Stability of Time-inconsistent Stopping for One-dimensional Diffusion -- A Longer Version

Erhan Bayraktar; Zhenhua Wang; Zhou Zhou

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arXiv · 2207.08158

Stability of Time-inconsistent Stopping for One-dimensional Diffusion -- A Longer Version

Erhan Bayraktar·Zhenhua Wang·Zhou Zhou

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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 $\varepsilon$-equilibria, we establish the relaxed continuity of the optimal value.

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BibTeX RIS

Erhan Bayraktar, Zhenhua Wang, Zhou Zhou. 2022-10-03. Stability of Time-inconsistent Stopping for One-dimensional Diffusion -- A Longer Version. https://arxiv.org/abs/2207.08158

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