Hostname: page-component-7f64f4797f-n5rmq Total loading time: 0 Render date: 2025-11-04T15:28:03.211Z Has data issue: false hasContentIssue false
  • English
  • Français

Life Annuitization: Why and how Much?

Published online by Cambridge University Press:  17 April 2015

Donatien Hainaut  and
Pierre Devolder
Donatien Hainaut
Affiliation:
Université Catholique de Louvain, Institute of actuarial sciences, Rue des Wallons, 6 B-1348, Louvain-La-Neuve Belgium, E-mail: hainaut@actu.ucl.ac.be
Pierre Devolder
Affiliation:
Université Catholique de Louvain, Institute of actuarial sciences, Rue des Wallons, 6 B-1348, Louvain-La-Neuve Belgium, E-mail: devolder@actu.ucl.ac.be
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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 policiesannuity puzzleMarkov chain approximationstochastic control

Information

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 36 , Issue 2 , November 2006 , pp. 629 - 654
Copyright
Copyright © ASTIN Bulletin 2006

References

Blake, D., Cairns, A.J.G. and Dowd, K. (2003) PensionMetrics II: stochastic pension plan design during the distribution phase. Insurance: Mathematics and Economics 33(1), 29–47.Google Scholar
Davidoff, T., Brown, J. and Diamond, P. (2005) Annuities and individual welfare. American Economic Review 95(5), 1573–1590.CrossRefGoogle Scholar
Devolder, P., Bosch, P.M. and Dominguez, F.I. (2003) Stochastic optimal control of annuity contracts. Insurance: Mathematics and Economics 33(2), 227–238.Google Scholar
Devolder, P. and Hainaut, D. (2005) The annuity puzzle revisited: a deterministic version with Lagrangian methods. 15th annual international AFIR Colloquium, Zurich.Google Scholar
Fleming, W.H. and Rishel, R.W. (1975) Deterministic and stochastic control. Springer Verlag.CrossRefGoogle Scholar
Fleming, W.H. and Soner, H.M. (1993) Controlled Markov processes and viscosity solutions. Springer Verlag.Google Scholar
Kapur, S. and Orszag, M. (1999) A portfolio approach to investment and annuitization during retirement, Working paper Birkbeck College London.Google Scholar
Kushner, H.J. and Dupuis, P.G. (2001) Numerical methods for stochastic control problems in continuous time. Springer Verlag. Second edition.CrossRefGoogle Scholar
Lachance, M. (2003) Optimal investment behavior as retirement looms, Working paper, Wharton School, University of Pensylvania Philadelphia.Google Scholar
Merton, R.C. (1969) Lifetime portfolio selection under uncertainty: The continuous-time case. Review of Economics and Statistics 51, 247–257.CrossRefGoogle Scholar
Merton, R.C. (1971) Optimum consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3, 373–413.CrossRefGoogle Scholar
Merton, R.C. (1990) On consumption-indexed public pension plans, in Bodie, Z., Shoven, J. (eds.), Financial aspects of the US pension plan system, University of Chicago Press, Chicago, 1983. (Reprinted as chapter 18 of Merton, R.C. “Continuous time finance”, Blackwell, Cambridge, MA.Google Scholar
Milevsky, M. (2001) Optimal annuitization policies: analysis of the options. North American Actuarial Journal 5(1), 57–69.CrossRefGoogle Scholar
Milevsky, M. (1998) Optimal asset allocation towards the end of the life cycle: to annuitize or not to annuitize?. The Journal of Risk and Insurance 65(3), 401–426.CrossRefGoogle Scholar
Milevsky, M. and Young, V. (2003) Annuitization and Asset Allocation. Working paper. Individual Finance and Insurance Decisions Centre Toronto.Google Scholar
Petrova, P. (2004) The annuity puzzle gets bigger. Working paper Boston College.Google Scholar
Purcal, S. and Piggott, J. (2004) Explaining annuity demand in Japan: an optimising approach. 8th congress on insurance: Mathematics & Economics. Rome 2004.Google Scholar
Purcal, S. (2004) A stochastic control model for individual asset-liability management. 14th annual international AFIR Colloquium, Boston.Google Scholar
Richard, S. (1975) Optimal consumption, portfolio and life insurance rules for an uncertain lived individual in a continuous time model. The Journal of Financial Economics 2 187–203.CrossRefGoogle Scholar
Yaari, M. (1965) Uncertain Lifetime, Life Insurance and the theory of the Consumer. Review of Economics Studies 32(2), 137–150.CrossRefGoogle Scholar