Time-consistent investment and consumption strategies under a general discount function - Ishak Alia; Farid Chighoub; Nabil Khelfallah; Josep Vives (Journal of Risk and Financial Management, 2021)
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: 330; equilibrium strategies; investment-consumption problem; Merton portfolio problem; non-exponential discounting; stochastic maximum principle; stochastic optimization; time inconsistency