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Upper and Lower Bounds of Optimal Stopping for a Random Sequence: The Case of Finite Horizon

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Abstract

This paper derives upper and lower bounds of the price in the optimal stopping problem for a an adapted random sequence in the case of finite horizon. As is demonstrated below, the bounds can be found by solving the maximax and maximin setups of optimal stopping problems. For these setups, we obtain conditions under which 1) a recurrent relation is satisfied for the upper (lower) truncated sequence of optimal stopping prices; 2) an optimality criterion is constructed for the stopping times; 3) the structure and invariance of the optimal stopping times are established. Some examples with explicit solutions of the maximax and maximin setups of optimal stopping problems are given.

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Authors and Affiliations

  1. National Research University Higher School of Economics, Moscow, Russia

    V. M. Khametov

  2. Moscow Aviation Institute (National Research University), Moscow, Russia

    V. M. Khametov

  3. Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow, Russia

    E. A. Shelemekh

Authors
  1. V. M. Khametov
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  2. E. A. Shelemekh
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Correspondence to V. M. Khametov or E. A. Shelemekh.

Additional information

Russian Text © V.M. Khametov, E.A. Shelemekh, 2019, published in Avtomatika i Telemekhanika, 2019, No. 3, pp. 152–172.

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Khametov, V.M., Shelemekh, E.A. Upper and Lower Bounds of Optimal Stopping for a Random Sequence: The Case of Finite Horizon. Autom Remote Control 80, 513–530 (2019). https://doi.org/10.1134/S000511791903010X

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  • DOI: https://doi.org/10.1134/S000511791903010X

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