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Fractal Dimension for Fractal Structures : With Applications to Finance - Manuel Fernandez-Martinez

Hardcover Published: 8th May 2019
ISBN: 9783030166441
Number Of Pages: 204

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This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure. The fractal dimension is the main invariant of a fractal set, and provides useful information regarding the irregularities it presents when examined at a suitable level of detail. New theoretical models for calculating the fractal dimension of any subset with respect to a fractal structure are posed to generalise both the Hausdorff and box-counting dimensions. Some specific results for self-similar sets are also proved. Unlike classical fractal dimensions, these new models can be used with empirical applications of fractal dimension including non-Euclidean contexts.



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 algorithms for properly calculating the self-similarity exponent of a wide range of processes, including (fractional) Brownian motion and Levy 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.

ISBN: 9783030166441
ISBN-10: 3030166449
Series: Sema Simai Springer
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 204
Published: 8th May 2019
Publisher: SPRINGER VERLAG GMBH
Country of Publication: CH
Dimensions (cm): 23.39 x 15.6  x 1.42
Weight (kg): 0.49

Earn 373 Qantas Points
on this Book