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Parameter estimation in stochastic differential equations

Financial processes as processes in nature, are subject to stochastic fluctuations. Stochastic differential equations turn out to be an advantageous representation of such noisy, real-world problems, and together with their identification, they play an important role in the sectors of finance, but a...

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Main Authors: Weber, Gerhard-Wilhelm, Gorgulu, Zafer-Korcan, Abd.Rahman, Haliza, Bahar, Arifah
Format: Article
Published: Springer-Verlag Berlin Heidelberg 2010
Subjects:
Q Science (General)
Online Access:http://eprints.utm.my/id/eprint/25964/
http://dx.doi.org/10.1007/978-3-642-14788-3_51
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spelling my.utm.259642018-03-22T10:54:48Z http://eprints.utm.my/id/eprint/25964/ Parameter estimation in stochastic differential equations Weber, Gerhard-Wilhelm Gorgulu, Zafer-Korcan Abd.Rahman, Haliza Bahar, Arifah Q Science (General) Financial processes as processes in nature, are subject to stochastic fluctuations. Stochastic differential equations turn out to be an advantageous representation of such noisy, real-world problems, and together with their identification, they play an important role in the sectors of finance, but also in physics and biotechnology. These equations, however, are often hard to represent and to resolve. Thus we express them in a simplified manner of approximation by discretization and additive models based on splines. This defines a trilevel problem consisting of an optimization and a representation problem (portfolio optimization), and a parameter estimation (Weber et al. Financial Regression and Organization. In: Special Issue on Optimization in Finance, DCDIS-B, 2010). Two types of parameters dependency, linear and nonlinear, are considered by constructing a penalized residual sum of squares and investigating the related Tikhonov regularization problem for the first one. In the nonlinear case Gauss–Newton’s method and Levenberg–Marquardt’s method are employed in determining the iteration steps. Both cases are treated using continuous optimization techniques by the elegant framework of conic quadratic programming. These convex problems are well-structured, hence, allowing the use of the efficient interior point methods. Furthermore, we present nonparametric and related methods, and introduce into research done at the moment in our research groups which ends with a conclusion. Springer-Verlag Berlin Heidelberg 2010 Article PeerReviewed Weber, Gerhard-Wilhelm and Gorgulu, Zafer-Korcan and Abd.Rahman, Haliza and Bahar, Arifah (2010) Parameter estimation in stochastic differential equations. Proceeding of the Conference DYNA2008, Dynamics, Games and Science Springer-Verlag 2010, 2 . pp. 703-733. http://dx.doi.org/10.1007/978-3-642-14788-3_51 DOI:10.1007/978-3-642-14788-3_51
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic Q Science (General)
spellingShingle Q Science (General)
Weber, Gerhard-Wilhelm
Gorgulu, Zafer-Korcan
Abd.Rahman, Haliza
Bahar, Arifah
Parameter estimation in stochastic differential equations
description Financial processes as processes in nature, are subject to stochastic fluctuations. Stochastic differential equations turn out to be an advantageous representation of such noisy, real-world problems, and together with their identification, they play an important role in the sectors of finance, but also in physics and biotechnology. These equations, however, are often hard to represent and to resolve. Thus we express them in a simplified manner of approximation by discretization and additive models based on splines. This defines a trilevel problem consisting of an optimization and a representation problem (portfolio optimization), and a parameter estimation (Weber et al. Financial Regression and Organization. In: Special Issue on Optimization in Finance, DCDIS-B, 2010). Two types of parameters dependency, linear and nonlinear, are considered by constructing a penalized residual sum of squares and investigating the related Tikhonov regularization problem for the first one. In the nonlinear case Gauss–Newton’s method and Levenberg–Marquardt’s method are employed in determining the iteration steps. Both cases are treated using continuous optimization techniques by the elegant framework of conic quadratic programming. These convex problems are well-structured, hence, allowing the use of the efficient interior point methods. Furthermore, we present nonparametric and related methods, and introduce into research done at the moment in our research groups which ends with a conclusion.
format Article
author Weber, Gerhard-Wilhelm
Gorgulu, Zafer-Korcan
Abd.Rahman, Haliza
Bahar, Arifah
author_facet Weber, Gerhard-Wilhelm
Gorgulu, Zafer-Korcan
Abd.Rahman, Haliza
Bahar, Arifah
author_sort Weber, Gerhard-Wilhelm
title Parameter estimation in stochastic differential equations
title_short Parameter estimation in stochastic differential equations
title_full Parameter estimation in stochastic differential equations
title_fullStr Parameter estimation in stochastic differential equations
title_full_unstemmed Parameter estimation in stochastic differential equations
title_sort parameter estimation in stochastic differential equations
publisher Springer-Verlag Berlin Heidelberg
publishDate 2010
url http://eprints.utm.my/id/eprint/25964/
http://dx.doi.org/10.1007/978-3-642-14788-3_51
_version_ 1643647639278845952
score 13.211869

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