Evaluation of extreme values of entropy functionals
Authors:
Yu. S. Mishura and H. S. Zhelezniak
Translated by:
N. N. Semenov
Journal:
Theor. Probability and Math. Statist. 99 (2019), 199-210
MSC (2010):
Primary 60G22, 60J65; Secondary 94A17
DOI:
https://doi.org/10.1090/tpms/1090
Published electronically:
February 27, 2020
MathSciNet review:
3908666
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Abstract: We consider the sum of two independent Wiener processes with a drift and construct a family of probability measures such that the drift with respect to each of them is zero. Among these measures, we search for those that minimize or maximize certain functionals, for example, entropy-type functionals.
References
- Hans Föllmer and Alexander Schied, Stochastic finance, De Gruyter Studies in Mathematics, vol. 27, Walter de Gruyter & Co., Berlin, 2002. An introduction in discrete time. MR 1925197
- Christian Léonard, Minimization of entropy functionals, J. Math. Anal. Appl. 346 (2008), no. 1, 183–204. MR 2428283, DOI https://doi.org/10.1016/j.jmaa.2008.04.048
- Y. Mishura and H. Zhelezniak, Extreme measures for entropy functionals, Bull. Taras Shevchenko National University of Kyiv. Series: Physics & Mathematics (2017), no. 4, 15–20.
References
- H. Föllmer and A. Schied, Stochastic Finance: An Introduction in Discrete Time, Walter de Gruyter, Berlin, 2002, pp. 121–130. MR 1925197
- C. Leonard, Minimization of entropy functionals, J. Math. Anal. Appl. 346 (2008), no. 1, 183–204. MR 2428283
- Y. Mishura and H. Zhelezniak, Extreme measures for entropy functionals, Bull. Taras Shevchenko National University of Kyiv. Series: Physics & Mathematics (2017), no. 4, 15–20.
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Additional Information
Yu. S. Mishura
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email:
myus@univ.kiev.ua
H. S. Zhelezniak
Affiliation:
Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, Kyiv Taras Shevchenko National University, Volodymyrs’ka Street, 64/13, Kyiv 01601, Ukraine
Email:
hanna.zhelezniak@gmail.com
Keywords:
Wiener process,
Radon–Nikodym derivative,
entropy functional,
minimization,
maximization
Received by editor(s):
October 15, 2018
Published electronically:
February 27, 2020
Article copyright:
© Copyright 2020
American Mathematical Society
