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

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  • 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
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    1. 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.
    2. 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.
    3. Marco Magnani, 2020. "Precautionary retirement and precautionary saving," Journal of Economics, Springer, vol. 129(1), pages 49-77, January.
    4. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    5. Menoncin, Francesco, 2008. "The role of longevity bonds in optimal portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 343-358, February.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Duffie, Darrell & Epstein, Larry G, 1992. "Stochastic Differential Utility," Econometrica, Econometric Society, vol. 60(2), pages 353-394, March.
    11. 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.
    12. Brugiavini, Agar, 1993. "Uncertainty resolution and the timing of annuity purchases," Journal of Public Economics, Elsevier, vol. 50(1), pages 31-62, January.
    13. 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.
    14. 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.
    15. 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.
    16. Peter A. Diamond & Peter R. Orszag, 2005. "Saving Social Security," Journal of Economic Perspectives, American Economic Association, vol. 19(2), pages 11-32, Spring.
    17. 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.
    18. Duffie, Darrell & Epstein, Larry G, 1992. "Asset Pricing with Stochastic Differential Utility," The Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 411-436.
    19. 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.
    20. Rob Rusconi, 2008. "National Annuity Markets: Features and Implications," OECD Working Papers on Insurance and Private Pensions 24, OECD Publishing.
    21. 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.
    22. Martin Feldstein & Horst Siebert, 2002. "Social Security Pension Reform in Europe," NBER Books, National Bureau of Economic Research, Inc, number feld02-2, June.
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    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

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