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In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithmsfor properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Lévy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes.
This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.
In addition, the book applies these fractal dimensions to explore long-memory in financial markets. In particular, novel results linking both fractal dimension and the Hurst exponent are provided. As such, the book provides a number of algorithmsfor properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Lévy stable processes. The algorithms also make it possible to analyse long-memory in real stocks and international indexes.
This book is addressed to those researchers interested in fractal geometry, self-similarity patterns, and computational applications involving fractal dimension and Hurst exponent.
Manuel Fernández-Martínez holds an international PhD in Mathematics from UCLA. His research interests include fractal structures, fractal dimension, self-similar sets, computational applications of fractal dimension, and self-similar processes and their applications to finance.
Miguel Ángel Sánchez-Granero is an Associate Professor at the Department of Mathematics, University of Almería, Spain. He is the author of a number of publications in international journals on asymmetric topology, self-similarity, fractal structures, and fractal dimension with application to financial series.
Juan E. Trinidad Segovia, PhD, is a Full Professor of Finances at the Department of Economics and Business, University of Almería, Spain. His research interests include financial modelling, portfolio selection, CAPM and, most recently, applications of Statistical Mechanics to financial markets. He has published over 20 papers in peer-reviewed journals.
Juan LuisGarcía Guirao is a Full Professor of Applied Mathematics at the Technical University of Cartagena, Spain. In 2011, at the age of 33, he became Spain's youngest Full Professor of Mathematics. The author of more than 100 research papers and Editor in Chief of Applied Mathematics and Nonlinear Sciences, his work has been recognised with the 2017 NSP award for researchers younger than 40 years old, and with the 2017 JDEA best paper award.
Develops a new theory of fractal dimension using the topological concept of a fractal structure
Provides a rigorous description of the first-known (and currently, the only) general algorithm for calculating the Hausdorff dimension in applications
Shares detailed theoretical results to generalize the classical fractal dimensions, namely, both the box-counting and the Hausdorff dimensions
Erscheinungsjahr: | 2019 |
---|---|
Fachbereich: | Analysis |
Genre: | Mathematik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Buch |
Reihe: | SEMA SIMAI Springer Series |
Inhalt: |
xvii
204 S. 6 s/w Illustr. 25 farbige Illustr. 204 p. 31 illus. 25 illus. in color. |
ISBN-13: | 9783030166441 |
ISBN-10: | 3030166449 |
Sprache: | Englisch |
Herstellernummer: | 978-3-030-16644-1 |
Ausstattung / Beilage: | HC runder Rücken kaschiert |
Einband: | Gebunden |
Autor: |
Fernández-Martínez, Manuel
Trinidad Segovia, Juan Evangelista Sánchez-Granero, Miguel Ángel García Guirao, Juan Luis |
Auflage: | 1st ed. 2019 |
Hersteller: |
Springer International Publishing
Springer International Publishing AG SEMA SIMAI Springer Series |
Maße: | 241 x 160 x 18 mm |
Von/Mit: | Manuel Fernández-Martínez (u. a.) |
Erscheinungsdatum: | 08.05.2019 |
Gewicht: | 0,506 kg |
Manuel Fernández-Martínez holds an international PhD in Mathematics from UCLA. His research interests include fractal structures, fractal dimension, self-similar sets, computational applications of fractal dimension, and self-similar processes and their applications to finance.
Miguel Ángel Sánchez-Granero is an Associate Professor at the Department of Mathematics, University of Almería, Spain. He is the author of a number of publications in international journals on asymmetric topology, self-similarity, fractal structures, and fractal dimension with application to financial series.
Juan E. Trinidad Segovia, PhD, is a Full Professor of Finances at the Department of Economics and Business, University of Almería, Spain. His research interests include financial modelling, portfolio selection, CAPM and, most recently, applications of Statistical Mechanics to financial markets. He has published over 20 papers in peer-reviewed journals.
Juan LuisGarcía Guirao is a Full Professor of Applied Mathematics at the Technical University of Cartagena, Spain. In 2011, at the age of 33, he became Spain's youngest Full Professor of Mathematics. The author of more than 100 research papers and Editor in Chief of Applied Mathematics and Nonlinear Sciences, his work has been recognised with the 2017 NSP award for researchers younger than 40 years old, and with the 2017 JDEA best paper award.
Develops a new theory of fractal dimension using the topological concept of a fractal structure
Provides a rigorous description of the first-known (and currently, the only) general algorithm for calculating the Hausdorff dimension in applications
Shares detailed theoretical results to generalize the classical fractal dimensions, namely, both the box-counting and the Hausdorff dimensions
Erscheinungsjahr: | 2019 |
---|---|
Fachbereich: | Analysis |
Genre: | Mathematik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Buch |
Reihe: | SEMA SIMAI Springer Series |
Inhalt: |
xvii
204 S. 6 s/w Illustr. 25 farbige Illustr. 204 p. 31 illus. 25 illus. in color. |
ISBN-13: | 9783030166441 |
ISBN-10: | 3030166449 |
Sprache: | Englisch |
Herstellernummer: | 978-3-030-16644-1 |
Ausstattung / Beilage: | HC runder Rücken kaschiert |
Einband: | Gebunden |
Autor: |
Fernández-Martínez, Manuel
Trinidad Segovia, Juan Evangelista Sánchez-Granero, Miguel Ángel García Guirao, Juan Luis |
Auflage: | 1st ed. 2019 |
Hersteller: |
Springer International Publishing
Springer International Publishing AG SEMA SIMAI Springer Series |
Maße: | 241 x 160 x 18 mm |
Von/Mit: | Manuel Fernández-Martínez (u. a.) |
Erscheinungsdatum: | 08.05.2019 |
Gewicht: | 0,506 kg |