Local time pushed mixed stopping and smooth fit for time-inconsistent stopping problems
Probability
2022-07-01 v1 Optimization and Control
Abstract
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 function. In particular, we study (weak) equilibria for this problem in a novel class of mixed (i.e., randomized) stopping times based on a local time construction of the stopping intensity. For a general formulation of the problem we provide a verification theorem giving sufficient conditions for mixed (and pure) equilibria in terms of a set of variational inequalities, including a smooth fit condition. We apply the theory to prove the existence of (mixed) equilibria in a recently studied real options problem in which no pure equilibria exist.
Keywords
Cite
@article{arxiv.2206.15124,
title = {Local time pushed mixed stopping and smooth fit for time-inconsistent stopping problems},
author = {Andi Bodnariu and Sören Christensen and Kristoffer Lindensjö},
journal= {arXiv preprint arXiv:2206.15124},
year = {2022}
}