Life Annuitization: Why and How Much?

ASTIN Bulletin, Vol 36(2), 2006, p. 629-654

23 Pages Posted: 22 Oct 2013

See all articles by Donatien Hainaut

Donatien Hainaut

Université Catholique de Louvain

Pierre Devolder

Catholic University of Louvain

Date Written: October 22, 2013

Abstract

This paper addresses some of the problems a majority of retired individuals face: Why and in what proportion should they invest in a life annuity to maximize the utility of their future consumption or a bequest? The market considered in this work is made up of three assets: a life annuity, a risky asset and a cash account. As this problem doesn't accept any suitable explicit solution, it is numerically solved by the Markov Chain approximation developed by Kushner and Dupuis. Without a bequest motive, we observe that the optimal planning of consumption is divided into two periods and that optimal asset allocation should include the risky asset. Next, the influence of a bequest on consumption and investment pattern is developed. We demonstrate that even with a bequest motive, pensioners should allocate a part of their wealth to the purchase of life annuities.

Keywords: optimal consumption and portfolio policies, annuity puzzle, Markov chain approximation, stochastic control, annuity puzzle

JEL Classification: C61

Suggested Citation

Hainaut, Donatien and Devolder, Pierre, Life Annuitization: Why and How Much? (October 22, 2013). ASTIN Bulletin, Vol 36(2), 2006, p. 629-654, Available at SSRN: https://ssrn.com/abstract=2343529

Donatien Hainaut (Contact Author)

Université Catholique de Louvain ( email )

Voie du Roman Pays 20,
Louvain La Neuve, 1348
Belgium

Pierre Devolder

Catholic University of Louvain ( email )

Place Montesquieu, 3
B-1348 Louvain-la-Neuve, 1348
Belgium

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