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Fractional Calculus And Fractional Processes With Applications To Financial Economics

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Fractional Calculus and Fractional Processes with Applications to Financial Economics

Fractional Calculus and Fractional Processes with Applications to Financial Economics Book
Author : Hasan Fallahgoul,Sergio Focardi,Frank Fabozzi
Publisher : Academic Press
Release : 2016-10-06
ISBN : 0128042842
Language : En, Es, Fr & De

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Book Description :

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

Mathematical Economics

Mathematical Economics Book
Author : Vasily E. Tarasov
Publisher : MDPI
Release : 2020-06-03
ISBN : 303936118X
Language : En, Es, Fr & De

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Book Description :

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 nonlocality. Generalizations of basic economic concepts and notions the economic processes with memory were proposed. New mathematical models with continuous time are proposed to describe economic dynamics with long memory. This book is a collection of articles reflecting the latest mathematical and conceptual developments in mathematical economics with memory and non-locality based on applications of fractional calculus.

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 Book
Author : Vishwesh Vyawahare,Paluri S. V. Nataraj
Publisher : Springer
Release : 2018-02-03
ISBN : 9811075875
Language : En, Es, Fr & De

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Book Description :

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 non-integer orders (real or complex), which has recently been found to provide a more compact and realistic representation to the dynamics of diverse physical systems. Including extensive simulation results and discussing important issues related to the fractional-order modeling of nuclear reactors, the book offers a valuable resource for students and researchers working in the areas of fractional-order modeling and control and nuclear reactor modeling.

Advances in Differential and Difference Equations with Applications 2020

Advances in Differential and Difference Equations with Applications 2020 Book
Author : Dumitru Baleanu
Publisher : MDPI
Release : 2021-01-20
ISBN : 3039368702
Language : En, Es, Fr & De

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Book Description :

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 equations is represented by their respective fractional forms, which have been utilized to better describe non-local phenomena appearing in all branches of science and engineering. The purpose of this book is to present some common results given by mathematicians together with physicists, engineers, as well as other scientists, for whom differential and difference equations are valuable research tools. The reported results can be used by researchers and academics working in both pure and applied differential equations.

Basic Theory

Basic Theory Book
Author : Anatoly Kochubei,Yuri Luchko
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2019-02-19
ISBN : 3110571625
Language : En, Es, Fr & De

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Book Description :

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.

Applications in Engineering Life and Social Sciences

Applications in Engineering  Life and Social Sciences Book
Author : Dumitru Bǎleanu,António Mendes Lopes
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2019-04-01
ISBN : 3110571927
Language : En, Es, Fr & De

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Book Description :

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.

Recent Investigations of Differential and Fractional Equations and Inclusions

Recent Investigations of Differential and Fractional Equations and Inclusions Book
Author : Snezhana Hristova
Publisher : MDPI
Release : 2021-02-22
ISBN : 303650074X
Language : En, Es, Fr & De

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Book Description :

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 analytical and numerical research for such kinds of equations. This book is a compilation of articles from a Special Issue of Mathematics devoted to the topic of “Recent Investigations of Differential and Fractional Equations and Inclusions”. It contains some theoretical works and approximate methods in fractional differential equations and inclusions as well as fuzzy integrodifferential equations. Many of the papers were supported by the Bulgarian National Science Fund under Project KP-06-N32/7. Overall, the volume is an excellent witness of the relevance of the theory of fractional differential equations.

Boundary Value Problems For Fractional Differential Equations And Systems

Boundary Value Problems For Fractional Differential Equations And Systems Book
Author : Bashir Ahmad,Johnny L Henderson,Rodica Luca
Publisher : World Scientific
Release : 2021-02-18
ISBN : 9811224471
Language : En, Es, Fr & De

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Book Description :

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 include results from the fixed point theory and fixed point index theory. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.

Fractional Differential Equations Inclusions and Inequalities with Applications

Fractional Differential Equations  Inclusions and Inequalities with Applications Book
Author : Sotiris K. Ntouyas
Publisher : MDPI
Release : 2020-11-09
ISBN : 3039432184
Language : En, Es, Fr & De

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Book Description :

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 Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering.

Beyond The Triangle Brownian Motion Ito Calculus And Fokker planck Equation Fractional Generalizations

Beyond The Triangle  Brownian Motion  Ito Calculus  And Fokker planck Equation   Fractional Generalizations Book
Author : Sabir Umarov,Marjorie Hahn,Kei Kobayashi
Publisher : World Scientific
Release : 2018-02-13
ISBN : 9813230991
Language : En, Es, Fr & De

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Book Description :

The book is devoted to the fundamental relationship between three objects: a stochastic process, stochastic differential equations driven by that process and their associated Fokker-Planck-Kolmogorov equations. This book discusses wide fractional generalizations of this fundamental triple relationship, where the driving process represents a time-changed stochastic process; the Fokker-Planck-Kolmogorov equation involves time-fractional order derivatives and spatial pseudo-differential operators; and the associated stochastic differential equation describes the stochastic behavior of the solution process. It contains recent results obtained in this direction.This book is important since the latest developments in the field, including the role of driving processes and their scaling limits, the forms of corresponding stochastic differential equations, and associated FPK equations, are systematically presented. Examples and important applications to various scientific, engineering, and economics problems make the book attractive for all interested researchers, educators, and graduate students.

Stochastic Calculus for Fractional Brownian Motion and Related Processes

Stochastic Calculus for Fractional Brownian Motion and Related Processes Book
Author : Yuliya Mishura
Publisher : Springer
Release : 2008-04-12
ISBN : 3540758739
Language : En, Es, Fr & De

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Book Description :

This volume examines the theory of fractional Brownian motion and other long-memory processes. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. It proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional market.

Stochastic Calculus for Fractional Brownian Motion and Applications

Stochastic Calculus for Fractional Brownian Motion and Applications Book
Author : Francesca Biagini,Yaozhong Hu,Bernt Øksendal,Tusheng Zhang
Publisher : Springer Science & Business Media
Release : 2008-02-17
ISBN : 1846287979
Language : En, Es, Fr & De

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Book Description :

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 in the appendices. This book will be a valuable reference for graduate students and researchers in mathematics, biology, meteorology, physics, engineering and finance.

Risks

Risks Book
Author : Mogens Steffensen
Publisher : MDPI
Release : 2021-06-03
ISBN : 3036507124
Language : En, Es, Fr & De

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Book Description :

This book is a collection of feature articles published in Risks in 2020. They were all written by experts in their respective fields. In these articles, they all develop and present new aspects and insights that can help us to understand and cope with the different and ever-changing aspects of risks. In some of the feature articles the probabilistic risk modeling is the central focus, whereas impact and innovation, in the context of financial economics and actuarial science, is somewhat retained and left for future research. In other articles it is the other way around. Ideas and perceptions in financial markets are the driving force of the research but they do not necessarily rely on innovation in the underlying risk models. Together, they are state-of-the-art, expert-led, up-to-date contributions, demonstrating what Risks is and what Risks has to offer: articles that focus on the central aspects of insurance and financial risk management, that detail progress and paths of further development in understanding and dealing with...risks. Asking the same type of questions (which risk allocation and mitigation should be provided, and why?) creates value from three different perspectives: the normative perspective of market regulator; the existential perspective of the financial institution; the phenomenological perspective of the individual consumer or policy holder.

Fractional Calculus

Fractional Calculus Book
Author : Dumitru Baleanu,Kai Diethelm,Enrico Scalas
Publisher : World Scientific
Release : 2012
ISBN : 9814355208
Language : En, Es, Fr & De

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Book Description :

This title 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.

Fractional Modeling and Controller Design of Robotic Manipulators

Fractional Modeling and Controller Design of Robotic Manipulators Book
Author : Abhaya Pal Singh
Publisher : Springer Nature
Release : 2021-07-25
ISBN : 3030582477
Language : En, Es, Fr & De

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Book Description :

Download Fractional Modeling and Controller Design of Robotic Manipulators book written by Abhaya Pal Singh, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Integral Transforms and Operational Calculus

Integral Transforms and Operational Calculus Book
Author : H. M. Srivastava
Publisher : MDPI
Release : 2019-11-20
ISBN : 303921618X
Language : En, Es, Fr & De

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Book Description :

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 multidisciplinary applications

Fractional Calculus

Fractional Calculus Book
Author : Dumitru Baleanu,Kai Diethelm,Enrico Scalas,Juan J Trujillo
Publisher : World Scientific
Release : 2016-09-15
ISBN : 9813140054
Language : En, Es, Fr & De

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Book Description :

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, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models. All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book will keep in mind the trade-off between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. The second edition of the book has been expanded and now includes a discussion of additional, newly developed numerical methods for fractional calculus and a chapter on the application of fractional calculus for modeling processes in the life sciences.

Hidden Markov Models in Finance

Hidden Markov Models in Finance Book
Author : Rogemar S. Mamon,Robert J Elliott
Publisher : Springer Science & Business Media
Release : 2007-04-26
ISBN : 0387711635
Language : En, Es, Fr & De

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Book Description :

A number of methodologies have been employed to provide decision making solutions globalized markets. Hidden Markov Models in Finance offers the first systematic application of these methods to specialized financial problems: option pricing, credit risk modeling, volatility estimation and more. The book provides tools for sorting through turbulence, volatility, emotion, chaotic events – the random "noise" of financial markets – to analyze core components.

Nonlocal and Fractional Operators

Nonlocal and Fractional Operators Book
Author : Luisa Beghin,Francesco Mainardi,Roberto Garrappa
Publisher : Springer Nature
Release : 2021-08-24
ISBN : 3030692361
Language : En, Es, Fr & De

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Book Description :

The purpose of this volume is to explore new bridges between different research areas involved in the theory and applications of the fractional calculus. In particular, it collects scientific and original contributions to the development of the theory of nonlocal and fractional operators. Special attention is given to the applications in mathematical physics, as well as in probability. Numerical methods aimed to the solution of problems with fractional differential equations are also treated in the book. The contributions have been presented during the international workshop "Nonlocal and Fractional Operators", held in Sapienza University of Rome, in April 2019, and dedicated to the retirement of Prof. Renato Spigler (University Roma Tre). Therefore we also wish to dedicate this volume to this occasion, in order to celebrate his scientific contributions in the field of numerical analysis and fractional calculus. The book is suitable for mathematicians, physicists and applied scientists interested in the various aspects of fractional calculus.

New Trends in Fractional Differential Equations with Real World Applications in Physics

New Trends in Fractional Differential Equations with Real World Applications in Physics Book
Author : Jagdev Singh,Jordan Yankov Hristov,Zakia Hammouch
Publisher : Frontiers Media SA
Release : 2020-12-30
ISBN : 2889663043
Language : En, Es, Fr & De

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Book Description :

Download New Trends in Fractional Differential Equations with Real World Applications in Physics book written by Jagdev Singh,Jordan Yankov Hristov,Zakia Hammouch, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.