Fractional Calculus and Fractional Processes with Applications to Financial Economics

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. 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

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  • Author : Hasan Fallahgoul
  • Publisher : Academic Press
  • Pages : 118 pages
  • ISBN : 0128042842
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKFractional Calculus and Fractional Processes with Applications to Financial Economics

Fractional Calculus and Fractional Processes with Applications to Financial Economics

Fractional Calculus and Fractional Processes with Applications to Financial Economics
  • Author : Hasan Fallahgoul,Sergio Focardi,Frank Fabozzi
  • Publisher : Academic Press
  • Release : 06 October 2016
GET THIS BOOKFractional Calculus and Fractional Processes with Applications to Financial Economics

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,

Fractional-order Modeling of Nuclear Reactor: From Subdiffusive Neutron Transport to Control-oriented Models

Fractional-order Modeling of Nuclear Reactor: From Subdiffusive Neutron Transport to Control-oriented Models
  • Author : Vishwesh Vyawahare,Paluri S. V. Nataraj
  • Publisher : Springer
  • Release : 03 February 2018
GET THIS BOOKFractional-order Modeling of Nuclear Reactor: From Subdiffusive Neutron Transport to Control-oriented Models

This book addresses the topic of fractional-order modeling of nuclear reactors. Approaching neutron transport in the reactor core as anomalous diffusion, specifically subdiffusion, it starts with the development of fractional-order neutron telegraph equations. Using a systematic approach, the book then examines the development and analysis of various fractional-order models representing nuclear reactor dynamics, ultimately leading to the fractional-order linear and nonlinear control-oriented models. The book utilizes the mathematical tool of fractional calculus, the calculus of derivatives and integrals with arbitrary

Mathematical Economics

Mathematical Economics
  • Author : Vasily E. Tarasov
  • Publisher : MDPI
  • Release : 03 June 2020
GET THIS BOOKMathematical Economics

This book is devoted to the application of fractional calculus in economics to describe processes with memory and non-locality. Fractional calculus is a branch of mathematics that studies the properties of differential and integral operators that are characterized by real or complex orders. Fractional calculus methods are powerful tools for describing the processes and systems with memory and nonlocality. Recently, fractional integro-differential equations have been used to describe a wide class of economical processes with power law memory and spatial

Advances in Differential and Difference Equations with Applications 2020

Advances in Differential and Difference Equations with Applications 2020
  • Author : Dumitru Baleanu
  • Publisher : MDPI
  • Release : 20 January 2021
GET THIS BOOKAdvances in Differential and Difference Equations with Applications 2020

It is very well known that differential equations are related with the rise of physical science in the last several decades and they are used successfully for models of real-world problems in a variety of fields from several disciplines. Additionally, difference equations represent the discrete analogues of differential equations. These types of equations started to be used intensively during the last several years for their multiple applications, particularly in complex chaotic behavior. A certain class of differential and related difference

Recent Investigations of Differential and Fractional Equations and Inclusions

Recent Investigations of Differential and Fractional Equations and Inclusions
  • Author : Snezhana Hristova
  • Publisher : MDPI
  • Release : 22 February 2021
GET THIS BOOKRecent Investigations of Differential and Fractional Equations and Inclusions

During the past decades, the subject of calculus of integrals and derivatives of any arbitrary real or complex order has gained considerable popularity and impact. This is mainly due to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. In connection with this, great importance is attached to the publication of results that focus on recent and novel developments in the theory of any types of differential and fractional differential equation and inclusions, especially covering

Stochastic Calculus for Fractional Brownian Motion and Applications

Stochastic Calculus for Fractional Brownian Motion and Applications
  • Author : Francesca Biagini,Yaozhong Hu,Bernt Øksendal,Tusheng Zhang
  • Publisher : Springer Science & Business Media
  • Release : 17 February 2008
GET THIS BOOKStochastic Calculus for Fractional Brownian Motion and Applications

The purpose of this book is to present a comprehensive account of the different definitions of stochastic integration for fBm, and to give applications of the resulting theory. Particular emphasis is placed on studying the relations between the different approaches. Readers are assumed to be familiar with probability theory and stochastic analysis, although the mathematical techniques used in the book are thoroughly exposed and some of the necessary prerequisites, such as classical white noise theory and fractional calculus, are recalled

Stochastic Calculus for Fractional Brownian Motion and Related Processes

Stochastic Calculus for Fractional Brownian Motion and Related Processes
  • Author : IUliia S. Mishura,I︠U︡lii︠a︡ S. Mishura,Yuliya Mishura,Julija S. Mišura,Ûliâ Stepanovna Mišura
  • Publisher : Springer Science & Business Media
  • Release : 02 January 2008
GET THIS BOOKStochastic Calculus for Fractional Brownian Motion and Related Processes

This volume grew out of a series of preprints which were written and circulated - tween 1993 and 1994. Around the same time, related work was done independently by Harder 40] and Laumon 62]. In writing this text based on a revised version of these preprints that were widely distributed in summer 1995, I ?nally did not p- sue the original plan to completely reorganize the original preprints. After the long delay, one of the reasons was that an overview of the results is now

Fractional Calculus

Fractional Calculus
  • Author : Dumitru Baleanu,Kai Diethelm,Enrico Scalas,Juan J Trujillo
  • Publisher : World Scientific
  • Release : 15 September 2016
GET THIS BOOKFractional Calculus

This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation,

Stochastic Models for Fractional Calculus

Stochastic Models for Fractional Calculus
  • Author : Mark M. Meerschaert,Alla Sikorskii
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 21 October 2019
GET THIS BOOKStochastic Models for Fractional Calculus

Fractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics. It is used to model anomalous diffusion, in which a cloud of particles spreads in a different manner than traditional diffusion. This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level,

Fractional Calculus with Applications in Mechanics

Fractional Calculus with Applications in Mechanics
  • Author : Teodor M. Atanackovic,Stevan Pilipovic,Bogoljub Stankovic,Dusan Zorica
  • Publisher : John Wiley & Sons
  • Release : 19 February 2014
GET THIS BOOKFractional Calculus with Applications in Mechanics

The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation, Impact and Variational Principles contain various applications of fractional calculus to the fields of classical mechanics. Namely, the books study problems in fields such as viscoelasticity of fractional order, lateral vibrations of a rod of fractional order type, lateral vibrations of a rod positioned on fractional order viscoelastic foundations, diffusion-wave phenomena, heat conduction, wave propagation, forced oscillations of a

Applications of Fractional Calculus in Physics

Applications of Fractional Calculus in Physics
  • Author : R Hilfer
  • Publisher : World Scientific
  • Release : 02 March 2000
GET THIS BOOKApplications of Fractional Calculus in Physics

Fractional calculus is a collection of relatively little-known mathematical results concerning generalizations of differentiation and integration to noninteger orders. While these results have been accumulated over centuries in various branches of mathematics, they have until recently found little appreciation or application in physics and other mathematically oriented sciences. This situation is beginning to change, and there are now a growing number of research areas in physics which employ fractional calculus. This volume provides an introduction to fractional calculus for physicists,

Advanced Mathematical Methods for Finance

Advanced Mathematical Methods for Finance
  • Author : Julia Di Nunno,Bernt Øksendal
  • Publisher : Springer Science & Business Media
  • Release : 29 March 2011
GET THIS BOOKAdvanced Mathematical Methods for Finance

This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced

The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order

The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order
  • Author : Anonim
  • Publisher : Elsevier
  • Release : 05 September 1974
GET THIS BOOKThe Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods

Theory and Applications of Long-Range Dependence

Theory and Applications of Long-Range Dependence
  • Author : Paul Doukhan,George Oppenheim,Murad Taqqu
  • Publisher : Springer Science & Business Media
  • Release : 13 December 2002
GET THIS BOOKTheory and Applications of Long-Range Dependence

The area of data analysis has been greatly affected by our computer age. For example, the issue of collecting and storing huge data sets has become quite simplified and has greatly affected such areas as finance and telecommunications. Even non-specialists try to analyze data sets and ask basic questions about their structure. One such question is whether one observes some type of invariance with respect to scale, a question that is closely related to the existence of long-range dependence in