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Teoriya Veroyatnostei i ee Primeneniya, 2025, Volume 70, Issue 1, Pages 111–135
DOI: https://doi.org/10.4213/tvp5671 (Mi tvp5671) 		 
An iterative method for multiple stopping problem under Knightian uncertainty

H. Liab, H. Liuc

a Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Shandong, P. R. China
b Frontiers Science Center for Nonlinear Expectations (Ministry of Education), Shandong University, Shandong, P. R. China
c School of Economics, Ocean University of China, Shandong, P. R. China
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DOI: https://doi.org/10.4213/tvp5671
Abstract: In this paper, we introduce a new algorithm based on the one-step improvement to solve the optimal multiple stopping problem under Knightian uncertainty in the discrete time case. This algorithm induces a monotonically increasing sequence to approximate the value functions, which coincides with the value functions after finitely many iteration steps independent of the times of exercise rights. We also present the stability of this algorithm and some numerical simulations.
Keywords: optimal multiple stopping, Knightian uncertainty, $g$-expectation, one-step improvement.
Funding agency Grant number
Natural Science Foundation of Shandong Province ZR2022QA022
Natural Science Foundation of Shandong Province for Excellent Young Scientists Fund Program (Overseas) 2023HWYQ-049
National Natural Science Foundation of China 12201593
Qilu Young Scholars Program of Shandong University
Li's research was supported by the Natural Science Foundation of Shandong Province (№ ZR2022QA022), the Natural Science Foundation of Shandong Province for Excellent Young Scientists Fund Program (Overseas) (№ 2023HWYQ-049) and the Qilu Young Scholars Program of Shandong University. Liu's research was supported by the National Natural Science Foundation of China (№ 12201593).
Received: 14.07.2023
Accepted: 26.05.2024
Published: 27.01.2025
English version:
Theory of Probability and its Applications, 2025, Volume 70, Issue 1, Pages 92–112
DOI: https://doi.org/10.1137/S0040585X97T992252
Bibliographic databases:
Document Type: Article
MSC: 60G40
Language: Russian
Citation: H. Li, H. Liu, “An iterative method for multiple stopping problem under Knightian uncertainty”, Teor. Veroyatnost. i Primenen., 70:1 (2025), 111–135; Theory Probab. Appl., 70:1 (2025), 92–112
Citation in format AMSBIB
\Bibitem{LiLiu25}
\by H.~Li, H.~Liu
\paper An iterative method for multiple stopping problem under Knightian uncertainty
\jour Teor. Veroyatnost. i Primenen.
\yr 2025
\vol 70
\issue 1
\pages 111--135
\mathnet{http://mi.mathnet.ru/tvp5671}
\crossref{https://doi.org/10.4213/tvp5671}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4856750}
\transl
\jour Theory Probab. Appl.
\yr 2025
\vol 70
\issue 1
\pages 92--112
\crossref{https://doi.org/10.1137/S0040585X97T992252}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105005608514}
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