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 Teor. Veroyatnost. i Primenen., 2004, Volume 49, Issue 2, Pages 373–382 (Mi tvp227)

Short Communications

On an effective solution of the optimal stopping problem for random walks

A. A. Novikova, A. N. Shiryaevb

a University of Technology, Sydney
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We find a solution of the optimal stopping problem for the case when a reward function is an integer power function of a random walk on an infinite time interval. It is shown that an optimal stopping time is a first crossing time through a level defined as the largest root of Appell's polynomial associated with the maximum of the random walk. It is also shown that a value function of the optimal stopping problem on the finite interval $\{0,1\ldots T\}$ converges with an exponential rate as $T\to\infty$ to the limit under the assumption that jumps of the random walk are exponentially bounded.

Keywords: optimal stopping, random walk, rate of convergence, Appell polynomials.

DOI: https://doi.org/10.4213/tvp227

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English version:
Theory of Probability and its Applications, 2005, 49:2, 344–354

Bibliographic databases:

Citation: A. A. Novikov, A. N. Shiryaev, “On an effective solution of the optimal stopping problem for random walks”, Teor. Veroyatnost. i Primenen., 49:2 (2004), 373–382; Theory Probab. Appl., 49:2 (2005), 344–354

Citation in format AMSBIB
\Bibitem{NovShi04} \by A.~A.~Novikov, A.~N.~Shiryaev \paper On an effective solution of the optimal stopping problem for random walks \jour Teor. Veroyatnost. i Primenen. \yr 2004 \vol 49 \issue 2 \pages 373--382 \mathnet{http://mi.mathnet.ru/tvp227} \crossref{https://doi.org/10.4213/tvp227} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2144307} \zmath{https://zbmath.org/?q=an:1092.60018} \transl \jour Theory Probab. Appl. \yr 2005 \vol 49 \issue 2 \pages 344--354 \crossref{https://doi.org/10.1137/S0040585X97981093} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000230308000011} 

• http://mi.mathnet.ru/eng/tvp227
• https://doi.org/10.4213/tvp227
• http://mi.mathnet.ru/eng/tvp/v49/i2/p373

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Related articles on Google Scholar: Russian articles, English articles

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