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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 79, 2007 - Issue 1-2: Optimal Stopping and Applications Part I
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Original Articles

Filling the gap between American and Russian options: adjustable regret

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Pages 61-83 | Received 07 Apr 2006, Accepted 29 Sep 2006, Published online: 05 Nov 2008
 

Abstract

We study several infinite-horizon optimal multiple-stopping problems for (geometric) Brownian motion. In finance, they naturally span between the American and Russian option formulations in terms of price and reduced regret. In statistics, they are continuous-time examples of best-choice problems with multiple rights. We find explicit formulas for the value functions and describe completely optimal exercise strategies whenever one exists. We also conjecture a new characterization of the value function for the open problem of the Russian option for arithmetic Brownian motion with drift.

AMS Subject Classification::

Acknowledgements

This work was initiated while both authors were attending the Symposium on Optimal Stopping with Applications in Manchester, United Kingdom between 22 and 27 January 2006. They are very grateful to the organizers for this stimulating event.

Notes

Additional information

Notes on contributors

Michael Ludkovski

¶ ¶ [email protected]

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