Paper Info
Title
ON THE EQUILIBRIUM STRATEGIES FOR TIME-INCONSISTENT PROBLEMS IN CONTINUOUS TIME
Abstract
In a continuous-time setting, the existing notion of equilibrium strategies for time inconsistent problems in the literature, referred to as weak equilibrium, is not fully aligned with the standard definition of equilibrium in game theory in that the agent may be willing to deviate from a given weak equilibrium strategy. To address this issue, [Y.-J. Huang and Z. Zhou, Math. Oper. Res., 46 (2021), pp. 428-451] propose the notion of strong equilibrium for an infinite-time stochastic control problem in which an agent can control the generator of a time-homogeneous, continuous-time, finite-state Markov chain at each time. We study weak and strong equilibria in a general diffusion framework, provide necessary conditions for a strategy to be a strong equilibrium, and prove that strong equilibrium strategies do not exist for three investment and consumption problems. Finally, we propose a new notion of equilibrium strategies, referred to as regular equilibrium, show that it implies weak equilibrium, provide a sufficient condition under which a weak equilibrium strategy becomes a regular equilibrium, and show that this condition holds for many time-inconsistent problems.
Year
DOI
Venue
2021
10.1137/20M1382106
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Keywords
DocType
Volume
stochastic control, time-inconsistency, continuous-time setting, equilibrium strategies, portfolio selection
Journal
59
Issue
ISSN
Citations 
5
0363-0129
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Xue Dong He100.68
Zhaoli Jiang200.68