## Optimal annuity demand for general expected utility agents.(English)Zbl 1475.91284

Summary: We study the robustness of the results of M. A. Milevsky and H. Huang [N. Am. Actuar. J. 22, No. 4, 574–590 (2018; Zbl 1411.91307)] 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 M. E. Yaari [“Uncertain lifetime, life insurance, and the theory of the consumer”, Rev. Econ. Stud. 32, No. 2, 137–150 (1965; doi:10.2307/2296058)] and the annuity equivalent wealth problem for a general utility function. We show that the results of Milevsky and Huang [loc. cit.] on the optimal demand for annuities proved in the case of a CRRA and logarithmic utility maximizer hold more generally.

### MSC:

 91G05 Actuarial mathematics 91B16 Utility theory

Zbl 1411.91307