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

@inproceedings{Bayraktar2022EquilibriaOT, title={Equilibria of Time-inconsistent Stopping for One-dimensional Diffusion Processes}, author={Erhan Bayraktar and Zhenhua Wang and Zhou Zhou}, year={2022} }

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…

## 3 Citations

### Stability of Time-inconsistent Stopping for One-dimensional Diffusion

- Economics
- 2022

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

- Mathematics, Economics
- 2022

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

- Mathematics
- 2022

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…

## References

SHOWING 1-10 OF 18 REFERENCES

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

- EconomicsMath. Oper. Res.
- 2021

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

- EconomicsSIAM 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

- EconomicsSSRN Electronic Journal
- 2019

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

- EconomicsMathematical Finance
- 2019

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

- Mathematics, Economics
- 2021

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

- EconomicsSIAM J. Control. Optim.
- 2021

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

- EconomicsSIAM J. Control. Optim.
- 2018

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

- MathematicsStochastic Processes and their Applications
- 2020

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

- MathematicsMathematical Finance
- 2019

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

- Economics, MathematicsFinance Stochastics
- 2017

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.