Optimal Annuity Demand for General Expected Utility Agents

28 Pages Posted: 12 May 2020 Last revised: 7 Nov 2020

See all articles by Carole Bernard

Carole Bernard

Grenoble Ecole de Management; Vrije Universiteit Brussel (VUB)

Luca De Gennaro Aquino

Grenoble Ecole de Management

Lucia Levante

University of Rome I

Date Written: 2020

Abstract

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.

Keywords: Expected utility theory, annuity equivalent wealth, longevity risk pooling, life-cycle model, annuity puzzle

JEL Classification: D91, G11

Suggested Citation

Bernard, Carole and De Gennaro Aquino, Luca and Levante, Lucia, Optimal Annuity Demand for General Expected Utility Agents (2020). Insurance: Mathematics and Economics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3578370 or http://dx.doi.org/10.2139/ssrn.3578370

Carole Bernard

Grenoble Ecole de Management ( email )

12, rue Pierre Sémard
Grenoble Cedex, 38003
France

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
http://www.vub.ac.be/
Brussels, 1050
Belgium

Luca De Gennaro Aquino (Contact Author)

Grenoble Ecole de Management ( email )

12 Rue Pierre Semard
Grenoble, Cedex 01 38000
France

Lucia Levante

University of Rome I ( email )

Piazzale Aldo Moro 5
Roma, Rome 00185
Italy

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