• Corpus ID: 246035481

Equilibria of Time-inconsistent Stopping for One-dimensional Diffusion Processes

  title={Equilibria of Time-inconsistent Stopping for One-dimensional Diffusion Processes},
  author={Erhan Bayraktar and Zhenhua Wang and Zhou Zhou},
We consider three equilibrium concepts proposed in the literature for time-inconsistent stopping problems, including mild equilibria (introduced in [7]), weak equilibria (introduced in [4]) and strong equilibria (introduced in [1]). The discount function is assumed to be log sub-additive and the underlying process is one-dimensional diffusion. We first provide necessary and sufficient conditions for the characterization of weak equilibria. The smooth-fit condition is obtained as a by-product… 

Stability of Time-inconsistent Stopping for One-dimensional Diffusion

We investigate the stability of the equilibrium-induced optimal value in one-dimensional diffusion setting for a time-inconsistent stopping problem under non-exponential discounting. We show that the

Local time pushed mixed stopping and smooth fit for time-inconsistent stopping problems

We consider the game-theoretic approach to time-inconsistent stopping of a one-dimensional diffusion where the time-inconsistency is due to the presence of a non-exponential (weighted) discount

Stability of Equilibria in Time-inconsistent Stopping Problems

We investigate the stability of equilibrium-induced optimal values with respect to (w.r.t.) reward functions f and transition kernels Q for time-inconsistent stopping problems under nonexponential



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

It is demonstrated explicitly that there can be incentive to deviate from a weak equilibrium, which justifies the need for strong equilibria, and theoretic results are applied to a two-state model under non-exponential discounting.

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

  • X. HeZ. Jiang
  • Economics
    SIAM Journal on Control and Optimization
  • 2021
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

Equilibrium concepts for time-inconsistent stopping problems in continuous time

A \emph{new} notion of equilibrium, which we call \emph{strong equilibrium}, is introduced for time-inconsistent stopping problems in continuous time. Compared to the existing notions introduced in

Optimal equilibria for time‐inconsistent stopping problems in continuous time

For an infinite‐horizon continuous‐time optimal stopping problem under nonexponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on

Weak equilibriums for time-inconsistent stopping control problems, with applications to investment-withdrawal decision model

This paper studies time-inconsistent stopping control problems under general multidimensional controlled diffusion model. We first formulate the time-inconsistent stopping control problems and

Optimal Equilibria for Multidimensional Time-Inconsistent Stopping Problems

We study an optimal stopping problem under non-exponential discounting, where the state process is a multi-dimensional continuous strong Markov process. The discount function is taken to be log

On Finding Equilibrium Stopping Times for Time-Inconsistent Markovian Problems

This paper develops an iterative approach to finding such equilibrium stopping times for a general class of problems and applies this approach to one-sided stopping problems on the real line and proves a verification theorem based on a set of variational inequalities which also allows to find equilibria.

On time-inconsistent stopping problems and mixed strategy stopping times

General stopping behaviors of naïve and noncommitted sophisticated agents, with application to probability distortion

It is proved that any equilibrium can be obtained as a fixed point of an operator that takes the future selves' behaviors into account when the state process is one dimensional and the payoff functional satisfies some regularity conditions.

On time-inconsistent stochastic control in continuous time

This paper studies a class of continuous-time stochastic control problems which are time-inconsistent in the sense that they do not admit a Bellman optimality principle, and derives an extension of the standard Hamilton–Jacobi–Bellman equation in the form of a system of nonlinear equations for the determination of the equilibrium strategy as well as the equilibrium value function.