On the Notions of Equilibria for Time-Inconsistent Stopping Problems in Continuous Time

2019 ◽  
Author(s):  
Erhan Bayraktar ◽  
Jingjie Zhang ◽  
Zhou Zhou
Keyword(s):  
Continuous Time ◽  
Time Inconsistent

scholarly journals Optimal equilibria for time‐inconsistent stopping problems in continuous time

2019 ◽  
Vol 30 (3) ◽  
pp. 1103-1134 ◽  
Author(s):  
Yu‐Jui Huang ◽  
Zhou Zhou
Keyword(s):  
Continuous Time ◽  
Time Inconsistent

scholarly journals On time-inconsistent stochastic control in continuous time

2017 ◽  
Vol 21 (2) ◽  
pp. 331-360 ◽  
Author(s):  
Tomas Björk ◽  
Mariana Khapko ◽  
Agatha Murgoci
Keyword(s):  
Stochastic Control ◽  
Continuous Time ◽  
Time Inconsistent

Time-Inconsistent Stopping in Continuous Time

2021 ◽  
pp. 255-278
Author(s):  
Tomas Björk ◽  
Mariana Khapko ◽  
Agatha Murgoci
Keyword(s):  
Continuous Time ◽  
Time Inconsistent

scholarly journals Strong and Weak Equilibria for Time-Inconsistent Stochastic Control in Continuous Time

2020 ◽  
Author(s):  
Yu-Jui Huang ◽  
Zhou Zhou
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Infinite Horizon ◽  
State Process ◽  
Economic Interpretation ◽  
Strong Equilibria ◽  
General Existence ◽  
Time Inconsistent ◽  
Definition Of ◽  
Two State Model

A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined and allows for unambiguous economic interpretation. The terms “strong equilibria” and “weak equilibria” are coined for controls under the new and standard definitions, respectively. When the state process is a time-homogeneous continuous-time Markov chain, a careful asymptotic analysis gives complete characterizations of weak and strong equilibria. Thanks to the Kakutani–Fan fixed-point theorem, the general existence of weak and strong equilibria is also established under an additional compactness assumption. Our theoretic results are applied to a two-state model under nonexponential discounting. In particular, we demonstrate explicitly that there can be incentive to deviate from a weak equilibrium, which justifies the need for strong equilibria. Our analysis also provides new results for the existence and characterization of discrete-time equilibria under infinite horizon.

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