A bounded arbitrage strategy for a multiperiod model of a financial market in discrete time
Authors:
Yu. S. Mishura, P. S. Shelyazhenko and G. M. Shevchenko
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 77 (2008), 135-146
MSC (2000):
Primary 91B28
DOI:
https://doi.org/10.1090/S0094-9000-09-00752-2
Published electronically:
January 16, 2009
MathSciNet review:
2432777
Full-text PDF Free Access
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Additional Information
Abstract: The notion of $\varepsilon$-arbitrage strategy is introduced for a multiperiod model. A theorem, analogous to the classical first fundamental theorem for a usual arbitrage strategy, is proved for this model. The difference between single-period and multiperiod models is discussed.
References
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- Jia An Yan, CaractĂ©risation dâune classe dâensembles convexes de $L^{1}$ ou $H^{1}$, Seminar on Probability, XIV (Paris, 1978/1979) Lecture Notes in Math., vol. 784, Springer, Berlin, 1980, pp. 220â222 (French). MR 580127
References
- M. Harrison and S. Pliska, Martingales and stochastic integrals in the theory of continuous trading, Stochastic Process. Appl. 11 (1981), 215â260. MR 622165 (83a:90022)
- R. C. Dalang, A. Morton, and W. Willinger, Equivalent martingale measures and no-arbitrage in stochastic securities market models, Stochastics and Stochastics Reports 29 (1990), 185â201. MR 1041035 (91g:90056)
- F. Delbaen and W. Schachermayer, A general version of the fundamental theorem of asset pricing, Mathematische Annalen 300 (1994), 463â520. MR 1304434 (95m:90022b)
- Yu. Kabanov and C. Stricker, Remarks on the True No-Arbitrage Property, Manuscript, Laboratoire de Mathématiques de Besançon, 2003.
- A. N. Shiryaev, Essentials of Stochastic Finance. Facts, Models, Theory, âFazisâ, Moscow, 1998; English transl., World Scientific, River Edge, NJ, 1999. MR 1695318 (2000e:91085)
- H. Föllmer and A. Schied, Stochastic Finance. An Introduction in Discrete Time, 2nd edition, Walter de Gruyter, 2004. MR 2169807 (2006d:91002)
- Yu. S. Mishura, The fundamental theorem of financial mathematics for limited arbitrage, Applied Statistics. Actuarial and Financial Mathematics 2003, no. 1â2, 49â54. (Ukrainian)
- Yu. M. Kabanov and Ch. Stricker, A teachersâ note on no-arbitrage criteria, SĂ©minaire de ProbabilitĂ©s XXXV, pp. 149â152, Lecture Notes in Math., 1755, Springer, Berlin, 2001, MR 1837282 (2003c:60073)
- Ch. Stricker, Arbitrage et lois de martingale, Ann. Inst. H. PoincarĂ© Probab. Statist. 26 (1990), 451â460. MR 1066088 (91m:60080)
- J. A. Yan, CaractĂ©risation dâune classe dâensembles convexes de $L_{1}$ ou $H_{1}$, Seminar on Probability, XIV (Paris, 1978/1979), pp. 220â222, Lecture Notes in Math., 784, Springer, Berlin, 1980. MR 0580127 (82c:60090)
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Additional Information
Yu. S. Mishura
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:
myus@univ.kiev.ua
P. S. Shelyazhenko
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:
Pavlo.Shelyazhenko@gmail.com
G. M. Shevchenko
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:
zhora@univ.kiev.ua
Keywords:
Arbitrage strategy,
$\varepsilon$-arbitrage strategy,
financial market,
multiperiod model,
self-financing strategy
Received by editor(s):
July 29, 2005
Published electronically:
January 16, 2009
Article copyright:
© Copyright 2009
American Mathematical Society
