Properties of the optimal stopping domain in the Lévy model
Author:
A. G. Moroz
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 87 (2013), 163-170
MSC (2010):
Primary 60G40, 60G51
DOI:
https://doi.org/10.1090/S0094-9000-2014-00914-X
Published electronically:
March 21, 2014
MathSciNet review:
3241453
Full-text PDF Free Access
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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
- 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)
- A. G. Moroz and G. M. Shevchenko, The structure of the stopping domain in a Lévy model, Teor. Ĭmovīr. Mat. Stat. 84 (2011), 102–110 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 84 (2012), 107–115. MR 2857421, DOI https://doi.org/10.1090/S0094-9000-2012-00864-8
- A. G. Kukush, Yu. S. Mishura, and G. M. Shevchenko, On reselling of European option, Theory Stoch. Process. 12 (2006), no. 3-4, 75–87. MR 2316567
- Damien Lamberton and Mohammed Mikou, The critical price for the American put in an exponential Lévy model, Finance Stoch. 12 (2008), no. 4, 561–581. MR 2447412, DOI https://doi.org/10.1007/s00780-008-0073-9
- Philip E. Protter, Stochastic integration and differential equations, 2nd ed., Applications of Mathematics (New York), vol. 21, Springer-Verlag, Berlin, 2004. Stochastic Modelling and Applied Probability. MR 2020294
- S. Villeneuve, Exercise regions of American options on several assets, Finance Stoch. 3 (1999), no. 3, 295–322.
- Stéphane Villeneuve, On threshold strategies and the smooth-fit principle for optimal stopping problems, J. Appl. Probab. 44 (2007), no. 1, 181–198. MR 2312995, DOI https://doi.org/10.1239/jap/1175267171
References
- 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)
- 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)
- 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)
- 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)
- P. E. Protter, Stochastic Integration and Differential Equations, Springer-Verlag, Berlin–Heidelberg, 2004. MR 2020294 (2005k:60008)
- S. Villeneuve, Exercise regions of American options on several assets, Finance Stoch. 3 (1999), no. 3, 295–322.
- 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)
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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
Email:
mag-87@inbox.ru
Keywords:
Lévy 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
