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,

Mathematical Economics

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  • 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

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  • 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

Advances in Differential and Difference Equations with Applications 2020

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  • 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

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  • 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

Applications in Engineering, Life and Social Sciences

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  • Author : Dumitru Bǎleanu,António Mendes Lopes
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 01 April 2019
GET THIS BOOKApplications in Engineering, Life and Social Sciences

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This eighth volume collects authoritative chapters covering several applications of fractional calculus in engineering, life and social sciences, including applications in signal and image analysis, and chaos.

Integral Transforms and Operational Calculus

Integral Transforms and Operational Calculus
  • Author : H. M. Srivastava
  • Publisher : MDPI
  • Release : 20 November 2019
GET THIS BOOKIntegral Transforms and Operational Calculus

Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. This Special Issue contains a total of 36 carefully-selected and peer-reviewed articles which are authored by established researchers from many countries. Included in this Special Issue are review, expository and original research articles dealing with the recent advances on the topics of integral transforms and operational calculus as well as their

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  • Author : Bashir Ahmad,Johnny L Henderson,Rodica Luca
  • Publisher : World Scientific
  • Release : 18 February 2021
GET THIS BOOKBoundary Value Problems For Fractional Differential Equations And Systems

This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann-Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors' results, that have been obtained and highly cited in the literature in the last four years.In each chapter, various examples are presented which support the main results. The methods used in the proof of these theorems

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  • Author : Anatoly Kochubei,Yuri Luchko
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 19 February 2019
GET THIS BOOKBasic Theory

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.

Fractional Differential Equations, Inclusions and Inequalities with Applications

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  • Author : Sotiris K. Ntouyas
  • Publisher : MDPI
  • Release : 09 November 2020
GET THIS BOOKFractional Differential Equations, Inclusions and Inequalities with Applications

During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special

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  • Author : Vasily E. Tarasov,Valentina V. Tarasova
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 18 January 2021
GET THIS BOOKEconomic Dynamics with Memory

This book presents the applications of fractional calculus, fractional operators of non-integer orders and fractional differential equations in describing economic dynamics with long memory. Generalizations of basic economic concepts, notions and methods for the economic processes with memory are suggested. New micro and macroeconomic models with continuous time are proposed to describe the fractional economic dynamics with long memory as well.

Economic Dynamics with Memory

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  • Author : Vasily E. Tarasov,Valentina V. Tarasova
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release : 18 January 2021
GET THIS BOOKEconomic Dynamics with Memory

This book presents the applications of fractional calculus, fractional operators of non-integer orders and fractional differential equations in describing economic dynamics with long memory. Generalizations of basic economic concepts, notions and methods for the economic processes with memory are suggested. New micro and macroeconomic models with continuous time are proposed to describe the fractional economic dynamics with long memory as well.

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  • Author : Govindan Rangarajan,Mingzhou Ding
  • Publisher : Springer
  • Release : 11 January 2008
GET THIS BOOKProcesses with Long-Range Correlations

Processes with long range correlations occur in a wide variety of fields ranging from physics and biology to economics and finance. This book, suitable for both graduate students and specialists, brings the reader up to date on this rapidly developing field. A distinguished group of experts have been brought together to provide a comprehensive and well-balanced account of basic notions and recent developments. The book is divided into two parts. The first part deals with theoretical developments in the area.

Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities

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  • Author : Anatoliy Swishchuk
  • Publisher : World Scientific
  • Release : 03 June 2013
GET THIS BOOKModeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities

Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities is devoted to the modeling and pricing of various kinds of swaps, such as those for variance, volatility, covariance, correlation, for financial and energy markets with different stochastic volatilities, which include CIR process, regime-switching, delayed, mean-reverting, multi-factor, fractional, Levy-based, semi-Markov and COGARCH(1,1). One of the main methods used in this book is change of time method. The book outlines how the change of time method works for