Fractional Calculus and Fractional Processes with Applications to Financial Economics presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Research on fractional calculus started in full earnest in the second half of the twentieth century. The fractional paradigm applies not only to calculus, but also to stochastic processes, used in many applications in financial economics such as modelling volatility, interest rates, and modelling high-frequency data. The key features of fractional processes that make them interesting are long-range memory, path-dependence, non-Markovian properties, self-similarity, fractal paths, and anomalous diffusion behaviour. In this book, the authors discuss how fractional calculus and fractional processes are used in financial modelling and finance economic theory. It provides a practical guide that can be useful for students, researchers, and quantitative asset and risk managers interested in applying fractional calculus and fractional processes to asset pricing, financial time-series analysis, stochastic volatility modelling, and portfolio optimization.
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Part I: Theory
1: Fractional calculus and fractional processes: an overview
2: Fractional Calculus
3: Fractional Brownian Motion
4: Fractional Diffusion and Heavy Tail Distributions: Stable Distribution
5: Fractional Diffusion and Heavy Tail Distributions: Geo-Stable Distribution
Part II: Applications
6: Fractional Partial Differential Equation and Option Pricing
7: Continuous-Time Random Walk and Fractional Calculus
8: Applications of Fractional Processes
Hasan A. Fallahgoul is currently a postdoctoral researcher at the Swiss Finance Institute @ EPFL, in the team lead by Professor Loriano Mancini. Prior to this
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.
Sergio Focardi Professor of Finance and Director of the Master in Investment, Banking and Risk Management, Researcher at the Finance Group, ESILV EMLV of the Pole Universitaire De Vinci, Paris, France.
Sergio M. Focardi is a professor of finance, Director of the Master in Investment Banking and Risk Management and researcher at the Finance Group, ESILV
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.
Frank Fabozzi Professor of Finance, EDHEC Business School and a member of the EDHEC Risk Institute, USA.
Frank J. Fabozzi is a professor of finance at EDHEC Business School (Nice, France) and a senior scientific adviser at the EDHEC-Risk Institute. He taught
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.