IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v71y2016icp342-352.html
   My bibliography  Save this article

Asset allocation, sustainable withdrawal, longevity risk and non-exponential discounting

Author

Listed:
  • Delong, Łukasz
  • Chen, An

Abstract

The present paper studies an optimal withdrawal and investment problem for a retiree who is interested in sustaining her retirement consumption above a pre-specified minimum consumption level. Apparently, the withdrawal and investment policy depends substantially on the retiree’s health condition and her time preferences (subjective discount factor). We assume that the health of the retiree can worsen or improve in an unpredictable way over her lifetime and model the retiree’s mortality intensity by a stochastic process. In order to make the decision about the consumption and investment policy more realistic, we assume that the retiree applies a non-exponential discount factor (an exponential discount factor with a small amount of hyperbolic discounting) to value her future income. In other words, we consider an optimization problem by combining four important aspects: asset allocation, sustainable withdrawal, longevity risk and non-exponential discounting. Due to the non-exponential discount factor, we have to solve a time-inconsistent optimization problem. We derive a non-local HJB equation which characterizes the equilibrium optimal investment and consumption strategy. We establish the first-order expansions of the equilibrium value function and the equilibrium strategies by applying expansion techniques. The expansion is performed on the parameter controlling the degree of discounting in the hyperbolic discounting that is added to the exponential discount factors. The first-order equilibrium investment and consumption strategies can be calculated in a feasible way by solving PDEs.

Suggested Citation

  • Delong, Łukasz & Chen, An, 2016. "Asset allocation, sustainable withdrawal, longevity risk and non-exponential discounting," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 342-352.
  • Handle: RePEc:eee:insuma:v:71:y:2016:i:c:p:342-352
    DOI: 10.1016/j.insmatheco.2016.10.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668716301822
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Norberg, Ragnar, 2010. "Forward mortality and other vital rates -- Are they the way forward?," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 105-112, October.
    2. LUCIANO, Elisa & VIGNA, Elena, 2008. "Mortality risk via affine stochastic intensities: calibration and empirical relevance," MPRA Paper 59627, University Library of Munich, Germany.
    3. Erzo G. J. Luttmer & Thomas Mariotti, 2003. "Subjective Discounting in an Exchange Economy," Journal of Political Economy, University of Chicago Press, vol. 111(5), pages 959-989, October.
    4. repec:dau:papers:123456789/11473 is not listed on IDEAS
    5. Munk, Claus, 2008. "Portfolio and consumption choice with stochastic investment opportunities and habit formation in preferences," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3560-3589, November.
    6. Luciano, Elisa & Spreeuw, Jaap & Vigna, Elena, 2008. "Modelling stochastic mortality for dependent lives," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 234-244, October.
    7. George Loewenstein & Drazen Prelec, 1992. "Anomalies in Intertemporal Choice: Evidence and an Interpretation," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 573-597.
    8. Guambe, Calisto & Kufakunesu, Rodwell, 2015. "A note on optimal investment–consumption–insurance in a Lévy market," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 30-36.
    9. Menahem E. Yaari, 1965. "Uncertain Lifetime, Life Insurance, and the Theory of the Consumer," Review of Economic Studies, Oxford University Press, vol. 32(2), pages 137-150.
    10. Olivieri, Annamaria & Pitacco, Ermanno, 2009. "Stochastic Mortality: The Impact on Target Capital," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 39(02), pages 541-563, November.
    11. Huang, Huaxiong & Milevsky, Moshe A. & Salisbury, Thomas S., 2012. "Optimal retirement consumption with a stochastic force of mortality," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 282-291.
    12. Huaxiong Huang & Moshe A. Milevsky & Thomas S. Salisbury, 2012. "Optimal retirement consumption with a stochastic force of mortality," Papers 1205.2295, arXiv.org.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. repec:eee:dyncon:v:84:y:2017:i:c:p:58-76 is not listed on IDEAS

    More about this item

    Keywords

    Hyperbolic discounting; Time-inconsistent optimization problem; Non-local HJB equation; Equilibrium strategies; PDE;

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • G1 - Financial Economics - - General Financial Markets
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:71:y:2016:i:c:p:342-352. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.