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Optimal consumption and portfolio choice of retirees with longevity risk*

Published online by Cambridge University Press:  10 October 2013

ALEXANDER KREMER ,
FRIEDRICH LIESE ,
SUSANNE HOMÖLLE  and
JOHANN CLAUSEN
ALEXANDER KREMER
Affiliation:
Chair for Statistics, University of Rostock
FRIEDRICH LIESE
Affiliation:
Department of Mathematics, University of Rostock
SUSANNE HOMÖLLE*
Affiliation:
Chair of Banking and Finance, University of Rostock
JOHANN CLAUSEN
Affiliation:
Hamburg
*
(e-mail: [email protected])
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Abstract

The question how to optimize consumption and portfolio choice over the life cycle has been widely discussed in the literature so far. In this paper we concentrate on a retiree's optimal consumption and portfolio selection over his remaining years of life. We apply the logistic model of mortality thus modeling the empirically observed increase of mortality during the retirement period. The optimal consumption strategy and portfolio choice are established by reducing the Hamilton-Jacobi-Bellmann equation to the explicit solution of an ordinary differential function (ODF) that includes the mortality rate. A general finding is that the Merton-Samuelson result of constant portfolio choice for a constant mortality is confirmed for arbitrary mortality. The portfolio choice is only influenced by risk and return of assets and the retirees’ risk aversion. To get the specific optimal consumption strategy in a realistic situation the logistic model of mortality has been fitted to the data of the Statistical Yearbook for the Federal Republic of Germany 2006/2008. The optimal initial value for the ODF is obtained by numerical methods. The solution provides a large increase in the ratio of optimal consumption to wealth up to about 92 years followed by a sharp decrease. A bequest motive dampens the magnitudes of the ups and downs of the consumption ratio but does not change the basic shape.

Keywords

G11 (JEL)retirement periodmortalitylife time distributionasset allocation
Type
Articles
Information
Journal of Pension Economics & Finance , Volume 13 , Issue 3 , July 2014 , pp. 227 - 249
Copyright
Copyright © Cambridge University Press 2013 

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Footnotes

*

An earlier version of this paper was presented at the Annual Conference of the Swiss Society for Financial Market Research in Zurich. We thank the participants of these meeting, especially Alexandra Dias, and Roland Rau for many helpful comments. We are deeply indebted to an anonymous referee for providing valuable comments that led to a considerable improvement of the paper.

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