IDEAS home Printed from https://ideas.repec.org/p/ags/feemth/288459.html
   My bibliography  Save this paper

Optimal Stopping Time, Consumption, Labour, and Portfolio Decision for a Pension Scheme

Author

Listed:
  • Menoncin, Francesco
  • Vergalli, Sergio

Abstract

In this work we solve in a closed form the problem of an agent who wants to optimise the inter-temporal utility of both his consumption and leisure by choosing: (i) the optimal inter-temporal consumption, (ii) the optimal inter-temporal labour supply, (iii) the optimal share of wealth to invest in a risky asset, and (iv) 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. The martingale method is used for the first problem, and it allows to solve it for any value of the stopping time which is just considered as a stochastic variable. The problem of the agent is solved by assuming that after retirement he received a utility that is proportional to the remaining human capital. Finally, a numerical simulation is presented for showing the behaviour over time of the optimal solution.

Suggested Citation

  • Menoncin, Francesco & Vergalli, Sergio, 2019. "Optimal Stopping Time, Consumption, Labour, and Portfolio Decision for a Pension Scheme," ETA: Economic Theory and Applications 288459, Fondazione Eni Enrico Mattei (FEEM).
  • Handle: RePEc:ags:feemth:288459
    DOI: 10.22004/ag.econ.288459
    as

    Download full text from publisher

    File URL: https://ageconsearch.umn.edu/record/288459/files/NDL2019-009.pdf
    Download Restriction: no

    File URL: https://libkey.io/10.22004/ag.econ.288459?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. 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.
    2. Marco Magnani, 2020. "Precautionary retirement and precautionary saving," Journal of Economics, Springer, vol. 129(1), pages 49-77, January.
    3. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474, April.
    4. Menoncin, Francesco, 2008. "The role of longevity bonds in optimal portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 343-358, February.
    5. 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.
    6. Vasily Astrov & Mario Holzner & Sebastian Leitner & Isilda Mara & Leon Podkaminer & Armon Rezai, 2018. "Die Lohnentwicklung in den mittel- und osteuropäischen Mitgliedsländern der EU," wiiw Research Reports in German language 12, The Vienna Institute for International Economic Studies, wiiw.
    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. 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.
    9. Brugiavini, Agar, 1993. "Uncertainty resolution and the timing of annuity purchases," Journal of Public Economics, Elsevier, vol. 50(1), pages 31-62, January.
    10. 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.
    11. 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.
    12. 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.
    13. Benjamin M. Friedman & Mark J. Warshawsky, 1990. "The Cost of Annuities: Implications for Saving Behavior and Bequests," The Quarterly Journal of Economics, Oxford University Press, vol. 105(1), pages 135-154.
    14. Martin Feldstein & Horst Siebert, 2002. "Social Security Pension Reform in Europe," NBER Books, National Bureau of Economic Research, Inc, number feld02-2, May.
    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. Moshe A. Milevsky & Virginia R. Young, 2015. "Annuitization and asset allocation," Papers 1506.05990, arXiv.org.
    2. Kam Ki Tang & Jie Zhang, 2007. "Morbidity, Mortality, Health Expenditures and Annuitization," CESifo Working Paper Series 2086, CESifo.
    3. 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.
    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. 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. Hugo Benítez-Silva, 2003. "The Annuity Puzzle Revisited," Working Papers wp055, University of Michigan, Michigan Retirement Research Center.
    7. Amy Finkelstein & James Poterba, 2004. "Adverse Selection in Insurance Markets: Policyholder Evidence from the U.K. Annuity Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 183-208, February.
    8. Steinorth, Petra, 2012. "The demand for enhanced annuities," Journal of Public Economics, Elsevier, vol. 96(11), pages 973-980.
    9. Park, Seyoung, 2015. "A generalization of Yaari’s result on annuitization with optimal retirement," Economics Letters, Elsevier, vol. 137(C), pages 17-20.
    10. Amy Finkelstein & James Poterba, 2002. "Selection Effects in the United Kingdom Individual Annuities Market," Economic Journal, Royal Economic Society, vol. 112(476), pages 28-50, January.
    11. 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.
    12. Yogo, Motohiro, 2016. "Portfolio choice in retirement: Health risk and the demand for annuities, housing, and risky assets," Journal of Monetary Economics, Elsevier, vol. 80(C), pages 17-34.
    13. Tom Krebs & Moritz Kuhn & Mark L. J. Wright, 2015. "Human Capital Risk, Contract Enforcement, and the Macroeconomy," American Economic Review, American Economic Association, vol. 105(11), pages 3223-3272, November.
    14. 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.
    15. Ankush Agarwal & Christian-Oliver Ewald & Yongjie Wang, 2020. "Sharing of longevity basis risk in pension schemes with income-drawdown guarantees," Working Papers 2020_18, Business School - Economics, University of Glasgow.
    16. Gomes, Francisco J & Haliassos, Michael & Ramadorai, Tarun, 2020. "Household Finance," CEPR Discussion Papers 14502, C.E.P.R. Discussion Papers.
    17. William M. Gentry & Joseph Milano, 1998. "Taxes and Investment in Annuities," NBER Working Papers 6525, National Bureau of Economic Research, Inc.
    18. Jeffrey R. Brown & Mark J. Warshawsky, 2001. "Longevity-Insured Retirement Distributions from Pension Plans: Market and Regulatory Issues," NBER Working Papers 8064, National Bureau of Economic Research, Inc.
    19. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    20. Horneff, Vanya & Kaschãœtzke, Barbara & Maurer, Raimond & Rogalla, Ralph, 2014. "Welfare implications of product choice regulation during the payout phase of funded pensions," Journal of Pension Economics and Finance, Cambridge University Press, vol. 13(3), pages 272-296, July.

    More about this item

    Keywords

    Research Methods/ Statistical Methods;

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ags:feemth:288459. 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: . General contact details of provider: https://edirc.repec.org/data/feemmit.html .

    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: AgEcon Search (email available below). General contact details of provider: https://edirc.repec.org/data/feemmit.html .

    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.