Mean-field optimal stopping with endogenous quantile cutoffs

Erhan Bayraktar; Ibrahim Ekren; Xihao He

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arXiv · 2609.03277

Mean-field optimal stopping with endogenous quantile cutoffs

Erhan Bayraktar·Ibrahim Ekren·Xihao He

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Abstract

We study a mean-field optimal stopping problem with an endogenous population-level shutdown. All remaining agents stop when the survival mass falls below a prescribed threshold. We recast the discontinuous objective as the singular, nonconvex constraint that the survival mass lie in $\{0\}\cup[\alpha,1]$. We prove the equivalence of strong and weak values via an approximation and the existence of an optimal rule via compactness and penalization. We also prove a dynamic programming principle. The value is continuous away from the critical boundary but may be discontinuous at the boundary itself. Under strict initial feasibility, finite-population values converge to the mean-field value. In the same regime, the laws of near-optimal empirical measures are tight and every mean-field optimizer admits a recovery sequence. At the threshold, however, finite-population convergence may fail.

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Erhan Bayraktar, Ibrahim Ekren, Xihao He. 2026-09-03. Mean-field optimal stopping with endogenous quantile cutoffs. https://arxiv.org/abs/2609.03277

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