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Time-Consistent Investment and Consumption Strategies under a General Discount Function

Author

Listed:
  • Ishak Alia

    (Laboratory of Applied Mathematics, University Mohamed Khider, P.O. Box 145, Biskra 07000, Algeria)

  • Farid Chighoub

    (Laboratory of Applied Mathematics, University Mohamed Khider, P.O. Box 145, Biskra 07000, Algeria)

  • Nabil Khelfallah

    (Laboratory of Applied Mathematics, University Mohamed Khider, P.O. Box 145, Biskra 07000, Algeria)

  • Josep Vives

    (Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain)

Abstract

In the present paper, we investigate the Merton portfolio management problem in the context of non-exponential discounting, a context that gives rise to time-inconsistency of the decision-maker. We consider equilibrium policies within the class of open-loop controls that are characterized, in our context, by means of a variational method which leads to a stochastic system that consists of a flow of forward-backward stochastic differential equations and an equilibrium condition. An explicit representation of the equilibrium policies is provided for the special cases of power, logarithmic and exponential utility functions.

Suggested Citation

  • Ishak Alia & Farid Chighoub & Nabil Khelfallah & Josep Vives, 2021. "Time-Consistent Investment and Consumption Strategies under a General Discount Function," JRFM, MDPI, vol. 14(2), pages 1-27, February.
    • Handle: RePEc:gam:jjrfmx:v:14:y:2021:i:2:p:86-:d:502548
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    References listed on IDEAS

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