Stability of Time-inconsistent Stopping for One-dimensional Diffusion -- A Longer Version
Probability
2022-10-04 v2 Optimization and Control
Abstract
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 optimal value is semi-continuous with respect to the drift, volatility, and reward function. An example is provided showing that the exact continuity may fail. With equilibria extended to -equilibria, we establish the relaxed continuity of the optimal value.
Cite
@article{arxiv.2207.08158,
title = {Stability of Time-inconsistent Stopping for One-dimensional Diffusion -- A Longer Version},
author = {Erhan Bayraktar and Zhenhua Wang and Zhou Zhou},
journal= {arXiv preprint arXiv:2207.08158},
year = {2022}
}