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ISSN 1547-7363(online) ISSN 0094-9000(print)
Stochastic differential equations with generalized stochastic volatility and statistical estimators
Authors:
M. Bel Hadj Khlifa, Yu. Mishura, K. Ralchenko, G. Shevchenko and M. Zili
Journal:
Theor. Probability and Math. Statist. 96 (2018), 1-13
MSC (2010):
Primary 60H10, 62F10, 62F12
DOI:
https://doi.org/10.1090/tpms/1030
Published electronically:
October 5, 2018
MathSciNet review:
3666868
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We study a stochastic differential equation, the diffusion coefficient of which is a function of some adapted stochastic process. The various conditions for the existence and uniqueness of weak and strong solutions are presented. The drift parameter estimation in this model is investigated, and the strong consistency of the least squares and maximum likelihood estimators is proved. As an example, the Ornstein–Uhlenbeck model with stochastic volatility is considered.
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Additional Information
M. Bel Hadj Khlifa
Affiliation:
Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Avenue de l’Environnement, 5000, Monastir, Tunisia
Email:
meriem.bhk@outlook.fr
Yu. Mishura
Affiliation:
Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska, 64/13, Kyiv, Ukraine, 01601
Email:
myus@univ.kiev.ua
K. Ralchenko
Affiliation:
Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska, 64/13, Kyiv, Ukraine, 01601
Email:
k.ralchenko@gmail.com
G. Shevchenko
Affiliation:
Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska, 64/13, Kyiv, Ukraine, 01601
Email:
zhora@univ.kiev.ua
M. Zili
Affiliation:
Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Avenue de l’Environnement, 5000, Monastir, Tunisia
Email:
Mounir.Zili@fsm.rnu.tn
Keywords:
Stochastic differential equation,
weak and strong solutions,
stochastic volatility,
drift parameter estimation,
maximum likelihood estimator,
strong consistency
Received by editor(s):
January 25, 2017
Published electronically:
October 5, 2018
Article copyright:
© Copyright 2018
American Mathematical Society