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

2022/07/17 by Bayraktar, Erhan, Wang, Zhenhua, Zhou, Zhou
#49K40 #60G40 #91A11 #91A15 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2207.08158

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 ε-equilibria, we establish the relaxed continuity of the optimal value.

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