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

MathSciNet review:
2857413

Full-text PDF

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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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