Optimal Annuity Demand for General Expected Utility Agents

We study the robustness of the results of Milevsky and Huang (2018) on the optimal demand for annuities to the choice of the utility function. To do so, we first propose a new way to span the set of all increasing concave utility functions by exploiting a one-to-one correspondence with the set of probability distribution functions. For example, this approach makes it possible to present a five-parameter family of concave utility functions that encompasses a number of standard concave utility functions, e.g., CRRA, CARA and HARA. Second, we develop a novel numerical method to handle the life-cycle model of Yaari (1965) and the annuity equivalent wealth problem for a general utility function. We show that the results of Milevsky and Huang (2018) on the optimal demand for annuities proved in the case of a CRRA and logarithmic utility maximizer hold more generally.