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

Ishak Alia (), Farid Chighoub (), Nabil Khelfallah () and Josep Vives ()
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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

Journal of Risk and Financial Management, 2021, vol. 14, issue 2, 1-27

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.

Keywords: stochastic optimization; investment-consumption problem; Merton portfolio problem; non-exponential discounting; time inconsistency; equilibrium strategies; stochastic maximum principle (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2021
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