Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)



Properties of the optimal stopping domain in the Lévy model

Author: A. G. Moroz
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 87 (2012).
Journal: Theor. Probability and Math. Statist. 87 (2013), 163-170
MSC (2010): Primary 60G40, 60G51
Published electronically: March 21, 2014
MathSciNet review: 3241453
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The optimal exercise problem is considered for an American type contingent claim in a Lévy financial market model. Sufficient conditions are proposed under which the stopping domain is non-empty and has the threshold structure.

References [Enhancements On Off] (What's this?)

  • 1. A. Moroz and G. Shevchenko, Asymptotic behavior of the payoff function of an American type option in the Lévy model as the time interval in unboundedly extending, Visnyk Kyiv Univ. Mathematics. Mechanics 24 (2010), 39-43. (Ukrainian)
  • 2. A. Moroz and G. Shevchenko, The structure of the stopping region in a Lévy model, Teor. Imovir. Matem. Statyst. 84 (2011), 102-110; English transl. in Theor. Probability and Math. Statist. 84 (2012), 107-115. MR 2857421 (2012j:60107)
  • 3. A. Kukush, Yu. Mishura, and G. Shevchenko, On reselling of European option, Theory Stoch. Process. 12(28) (2006), no. 1-2, 75-87. MR 2316567 (2008e:62171)
  • 4. D. Lamberton and M. Mikou, The critical price for the American put in an exponential Levy model, Finance Stoch. 12 (2008), no. 4, 561-581. MR 2447412 (2009j:91100)
  • 5. P. E. Protter, Stochastic Integration and Differential Equations, Springer-Verlag, Berlin-Heidelberg, 2004. MR 2020294 (2005k:60008)
  • 6. S. Villeneuve, Exercise regions of American options on several assets, Finance Stoch. 3 (1999), no. 3, 295-322.
  • 7. S. Villeneuve, On threshold strategies and the smooth fit principle for optimal stopping problems, Appl. Prob. 44 (2007), no. 1, 181-198. MR 2312995 (2008b:60087)

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 60G40, 60G51

Retrieve articles in all journals with MSC (2010): 60G40, 60G51

Additional Information

A. G. Moroz
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine

Keywords: L\'evy model, stopping domain, non-emptiness, threshold structure
Received by editor(s): September 19, 2012
Published electronically: March 21, 2014
Article copyright: © Copyright 2014 American Mathematical Society

American Mathematical Society