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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}∪[α,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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Cite

BibTeXRIS
BibTeX
@misc{bayraktar2026meanfield,
  title = {{Mean-field optimal stopping with endogenous quantile cutoffs}},
  author = {Erhan Bayraktar and Ibrahim Ekren and Xihao He},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03277},
  eprint = {2609.03277},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03277},
}
RIS
TY  - UNPB
TI  - Mean-field optimal stopping with endogenous quantile cutoffs
AU  - Erhan Bayraktar
AU  - Ibrahim Ekren
AU  - Xihao He
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03277
UR  - https://arxiv.org/abs/2609.03277
AB  - 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}∪[α,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.
ER  -