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
DOI:
https://doi.org/10.1090/S0094-9000-2012-00861-2
Published electronically:
July 26, 2012
MathSciNet review:
2857413
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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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- 8. Yu. S. Mīshura, G. M. Shevchenko, and Yu. V. Yukhnovs′kiĭ, Functional limit theorems for stochastic integrals with applications to risk processes and to capital of self-financing strategies in a multidimensional market. I, Teor. Ĭmovīr. Mat. Stat. 81 (2009), 114–127 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 81 (2010), 131–146. MR 2667315, https://doi.org/10.1090/S0094-9000-2011-00815-0
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. I, Theor. Imovirnost. Matem. Statyst. 75 (2006), 45-59; English transl. in Theor. Probability and Math. Statist. 75 (2007), 51-64. Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 60G22, 91B24, 60G15
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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:
https://doi.org/10.1090/S0094-9000-2012-00861-2
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
