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

Journal of Risk and Financial Management

Josep Vives¹  Nabil Khelfallah²  Ishak Alia²  Farid Chighoub² 

[1] Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain;Laboratory of Applied Mathematics, University Mohamed Khider, Po. Box 145, Biskra 07000, Algeria;

关键词: stochastic optimization;    investment-consumption problem;    Merton portfolio problem;    non-exponential discounting;    time inconsistency;    equilibrium strategies;   

DOI  :  10.3390/jrfm14020086

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown