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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

The structure of the stopping region in a Lévy model


Authors: A. G. Moroz and G. M. Shevchenko
Translated by: S. V. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 84 (2011).
Journal: Theor. Probability and Math. Statist. 84 (2012), 107-115
MSC (2010): Primary 60G40, 60G51
Published electronically: July 31, 2012
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Abstract: The optimal stopping problem in a Lévy model is investigated. We show that the stopping region is nonempty for a wide class of models and payoff functions. In the general case, we establish sufficient conditions on the payoff function that provide nonemptiness of the stopping region. For a zero discounting rate we also give conditions for the stopping region to have a threshold structure.


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Additional Information

A. G. Moroz
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 4E, Kiev 03127, Ukraine
Email: mag-87@inbox.ru

G. M. Shevchenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 4E, Kiev 03127, Ukraine
Email: zhora@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2012-00864-8
PII: S 0094-9000(2012)00864-8
Keywords: Lévy processes, American option, payoff function, stopping region, threshold structure
Received by editor(s): April 11, 2011
Published electronically: July 31, 2012
Article copyright: © Copyright 2012 American Mathematical Society