On the Equilibrium Strategies for Time-Inconsistent Problems in Continuous Time

51 Pages Posted: 10 Jan 2019 Last revised: 31 Jan 2019

See all articles by Xue Dong He

Xue Dong He

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management

Zhao Li Jiang

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering and Engineering Management

Date Written: January 30, 2019

Abstract

In a continuous-time setting, the existing notion of equilibrium strategies for time-inconsistent problems in the literature, referred to as weak equilibria, is not fully aligned with the standard definition of equilibria in the game theory in that the agent may be willing to deviate from a given weak equilibrium strategy. To address this issue, we propose two new notions of equilibrium strategies for time-inconsistent problems, named regular equilibria and strong equilibria. For a large class of time-inconsistent problems, we derive sufficient conditions as well as necessary conditions for a strategy to be a regular equilibrium and to be a strong equilibrium. We examine three time-inconsistent portfolio selection problems in the literature and show that the weak equilibrium strategies derived therein are also regular equilibria but are not strong equilibria. We further provide an example to show that a weak equilibrium strategy may not be a regular equilibrium. Our results suggest that the notion of regular equilibria is preferred in the study of time-inconsistent problems.

Keywords: stochastic control, time inconsistency, continuous-time setting, equilibrium strategies, portfolio selection

JEL Classification: C61, C73

Suggested Citation

He, Xue Dong and Jiang, Zhao Li, On the Equilibrium Strategies for Time-Inconsistent Problems in Continuous Time (January 30, 2019). Available at SSRN: https://ssrn.com/abstract=3308274 or http://dx.doi.org/10.2139/ssrn.3308274

Xue Dong He (Contact Author)

The Chinese University of Hong Kong - Department of Systems Engineering and Engineering Management ( email )

505 William M.W. Mong Engineering Building
The Chinese University of Hong Kong, Shatin, N.T.
Hong Kong
Hong Kong

HOME PAGE: http://https://sites.google.com/site/xuedonghepage/home

Zhao Li Jiang

The Chinese University of Hong Kong (CUHK) - Department of Systems Engineering and Engineering Management ( email )

Hong Kong
China

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