English

Time-consistent investment and consumption strategies under a general discount function

Optimization and Control 2020-04-23 v2

Abstract

The paper [12] examines a concept of equilibrium policies instead of optimal controls in stochastic optimization to analyze a mean-variance portfolio selection problem. We follow the same approach in order to investigate the Merton portfolio management problem in the context of non-exponential discounting, a context that give rise to time-inconsistency of the decision maker. Equilibrium policies are characterized in this 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

Cite

@article{arxiv.1705.10602,
  title  = {Time-consistent investment and consumption strategies under a general discount function},
  author = {I. Alia and F. Chighoub and N. Khelfallah and J. Vives},
  journal= {arXiv preprint arXiv:1705.10602},
  year   = {2020}
}

Comments

28 pages. arXiv admin note: text overlap with arXiv:0901.2484, arXiv:0708.0588 by other authors

R2 v1 2026-06-22T20:03:27.150Z