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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 79, 2007 - Issue 3-4: Special issue on optimal stopping with applications
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Original Articles

Duration problem on trajectories

&
Pages 211-218 | Received 21 Apr 2006, Accepted 29 Sep 2006, Published online: 05 Nov 2008
 

Abstract

Imagine that an urn contains m minus balls and p plus balls. We draw balls from the urn one by one without replacement until we wish to stop. Determine , where is the value of the ball chosen at kth draw, . The problem which we consider in this paper is to stop with maximum duration of possessing the maximum value of the trajectory formed by . We derive the optimal stopping rule and then make some comparison of the asymptotics of the optimal rules between our problem and the related problems.

AMS 2000 Subject Classification::

Acknowledgements

The research was carried out while the first author was visiting the Department of Business Administration, Aichi University. He would like to thank the Department for the warm hospitality received here and Japan Society for the Promotion of Science (grant L 01530) and Russian Foundation for Basic Research (project N 06-01-00128) for the support.

Notes

Postal address: Institute of Applied Mathematical Research, Karelian Research Center of Russian Academy of Sciences, Pushkinskaya st. 11, Petrozavodsk 185610, Russia.

§Postal address: Department of Business Administration, Aichi University, Nagoya campus, 370 Kurozasa Miyoshi, Nishikamo, Aichi 470-0296, Japan. [email protected].

Additional information

Notes on contributors

Vladimir V. Mazalov

¶ ¶Postal address: Institute of Applied Mathematical Research, Karelian Research Center of Russian Academy of Sciences, Pushkinskaya st. 11, Petrozavodsk 185610, Russia.

Mitsushi Tamaki

§ §Postal address: Department of Business Administration, Aichi University, Nagoya campus, 370 Kurozasa Miyoshi, Nishikamo, Aichi 470-0296, Japan. [email protected].

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