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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)

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

  • Francesco Menoncin & Sergio Vergalli, 2019. "Optimal Stopping Time, Consumption, Labour, and Portfolio Decision for a Pension Scheme," Working Papers 2019.09, Fondazione Eni Enrico Mattei.
  • Handle: RePEc:fem:femwpa:2019.09
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    ptimal Stopping Time; Retirement Choice; Labour Supply; Asset Allocation; Mortality Risk;

    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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