
Fractional Calculus and Fractional Processes with Applications to Financial Economics
Theory and Application
Description
Key Features
- Provides the necessary background for the book's content as applied to financial economics
- Analyzes the application of fractional calculus and fractional processes from deterministic and stochastic perspectives
Readership
Graduate students of mathematical finance, statistics and probability, and applied mathematics
Table of Contents
- Dedication
- About the Authors
- Illustrations
- Part I: Theory
- 1: Fractional calculus and fractional processes: an overview
- Abstract
- 1.1 Fractional calculus
- 1.2 Fractional processes
- 2: Fractional Calculus
- Abstract
- 2.1 Different definitions for fractional derivatives
- 2.2 Computation with Matlab
- Key points of the chapter
- 3: Fractional Brownian Motion
- Abstract
- 3.1 Definition
- 3.2 Long-Range Dependency
- 3.3 Self-Similarity
- 3.4 Existence of Arbitrage
- Key points of the chapter
- 4: Fractional Diffusion and Heavy Tail Distributions: Stable Distribution
- Abstract
- 4.1 Univariate Stable Distribution
- 4.2 Multivariate Stable Distribution
- Key points of the chapter
- 5: Fractional Diffusion and Heavy Tail Distributions: Geo-Stable Distribution
- Abstract
- 5.1 Univariate Geo-stable Distribution
- 5.2 Multivariate Geo-stable Distribution
- Key points of the chapter
- 1: Fractional calculus and fractional processes: an overview
- Part II: Applications
- 6: Fractional Partial Differential Equation and Option Pricing
- Abstract
- 6.1 Option Pricing and Brownian Motion
- 6.2 Option Pricing and the Lévy Process
- Key points of the chapter
- 7: Continuous-Time Random Walk and Fractional Calculus
- Abstract
- 7.1 Continuous-Time Random Walk
- 7.2 Fractional Calculus and Probability Density Function
- 7.3 Applications
- Key points of the chapter
- 8: Applications of Fractional Processes
- Abstract
- 8.1 Fractionally Integrated Time Series
- 8.2 Stock-Returns and Volatility Processes
- 8.3 Interest-Rate Processes
- 8.4 Order Arrival Processes
- Key points of the chapter
- 6: Fractional Partial Differential Equation and Option Pricing
- References
- Index
Product details
- No. of pages: 118
- Language: English
- Copyright: © Academic Press 2016
- Published: September 22, 2016
- Imprint: Academic Press
- Hardcover ISBN: 9780128042489
- eBook ISBN: 9780128042847
About the Authors
Hassan Fallahgoul
position, he was a postdoctoral researcher at the European Center for Advanced Research in Economics and Statistics (ECARES), Universite Libre de Bruxelles,
Belgium. His research interests are in nancial econometrics, quantitative finance, Levy processes and fractional calculus. Specializing in heavy-tailed distributions
and their applications to finance. Dr. Fallahgoul has published several papers in scientific journals including Quantitative Finance, Applied Mathematics Letters,
and Journal of Statistical Theory and Practice. He holds a PhD and MSc in applied mathematics from the K. N. Toosi University of Technology.
Affiliations and Expertise
Sergio Focardi
EMLV of the Pole Universitaire De Vinci, Paris. He is a founding partner of The Intertek Group, Paris. Professor Focardi holds a degree in Electronic Engineering
from the University of Genoa, Italy, and a PhD in Mathematical Finance from the University of Karlsruhe, Germany. A member of the Editorial Advisory Board
of The Journal of Portfolio Management, he has authored numerous articles, monographs, and books.
Affiliations and Expertise
Frank Fabozzi
at Yale's School of Management for 17 years and served as a visiting professor at MIT's Sloan School of Management and Princeton University's Department of
Operations Research and Financial Engineering. Professor Fabozzi is the editor of The Journal of Portfolio Management and an associate editor of several journals,
including Quantitative Finance. The author of numerous numerous books and articles on quantitative finance, he holds a doctorate in economics from The
Graduate Center of the City University of New York.
Affiliations and Expertise
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