Threshold structure of optimal stopping strategies for American type option. I
Authors:
H. Jönsson, A. G. Kukush and D. S. Silvestrov
Journal:
Theor. Probability and Math. Statist. 71 (2005), 93-103
MSC (2000):
Primary 91B28, 62P05; Secondary 60J25, 60J20
DOI:
https://doi.org/10.1090/S0094-9000-06-00650-8
Published electronically:
January 4, 2006
MathSciNet review:
2144323
Full-text PDF Free Access
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Additional Information
Abstract: The paper presents results of theoretical studies of optimal stopping domains of American type options in discrete time. Sufficient conditions on the payoff functions and the price process for the optimal stopping domains to have one-threshold structure are given. We consider monotone, convex and inhomogeneous-in-time payoff functions. The underlying asset’s price is modelled by an inhomogeneous discrete time Markov process.
References
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References
- A. Basso, M. Nardon, and P. Planca, An analysis of the effects of continuous dividends on the exercise of American options, Rend. Studi Econ. Quant. 2001 (2002), 41–68. MR 1940220 (2003i:91048)
- P. Boyle, M. Broadie, and P. Detemple, Monte Carlo methods in security pricing, Option Pricing, Interest Rates and Risk Management (E. Jouini, J. Cvitanić, and M. Musiela, eds.), Cambridge University Press, 2001. MR 1848553
- M. Broadie and J. Detemple, American options on dividend-paying assets, Fields Institute Communications 22 (1999), 69–97. MR 1664664
- P. Carr, R. Jarrow, and R. Myneni, Alternative characterizations of American put options, Mathematical Finance 2 (1992), 87–106.
- Y. S. Chow, H. Robbins, and D. Siegmund, The Theory of Optimal Stopping, Houghton Mifflin Comp., 1971. MR 0331675 (48:10007)
- J. Jacka, Optimal stopping and the American put, Mathematical Finance 1 (1991), 1–14.
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- H. Jönsson, A. G. Kukush, and D. S. Silvestrov, Threshold Structure of Optimal Stopping Strategies for American Type Options, Research Report 2004-2, Department of Mathematics and Physics, Mälardalen University, 2004.
- I. J. Kim, The analytic valuation of American options, The Review of Financial Studies 3 (1990), 547–572.
- A. G. Kukush and D. S. Silvestrov, Optimal pricing of American type options with discrete time, Theory Stoch. Proces. 10(26) (2004), no. 1–2, 72–96.
- A. N. Shiryaev, Optimal Stopping Rules, Springer-Verlag, 1978. MR 0468067 (57:7906)
- A. N. Shiryaev, Yu. M. Kabanov, D. O. Kramkov, and A. V. Mel’nikov, Toward a theory of pricing options of European and American types. I. Discrete time, Theory Probab. Appl. 39 (1994), 14–60. MR 1348190 (97e:90008)
- D. S. Silvestrov, V. G. Galochkin, and V. G. Sibirtsev, Algorithms and programs for optimal Monte Carlo pricing of American type options, Theory of Stoch. Process. 5(21) (1999), no. 1–2, 175–187.
- D. S. Silvestrov, V. G. Galochkin, and A. A. Malyarenko, OPTAN — a pilot program system for analysis of options, Theory of Stoch. Process. 7(23) (2001), no. 1–2, 291–300.
- P. van Moerbeke, On optimal stopping and free boundary problems, Archive for Rational Mechanics and Analysis 60 (1976), 101–148. MR 0413250 (54:1367)
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Additional Information
H. Jönsson
Affiliation:
Mälardalen University, Box 883, SE-721 23 Västerås, Sweden
Email:
henrik.jonsson@mdh.se
A. G. Kukush
Affiliation:
Kyiv University, 01033 Kiev, Ukraine
Email:
alexander_kukush@univ.kiev.ua
D. S. Silvestrov
Affiliation:
Mälardalen University, Box 883, SE-721 23 Västerås, Sweden
Email:
dmitrii.silvestrov@mdh.se
Keywords:
Markov process,
discrete time,
American type option,
convex payoff function,
optimal stopping
Received by editor(s):
May 24, 2004
Published electronically:
January 4, 2006
Additional Notes:
Supported in part by the Visby programme (funded by the Swedish Institute), and by grants from the Knowledge Foundation and the Royal Swedish Academy of Science.
Article copyright:
© Copyright 2006
American Mathematical Society
