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Avtomatika i Telemekhanika, 2020, Issue 7, Pages 34–55
DOI: https://doi.org/10.31857/S000523102007003X (Mi at15536) 		 
Stochastic Systems

Optimal stopping time for geometric random walks with power payoff function

O. V. Zverevab, V. M. Khametovac, E. A. Shelemekhb

a National Research University Higher School of Economics, Moscow, Russia
b Central Economics and Mathematics Institute (CEMI), Russian Academy of Sciences, Moscow, Russia
c Moscow Aviation Institute (National Research University), Moscow, Russia
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DOI: https://doi.org/10.31857/S000523102007003X
Abstract: Two optimal stopping problems for geometric random walks with the observer's power payoff function, on the finite and infinite horizons, are solved. For these problems, an explicit form of the cut value and also optimal stopping rules are established. It is proved that the optimal stopping rules are nonrandomized thresholds and describe the corresponding free boundary. An explicit form of the free boundary is presented.
Keywords: geometric random walks, stopping time, stopping domain, domain of continuing observations, generating function.
Funding agency Grant number
Russian Foundation for Basic Research 18-010-00666_а
This work was supported by the Russian Foundation for Basic Research, project no. 18-010-00666.
Presented by the member of Editorial Board: A. I. Kibzun

Received: 11.12.2019
Revised: 16.01.2020
Accepted: 30.01.2020
English version:
Automation and Remote Control, 2020, Volume 81, Issue 7, Pages 1192–1210
DOI: https://doi.org/10.1134/S0005117920070036
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: O. V. Zverev, V. M. Khametov, E. A. Shelemekh, “Optimal stopping time for geometric random walks with power payoff function”, Avtomat. i Telemekh., 2020, no. 7, 34–55; Autom. Remote Control, 81:7 (2020), 1192–1210
Citation in format AMSBIB
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