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PreprintarXiv licencearXiv

On optimal stopping problems with full information and rank-dependent reward

  • Alexander Goldenshluger
  • Yaakov Malinovsky
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Abstract

In this paper we consider optimal stopping problems with full information and rank-dependent rewards. Our focus is on the following two problems: selecting one of the r best observations (Gusein-Zade's problem with full information) and minimizing the expected rank (Robbins' problem). In both settings we provide full characterization of the optimal stopping rules and corresponding optimal values. We also present numerical experiments in which the derived dynamic programming recursions are implemented, and approximations to optimal values are computed.

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Cite

BibTeXRIS
BibTeX
@misc{goldenshluger2026optimal,
  title = {{On optimal stopping problems with full information and rank-dependent reward}},
  author = {Alexander Goldenshluger and Yaakov Malinovsky},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33701},
  eprint = {2610.33701},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33701},
}
RIS
TY  - UNPB
TI  - On optimal stopping problems with full information and rank-dependent reward
AU  - Alexander Goldenshluger
AU  - Yaakov Malinovsky
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33701
UR  - https://arxiv.org/abs/2610.33701
AB  - In this paper we consider optimal stopping problems with full information and rank-dependent rewards. Our focus is on the following two problems: selecting one of the r best observations (Gusein-Zade's problem with full information) and minimizing the expected rank (Robbins' problem). In both settings we provide full characterization of the optimal stopping rules and corresponding optimal values. We also present numerical experiments in which the derived dynamic programming recursions are implemented, and approximations to optimal values are computed.
ER  -