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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Convergence of the maximum probability of success in the problem of quantile hedging for a model of an asset price process with long-range dependence


Authors: M. V. Bratyk, Yu. V. Kozachenko and Yu. S. Mishura
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 84 (2011).
Journal: Theor. Probability and Math. Statist. 84 (2012), 15-31
MSC (2010): Primary 60G22, 91B24; Secondary 60G15
Published electronically: July 26, 2012
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Abstract: The convergence in probability of the sets of maximum probability of success is studied in the problem of quantile hedging for a model of an asset price process involving Brownian and fractional Brownian motions.


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Additional Information

M. V. Bratyk
Affiliation: Department of Mathematics, Faculty for Informatics, National University “Kyiv Mohyla Academy”, Skovorody Street 2, Kyiv 04070, Ukraine
Email: mbratyk@ukr.net

Yu. V. Kozachenko
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 4E, Kiev 03127, Ukraine
Email: ykoz@univ.kiev.ua

Yu. S. Mishura
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 4E, Kiev 03127, Ukraine
Email: myus@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2012-00861-2
PII: S 0094-9000(2012)00861-2
Keywords: Quantile hedging, fractional Brownian motion, mixed model, limit theorems, probability of success
Received by editor(s): December 24, 2010
Published electronically: July 26, 2012
Additional Notes: The second author is supported by the grant #230804 “Multifractionality” of the European Commission
Article copyright: © Copyright 2012 American Mathematical Society