Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

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



On a constant related to American type options

Author: Georgiĭ Shevchenko
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 82 (2010).
Journal: Theor. Probability and Math. Statist. 82 (2011), 171-175
MSC (2010): Primary 60G40; Secondary 60J65, 35R35
Published electronically: August 5, 2011
MathSciNet review: 2790492
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We discuss a constant which arises in several problems related to optimal exercise of American derivative securities.

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

  • 1. M. Broadie and J. Detemple, The valuation of American options on multiple assets, Math. Finance 7 (1997), no. 3, 241-286. MR 1459060 (98b:90012)
  • 2. M. Ehrhardt and R. E. Mickens, A fast, stable and accurate numerical method for the Black-Scholes equation of American options, Int. J. Theor. Appl. Finance 11 (2008), no. 5, 471-501. MR 2450224 (2009f:91055)
  • 3. J. Evans, R. Kuske, and J. B. Keller, American options on assets with dividends near expiry, Math. Finance 12 (2002), no. 3, 219-237. MR 1910594 (2003e:91079)
  • 4. P. V. Johnson, N. J. Sharp, P. W. Duck, and D. P. Newton, A new class of option: the American delayed-exercise option, VIII Encontro Brasileiro de Finanças, Rio de Janeiro, 2008.
  • 5. D. Lamberton and S. Villeneuve, Critical price near maturity for an American option on a dividend-paying stock, Ann. Appl. Probab. 13 (2003), no. 2, 800-815. MR 1970287 (2004d:91116)
  • 6. Y. Mishura and G. Shevchenko, The optimal time to exchange one asset for another on finite interval, Optimality and Risk -- Modern Trends in Mathematical Finance. The Kabanov Festschrift (Delbaen, Freddy et al., eds.), Springer, Berlin, 2009, pp. 197-210. MR 2648604 (2011h:60096)
  • 7. S. Villeneuve, Exercise regions of American options on several assets, Finance Stoch. 3 (1999), no. 3, 295-322.
  • 8. P. Wilmott, S. Howison, and J. Dewynne, The Mathematics of Financial Derivatives. A Student Introduction, Cambridge Univ. Press, Cambridge, 1995. MR 1357666 (96h:90028)

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 60G40, 60J65, 35R35

Retrieve articles in all journals with MSC (2010): 60G40, 60J65, 35R35

Additional Information

Georgiĭ Shevchenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine

Keywords: Optimal stopping, geometric Brownian motion, American option, a free boundary problem
Received by editor(s): February 22, 2010
Published electronically: August 5, 2011
Additional Notes: The author is indebted to the European Commission for support in the framework of the “Marie Curie Actions” program, grant PIRSES-GA-2008-230804
Article copyright: © Copyright 2011 American Mathematical Society

American Mathematical Society