IDEAS home Printed from https://ideas.repec.org/a/kap/jeczfn/v132y2021i1d10.1007_s00712-020-00710-y.html
   My bibliography  Save this article

Optimal stopping time, consumption, labour, and portfolio decision for a pension scheme

Author

Listed:
  • Francesco Menoncin

    (Università degli Studi di Brescia)

  • Sergio Vergalli

    (Università degli Studi di Brescia
    Fondazione Eni Enrico Mattei, FEEM)

Abstract

In this work we solve in a closed form the problem of an agent who wants to optimise the inter-temporal recursive utility of both his consumption and leisure by choosing: (1) the optimal inter-temporal consumption, (2) the optimal inter-temporal labour supply, (3) the optimal share of wealth to invest in a risky asset, and (4) the optimal retirement age. The wage of the agent is assumed to be stochastic and correlated with the risky asset on the financial market. The problem is split into two sub-problems: the optimal consumption, labour, and portfolio problem is solved first, and then the optimal stopping time is approached. We compute the solution through both the so-called martingale approach and the solution of the Hamilton–Jacobi–Bellman partial differential equation. In the numerical simulations we compare two cases, with and without the opportunity, for the agent, to work after retirement, at a lower wage rate.

Suggested Citation

  • Francesco Menoncin & Sergio Vergalli, 2021. "Optimal stopping time, consumption, labour, and portfolio decision for a pension scheme," Journal of Economics, Springer, vol. 132(1), pages 67-98, January.
    • Handle: RePEc:kap:jeczfn:v:132:y:2021:i:1:d:10.1007_s00712-020-00710-y
    DOI: 10.1007/s00712-020-00710-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00712-020-00710-y
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s00712-020-00710-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Martin Feldstein & Andrew Samwick, 2002. "Potential Paths of Social Security Reform," NBER Chapters, in: Tax Policy and the Economy, Volume 16, pages 181-224, National Bureau of Economic Research, Inc.
    2. Marina Di Giacinto & Salvatore Federico & Fausto Gozzi, 2011. "Pension funds with a minimum guarantee: a stochastic control approach," Finance and Stochastics, Springer, vol. 15(2), pages 297-342, June.
    3. Jeffrey Brown, 2001. "Are the Elderly Really Over-Annuitized? New Evidence on Life Insurance and Bequests," NBER Chapters, in: Themes in the Economics of Aging, pages 91-126, National Bureau of Economic Research, Inc.
    4. Hugo Benitez-Silva, 2000. "A Dynamic Model of Labor Supply, Consumption/Saving, and Annuity Decisions under Uncertainty," Department of Economics Working Papers 00-06, Stony Brook University, Department of Economics.
    5. Bodie, Zvi & Merton, Robert C. & Samuelson, William F., 1992. "Labor supply flexibility and portfolio choice in a life cycle model," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 427-449.
    6. Rob Rusconi, 2008. "National Annuity Markets: Features and Implications," OECD Working Papers on Insurance and Private Pensions 24, OECD Publishing.
    7. Kotlikoff, Laurence J & Spivak, Avia, 1981. "The Family as an Incomplete Annuities Market," Journal of Political Economy, University of Chicago Press, vol. 89(2), pages 372-391, April.
    8. Michel Denuit & Pierre Devolder & Anne‐Cécile Goderniaux, 2007. "Securitization of Longevity Risk: Pricing Survivor Bonds With Wang Transform in the Lee‐Carter Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(1), pages 87-113, March.
    9. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    10. Brugiavini, Agar, 1993. "Uncertainty resolution and the timing of annuity purchases," Journal of Public Economics, Elsevier, vol. 50(1), pages 31-62, January.
    11. Vasily Astrov & Mario Holzner & Sebastian Leitner & Isilda Mara & Leon Podkaminer & Armon Rezai, 2018. "Die Lohnentwicklung in den mittel- und osteuropäischen Mitgliedsländern der EU," Working Paper Reihe der AK Wien - Materialien zu Wirtschaft und Gesellschaft 178, Kammer für Arbeiter und Angestellte für Wien, Abteilung Wirtschaftswissenschaft und Statistik.
    12. Martin Feldstein & Horst Siebert, 2002. "Social Security Pension Reform in Europe," NBER Books, National Bureau of Economic Research, Inc, number feld02-2, March.
    13. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    14. Menoncin, Francesco, 2008. "The role of longevity bonds in optimal portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 343-358, February.
    15. Pirvu, Traian A. & Zhang, Huayue, 2012. "Optimal investment, consumption and life insurance under mean-reverting returns: The complete market solution," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 303-309.
    16. Farhi, Emmanuel & Panageas, Stavros, 2007. "Saving and investing for early retirement: A theoretical analysis," Journal of Financial Economics, Elsevier, vol. 83(1), pages 87-121, January.
    17. Benjamin M. Friedman & Mark J. Warshawsky, 1990. "The Cost of Annuities: Implications for Saving Behavior and Bequests," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 105(1), pages 135-154.
    18. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    19. Marco Magnani, 2020. "Precautionary retirement and precautionary saving," Journal of Economics, Springer, vol. 129(1), pages 49-77, January.
    20. Menoncin, Francesco & Regis, Luca, 2017. "Longevity-linked assets and pre-retirement consumption/portfolio decisions," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 75-86.
    21. Peter A. Diamond & Peter R. Orszag, 2005. "Saving Social Security," Journal of Economic Perspectives, American Economic Association, vol. 19(2), pages 11-32, Spring.
    22. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Milevsky, Moshe A. & Young, Virginia R., 2007. "Annuitization and asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 31(9), pages 3138-3177, September.
    2. Hugo Benitez-Silva, 2000. "A Dynamic Model Of Labor Supply, Consumption/Saving, And Annuity Decisions Under Uncertainty," Computing in Economics and Finance 2000 128, Society for Computational Economics.
    3. Hugo Benítez-Silva, 2003. "The Annuity Puzzle Revisited," Working Papers wp055, University of Michigan, Michigan Retirement Research Center.
    4. Castañeda, Pablo & Reus, Lorenzo, 2019. "Suboptimal investment behavior and welfare costs: A simulation based approach," Finance Research Letters, Elsevier, vol. 30(C), pages 170-180.
    5. Hugo Benitez-Silva, 2000. "A Joint Model of Labor Supply and Consumption Decisions Under Uncertainty," Econometric Society World Congress 2000 Contributed Papers 0196, Econometric Society.
    6. Francesco Menoncin & Luca Regis, 2015. "Longevity assets and pre-retirement consumption/portfolio decisions," Working Papers 2/2015, IMT School for Advanced Studies Lucca, revised May 2015.
    7. Menoncin, Francesco & Regis, Luca, 2017. "Longevity-linked assets and pre-retirement consumption/portfolio decisions," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 75-86.
    8. Kaschützke, B. & Maurer, R., 2016. "Investing and Portfolio Allocation for Retirement," Handbook of the Economics of Population Aging, in: Piggott, John & Woodland, Alan (ed.), Handbook of the Economics of Population Aging, edition 1, volume 1, chapter 0, pages 567-608, Elsevier.
    9. Brown, Jeffrey R., 2001. "Private pensions, mortality risk, and the decision to annuitize," Journal of Public Economics, Elsevier, vol. 82(1), pages 29-62, October.
    10. Park, Kyunghyun & Wong, Hoi Ying & Yan, Tingjin, 2023. "Robust retirement and life insurance with inflation risk and model ambiguity," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 1-30.
    11. Andrew Ang & Dimitris Papanikolaou & Mark M. Westerfield, 2014. "Portfolio Choice with Illiquid Assets," Management Science, INFORMS, vol. 60(11), pages 2737-2761, November.
    12. Francisco Gomes & Michael Haliassos & Tarun Ramadorai, 2021. "Household Finance," Journal of Economic Literature, American Economic Association, vol. 59(3), pages 919-1000, September.
    13. William M. Gentry & Joseph Milano, 1998. "Taxes and Investment in Annuities," NBER Working Papers 6525, National Bureau of Economic Research, Inc.
    14. Jeon, Junkee & Park, Kyunghyun, 2023. "Optimal job switching and retirement decision," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    15. van den Bremer, Ton & van der Ploeg, Frederick & Wills, Samuel, 2016. "The Elephant In The Ground: Managing Oil And Sovereign Wealth," European Economic Review, Elsevier, vol. 82(C), pages 113-131.
    16. Olivia S. Mitchell, 1999. "New Evidence on the Money's Worth of Individual Annuities," American Economic Review, American Economic Association, vol. 89(5), pages 1299-1318, December.
    17. Gabay, Daniel & Grasselli, Martino, 2012. "Fair demographic risk sharing in defined contribution pension systems," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 657-669.
    18. Beetsma, R. & Romp, W., 2016. "Intergenerational Risk Sharing," Handbook of the Economics of Population Aging, in: Piggott, John & Woodland, Alan (ed.), Handbook of the Economics of Population Aging, edition 1, volume 1, chapter 0, pages 311-380, Elsevier.
    19. Doriana Ruffino, 2014. "Resuscitating Businessman Risk: A Rationale for Familiarity-Based Portfolios," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(1), pages 107-130, January.
    20. Schroder, Mark & Skiadas, Costis, 2005. "Lifetime consumption-portfolio choice under trading constraints, recursive preferences, and nontradeable income," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 1-30, January.

    More about this item

    Keywords

    Optimal Stopping Time; Retirement Choice; Labour Supply; Asset Allocation; Mortality Risk;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • J22 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Time Allocation and Labor Supply

    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:kap:jeczfn:v:132:y:2021:i:1:d:10.1007_s00712-020-00710-y. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.