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
DOI:
https://doi.org/10.1090/S0094-9000-2011-00836-8
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.
- 1. Mark Broadie and Jérôme Detemple, The valuation of American options on multiple assets, Math. Finance 7 (1997), no. 3, 241–286. MR 1459060, https://doi.org/10.1111/1467-9965.00032
- 2. Matthias Ehrhardt and Ronald 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, https://doi.org/10.1142/S0219024908004890
- 3. J. D. Evans, R. Kuske, and Joseph B. Keller, American options of assets with dividends near expiry, Math. Finance 12 (2002), no. 3, 219–237. MR 1910594, https://doi.org/10.1111/1467-9965.02008
- 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. Damien Lamberton and Stéphane 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, https://doi.org/10.1214/aoap/1050689604
- 6. Yuliya Mishura and Georgiy Shevchenko, The optimal time to exchange one asset for another on finite interval, Optimality and risk—modern trends in mathematical finance, Springer, Berlin, 2009, pp. 197–210. MR 2648604, https://doi.org/10.1007/978-3-642-02608-9_10
- 7. S. Villeneuve, Exercise regions of American options on several assets, Finance Stoch. 3 (1999), no. 3, 295-322.
- 8. Paul Wilmott, Sam Howison, and Jeff Dewynne, The mathematics of financial derivatives, Cambridge University Press, Cambridge, 1995. A student introduction. MR 1357666
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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
Email:
zhora@univ.kiev.ua
DOI:
https://doi.org/10.1090/S0094-9000-2011-00836-8
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
