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 Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 3, Pages 557–575 (Mi tvp270)

Approximate optimal stopping of dependent sequences

R. Kühne, L. Rüschendorf

Albert Ludwigs University of Freiburg

Abstract: We consider optimal stopping of sequences of random variables satisfying some asymptotic independence property. Assuming that the embedded planar point processes converge to a Poisson process, we introduce some further conditions to obtain approximation of the optimal stopping problem of the discrete time sequence by the optimal stopping of the limiting Poisson process. This limiting problem can be solved in several cases. We apply this method to obtain approximations for the stopping of moving average sequences, of hidden Markov chains, and of max-autoregressive sequences. We also briefly discuss extensions to the case of Poisson cluster processes in the limit.

Keywords: optimal stopping, Poisson processes, asymptotic independence, moving average processes, hidden Markov chains.

DOI: https://doi.org/10.4213/tvp270

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English version:
Theory of Probability and its Applications, 2004, 48:3, 465–480

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Revised: 28.02.2003
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Citation: R. Kühne, L. Rüschendorf, “Approximate optimal stopping of dependent sequences”, Teor. Veroyatnost. i Primenen., 48:3 (2003), 557–575; Theory Probab. Appl., 48:3 (2004), 465–480

Citation in format AMSBIB
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• https://doi.org/10.4213/tvp270
• http://mi.mathnet.ru/eng/tvp/v48/i3/p557

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This publication is cited in the following articles:
1. Parlar M., Perry D., Stadje W., “Optimal shopping when the sales are on – A Markovian full–information best–choice problem”, Stochastic Models, 23:3 (2007), 351–371
2. Faller A., Rueschendorf L., “On Approximative Solutions of Optimal Stopping Problems”, Adv in Appl Probab, 43:4 (2011), 1086–1108
3. Faller A., Rueschendorf L., “On Approximative Solutions of Multistopping Problems”, Ann Appl Probab, 21:5 (2011), 1965–1993
4. Gordienko E., Novikov A., “Characterizations of Optimal Policies in a General Stopping Problem and Stability Estimating”, Probab. Eng. Inform. Sci., 28:3 (2014), 335–352
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