choice after the resolution of this form of uncertainty. It is shown that consumers purchase insurance against their own survival-probability type at a very young age and do not undertake further transactions. This characterization is then used to analze the effects of introducing future income uncertainty and to investigate the trade-off between old age insurance motive and portfilio flexibility.