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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.

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

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.

Economic Dynamics with Memory

Economic Dynamics with Memory Book
Author : Vasily E. Tarasov,Valentina V. Tarasova
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2021-01-18
ISBN : 3110624818
Language : En, Es, Fr & De

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Book Description :

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.

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.

Advanced Mathematical Methods

Advanced Mathematical Methods Book
Author : Francesco Mainardi,Andrea Giusti
Publisher : MDPI
Release : 2020-02-05
ISBN : 3039282468
Language : En, Es, Fr & De

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Book Description :

The many technical and computational problems that appear to be constantly emerging in various branches of physics and engineering beg for a more detailed understanding of the fundamental mathematics that serves as the cornerstone of our way of understanding natural phenomena. The purpose of this Special Issue was to establish a brief collection of carefully selected articles authored by promising young scientists and the world's leading experts in pure and applied mathematics, highlighting the state-of-the-art of the various research lines focusing on the study of analytical and numerical mathematical methods for pure and applied sciences.

Stochastic Calculus for Fractional Brownian Motion and Related Processes

Stochastic Calculus for Fractional Brownian Motion and Related Processes Book
Author : IUliia S. Mishura,I͡Ulii͡a S. Mishura,Julija S. Mišura,Yuliya Mishura,Ûliâ Stepanovna Mišura
Publisher : Springer Science & Business Media
Release : 2008-01-02
ISBN : 3540758720
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.

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.

Computational Science and its Applications

Computational Science and its Applications Book
Author : A. H. Siddiqi,R. C. Singh,G. D. Veerappa Gowda
Publisher : CRC Press
Release : 2020-10-21
ISBN : 1000193691
Language : En, Es, Fr & De

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Book Description :

Computational science is a rapidly growing multidisciplinary field concerned with the design, implementation, and use of mathematical models to analyze and solve real-world problems. It is an area of science that spans many disciplines and which involves the development of models and allows the use of computers to perform simulations or numerical analysis to understand problems that are computational and theoretical. Computational Science and its Applications provides an opportunity for readers to develop abilities to pose and solve problems that combine insights from one or more disciplines from the natural sciences with mathematical tools and computational skills. This requires a unique combination of applied and theoretical knowledge and skills. The topics covered in this edited book are applications of wavelet and fractals, modeling by partial differential equations on flat structure as well as on graphs and networks, computational linguistics, prediction of natural calamities and diseases like epilepsy seizure, heart attack, stroke, biometrics, modeling through inverse problems, interdisciplinary topics of physics, mathematics, and medical science, and modeling of terrorist attacks and human behavior. The focus of this book is not to educate computer specialists, but to provide readers with a solid understanding of basic science as well as an integrated knowledge on how to use essential methods from computational science. Features: Modeling of complex systems Cognitive computing systems for real-world problems Presentation of inverse problems in medical science and their numerical solutions Challenging research problems in many areas of computational science This book could be used as a reference book for researchers working in theoretical research as well as those who are doing modeling and simulation in such disciplines as physics, biology, geoscience, and mathematics, and those who have a background in computational science.

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.

Fractional Modeling and Controller Design of Robotic Manipulators

Fractional Modeling and Controller Design of Robotic Manipulators Book
Author : Abhaya Pal Singh,Dipankar Deb,Himanshu Agrawal,Valentina E. Balas
Publisher : Springer Nature
Release : 2020-10-15
ISBN : 3030582477
Language : En, Es, Fr & De

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Book Description :

This book at hand is an appropriate addition to the field of fractional calculus applied to control systems. If an engineer or a researcher wishes to delve into fractional-order systems, then this book has many collections of such systems to work upon, and this book also tells the reader about how one can convert an integer-order system into an appropriate fractional-order one through an efficient and simple algorithm. If the reader further wants to explore the controller design for the fractional-order systems, then for them, this book provides a variety of controller design strategies. The use of fractional-order derivatives and integrals in control theory leads to better results than integer-order approaches and hence provides solid motivation for further development of control theory. Fractional-order models are more useful than the integer-order models when accuracy is of paramount importance. Real-time experimental validation of controller design strategies for the fractional-order plants is available. This book is beneficial to the academic institutes for postgraduate and advanced research-level that need a specific textbook on fractional control and its applications in srobotic manipulators. The book is also a valuable teaching and learning resource for undergraduate and postgraduate students.

Probability Finance and Insurance

Probability  Finance and Insurance Book
Author : T. L. Lai,Hailiang Yang,Siu Pang Yung
Publisher : World Scientific
Release : 2004
ISBN : 9812388532
Language : En, Es, Fr & De

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Book Description :

This workshop was the first of its kind in bringing together researchers in probability theory, stochastic processes, insurance and finance from mainland China, Taiwan, Hong Kong, Singapore, Australia and the United States. In particular, as China has joined the WTO, there is a growing demand for expertise in actuarial sciences and quantitative finance. The strong probability research and graduate education programs in many of China's universities can be enriched by their outreach in fields that are of growing importance to the country's expanding economy, and the workshop and its proceedings can be regarded as the first step in this direction.This book presents the most recent developments in probability, finance and actuarial sciences, especially in Chinese probability research. It focuses on the integration of probability theory with applications in finance and insurance. It also brings together academic researchers and those in industry and government. With contributions by leading authorities on probability theory ? particularly limit theory and large derivations, valuation of credit derivatives, portfolio selection, dynamic protection and ruin theory ? it is an essential source of ideas and information for graduate students and researchers in probability theory, mathematical finance and actuarial sciences, and thus every university should acquire a copy.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? Index to Social Sciences & Humanities Proceedings? (ISSHP? / ISI Proceedings)? Index to Social Sciences & Humanities Proceedings (ISSHP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences