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Mathematical Methods And Quantum Mathematics For Economics And Finance
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Book Synopsis Mathematical Methods and Quantum Mathematics for Economics and Finance by : Belal Ehsan Baaquie
Download or read book Mathematical Methods and Quantum Mathematics for Economics and Finance written by Belal Ehsan Baaquie and published by Springer Nature. This book was released on 2020-08-10 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given the rapid pace of development in economics and finance, a concise and up-to-date introduction to mathematical methods has become a prerequisite for all graduate students, even those not specializing in quantitative finance. This book offers an introductory text on mathematical methods for graduate students of economics and finance–and leading to the more advanced subject of quantum mathematics. The content is divided into five major sections: mathematical methods are covered in the first four sections, and can be taught in one semester. The book begins by focusing on the core subjects of linear algebra and calculus, before moving on to the more advanced topics of probability theory and stochastic calculus. Detailed derivations of the Black-Scholes and Merton equations are provided – in order to clarify the mathematical underpinnings of stochastic calculus. Each chapter of the first four sections includes a problem set, chiefly drawn from economics and finance. In turn, section five addresses quantum mathematics. The mathematical topics covered in the first four sections are sufficient for the study of quantum mathematics; Black-Scholes option theory and Merton’s theory of corporate debt are among topics analyzed using quantum mathematics.
Book Synopsis Mathematical Methods and Quantum Mathematics for Economics and Finance by : Belal Ehsan Baaquie
Download or read book Mathematical Methods and Quantum Mathematics for Economics and Finance written by Belal Ehsan Baaquie and published by Springer. This book was released on 2020-10-23 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given the rapid pace of development in economics and finance, a concise and up-to-date introduction to mathematical methods has become a prerequisite for all graduate students, even those not specializing in quantitative finance. This book offers an introductory text on mathematical methods for graduate students of economics and finance–and leading to the more advanced subject of quantum mathematics. The content is divided into five major sections: mathematical methods are covered in the first four sections, and can be taught in one semester. The book begins by focusing on the core subjects of linear algebra and calculus, before moving on to the more advanced topics of probability theory and stochastic calculus. Detailed derivations of the Black-Scholes and Merton equations are provided – in order to clarify the mathematical underpinnings of stochastic calculus. Each chapter of the first four sections includes a problem set, chiefly drawn from economics and finance. In turn, section five addresses quantum mathematics. The mathematical topics covered in the first four sections are sufficient for the study of quantum mathematics; Black-Scholes option theory and Merton’s theory of corporate debt are among topics analyzed using quantum mathematics.
Book Synopsis Quantum Field Theory for Economics and Finance by : B. E. Baaquie
Download or read book Quantum Field Theory for Economics and Finance written by B. E. Baaquie and published by Cambridge University Press. This book was released on 2018-08-23 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to how the mathematical tools from quantum field theory can be applied to economics and finance. Providing a range of quantum mathematical techniques for designing financial instruments, it demonstrates how a range of topics have quantum mechanical formulations, from asset pricing to interest rates.
Book Synopsis Quantum Economics and Finance by : David Orrell
Download or read book Quantum Economics and Finance written by David Orrell and published by . This book was released on 2021-05-16 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The word "quantum" is from the Latin for "how much" and in this book mathematician David Orrell shows how it applies to the world of economic transactions. Written in clear and accessible language, the book covers the essential mathematics behind topics such as quantum cognition, option pricing, and quantum game theory, and delves into the nuts and bolts of quantum mechanics, the principles of quantum economic modelling, and the basics of quantum computation. On the way the reader will learn how quantum interference can be used to model cognitive dissonance, how a quantum walk goes further than a random walk, and how financial entanglement explains the rate of mortgage default. It is aimed at anyone who wants to understand the quantum ideas working their way into economics and finance, without getting drowned in wave equations. As interest in quantum computing grows, many companies from established banks to startups are looking at ways to perform financial simulations using quantum algorithms. But what if we should be using quantum models anyway - because the monetary system has quantum properties of its own, and because they work? The field is developing rapidly, and this second edition contains many updates including new material on quantum logic and quantum agent-based models, and a guest chapter from Ramy Aboushelbaya and Marko Mayr of Quantum Dice on quantum hardware. David Orrell is an applied mathematician with extensive experience in mathematical modelling, and the author of a dozen books on science and economics.
Book Synopsis Mathematical Methods in Quantum Mechanics by : Gerald Teschl
Download or read book Mathematical Methods in Quantum Mechanics written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2009 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).
Book Synopsis Quantum Computers by : Belal Ehsan Baaquie
Download or read book Quantum Computers written by Belal Ehsan Baaquie and published by Springer Nature. This book was released on 2023-01-03 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents various theories and algorithms to create a quantum computer. The concept of the classical and quantum computers, and the concept of circuits and gates are reviewed. The example of the Deutsch and the Deutsch-Josca algorithm is discussed to illustrate some key features of quantum computing. The Grover algorithm, considered to be of major milestone of the subject, is discussed in detail to exemplify the techniques used in computer algorithms. The role of quantum superposition (also called quantum parallelism) and of quantum entanglement is discussed in order to understand the key advantages of a quantum over a classical computer.
Download or read book Quantum Economics written by David Orrell and published by Icon Books. This book was released on 2018-07-05 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: A decade after the financial crisis, there is a growing consensus that economics has failed and needs to go back to the drawing board. David Orrell argues that it has been trying to solve the wrong problem all along. Economics sees itself as the science of scarcity. Instead, it should be the science of money (which plays a surprisingly small role in mainstream theory). And money is a substance that turns out to have a quantum nature of its own. Just as physicists learn about matter by studying the exchange of particles at the subatomic level, so economics should begin by analysing the nature of money-based transactions. Quantum Economics therefore starts with the meaning of the phrase 'how much' – or, to use the Latin word, quantum. From quantum physics to the dualistic properties of money, via the emerging areas of quantum finance and quantum cognition, this profoundly important book reveals that quantum economics is to neoclassical economics what quantum physics is to classical physics – a genuine turning point in our understanding.
Book Synopsis Quantum Finance by : Belal E. Baaquie
Download or read book Quantum Finance written by Belal E. Baaquie and published by Cambridge University Press. This book was released on 2007-07-23 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book applies the mathematics and concepts of quantum mechanics and quantum field theory to the modelling of interest rates and the theory of options. Particular emphasis is placed on path integrals and Hamiltonians. Financial mathematics is dominated by stochastic calculus. The present book offers a formulation that is completely independent of that approach. As such many results emerge from the ideas developed by the author. This work will be of interest to physicists and mathematicians working in the field of finance, to quantitative analysts in banks and finance firms and to practitioners in the field of fixed income securities and foreign exchange. The book can also be used as a graduate text for courses in financial physics and financial mathematics.
Book Synopsis Looking Beyond The Frontiers Of Science: Dedicated To The 80th Birthday Of Kk Phua by : Lars Brink
Download or read book Looking Beyond The Frontiers Of Science: Dedicated To The 80th Birthday Of Kk Phua written by Lars Brink and published by World Scientific. This book was released on 2022-07-25 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Kok Khoo Phua is the Founding Director and Emeritus Professor of the Institute of Advanced Studies (IAS) at Nanyang Technological University (NTU) and Adjunct Professor of Department of Physics both at Nanyang Technological University (NTU) and National University of Singapore (NUS). He is the Chairman and Editor-in-Chief of World Scientific Publishing Co Pte Ltd.When he was elected a Fellow of the American Physical Society (APS) in 2009, the citation read: 'For tireless efforts to strengthen scientific research throughout Asia and promote international physics education and scholarly exchanges, and for enriching science and education through the World Scientific Publishing Company he founded.'This unique volume on the occasion of his 80th birthday is a compilation of tributes from his friends who have known him for decades along with scientific articles that celebrate his visionary approach to promote science worldwide.
Book Synopsis Mathematical Horizons for Quantum Physics by : Huzihiro Araki
Download or read book Mathematical Horizons for Quantum Physics written by Huzihiro Araki and published by World Scientific. This book was released on 2010 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control of the molecular alignment or orientation by laser pulses / Arne Keller -- Quantum computing and devices : A short introduction / Zhigang Zhang, Viswanath Ramakrishna and Goong Chen -- Dynamics of mixed classical-quantum systems, geometric quantization and coherent states / Hans-Rudolf Jauslin and Dominique Sugny -- Quantum memories as open systems / Robert Alicki -- Two mathematical problems in quantum information theory / Alexander S. Holevo -- Dissipatively induced bipartite entanglement / Fabio Benatti -- Scattering in nonrelativistic quantum field theory / Jan Derezinski -- Mathematical theory of atoms and molecules / Volker Bach
Book Synopsis Ubiquitous Quantum Structure by : Andrei Y. Khrennikov
Download or read book Ubiquitous Quantum Structure written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2010-01-23 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum-like structure is present practically everywhere. Quantum-like (QL) models, i.e. models based on the mathematical formalism of quantum mechanics and its generalizations can be successfully applied to cognitive science, psychology, genetics, economics, finances, and game theory. This book is not about quantum mechanics as a physical theory. The short review of quantum postulates is therefore mainly of historical value: quantum mechanics is just the first example of the successful application of non-Kolmogorov probabilities, the first step towards a contextual probabilistic description of natural, biological, psychological, social, economical or financial phenomena. A general contextual probabilistic model (Växjö model) is presented. It can be used for describing probabilities in both quantum and classical (statistical) mechanics as well as in the above mentioned phenomena. This model can be represented in a quantum-like way, namely, in complex and more general Hilbert spaces. In this way quantum probability is totally demystified: Born's representation of quantum probabilities by complex probability amplitudes, wave functions, is simply a special representation of this type.
Book Synopsis Quantitative Methods in Economics and Finance by : Tomas Kliestik
Download or read book Quantitative Methods in Economics and Finance written by Tomas Kliestik and published by MDPI. This book was released on 2021-04-08 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the Special Issue “Quantitative Methods in Economics and Finance” of the journal Risks was to provide a collection of papers that reflect the latest research and problems of pricing complex derivates, simulation pricing, analysis of financial markets, and volatility of exchange rates in the international context. This book can be used as a reference for academicians and researchers who would like to discuss and introduce new developments in the field of quantitative methods in economics and finance and explore applications of quantitative methods in other business areas.
Book Synopsis Mathematical Economics by : Vasily E. Tarasov
Download or read book Mathematical Economics written by Vasily E. Tarasov and published by MDPI. This book was released on 2020-06-03 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Methods for Economic Theory 1 by : James C. Moore
Download or read book Mathematical Methods for Economic Theory 1 written by James C. Moore and published by Springer Science & Business Media. This book was released on 1999-10-19 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work functions both as a textbook for graduates and as a reference for economic scholars. Assuming only the minimal mathematics background required of every second-year graduate, the two volumes provide a self-contained and careful development of mathematics through locally convex topological vector spaces, and fixed-point, separation, and selection theorems in such spaces. Volume One covers basic set theory, sequences and series, continuous and semi-continuous functions, an introduction to general linear spaces, basic convexity theory, and applications to economics.
Book Synopsis The Unity of Science and Economics by : Jing Chen
Download or read book The Unity of Science and Economics written by Jing Chen and published by Springer. This book was released on 2015-11-06 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a new economic theory developed from physical and biological principles. It explains how technology, social systems and economic values are intimately related to resources. Many people have recognized that mainstream (neoclassical) economic theories are not consistent with physical laws and often not consistent with empirical patterns, but most feel that economic activities are too complex to be described by a simple and coherent mathematical theory. While social systems are indeed complex, all life systems, including social systems, satisfy two principles. First, all systems need to extract resources from the external environment to compensate for their consumption. Second, for a system to be viable, the amount of resource extraction has to be no less than the level of consumption. From these two principles, we derive a quantitative theory of major factors in economic activities, such as fixed cost, variable cost, discount rate, uncertainty and duration. The mathematical theory enables us to systematically measure the effectiveness of different policies and institutional structures at varying levels of resource abundance and cost.The theory presented in this book shows that there do not exist universally optimal policies or institutional structures. Instead, the impacts of different policies or social structures have to be measured within the context of existing levels of resource abundance. As the physical costs of extracting resources rise steadily, many policy assumptions adopted in mainstream economic theories, and workable in times of cheap and abundant energy supplies and other resources, need to be reconsidered. In this rapidly changing world, the theory presented here provides a solid foundation for examining the long-term impacts of today's policy decisions.
Book Synopsis Path Integrals and Hamiltonians by : Belal E. Baaquie
Download or read book Path Integrals and Hamiltonians written by Belal E. Baaquie and published by Cambridge University Press. This book was released on 2014-03-27 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a pedagogical introduction to the essential principles of path integrals and Hamiltonians, this book describes cutting-edge quantum mathematical techniques applicable to a vast range of fields, from quantum mechanics, solid state physics, statistical mechanics, quantum field theory, and superstring theory to financial modeling, polymers, biology, chemistry, and quantum finance. Eschewing use of the Schrödinger equation, the powerful and flexible combination of Hamiltonian operators and path integrals is used to study a range of different quantum and classical random systems, succinctly demonstrating the interplay between a system's path integral, state space, and Hamiltonian. With a practical emphasis on the methodological and mathematical aspects of each derivation, this is a perfect introduction to these versatile mathematical methods, suitable for researchers and graduate students in physics and engineering.
Book Synopsis Quantum Social Science by : Emmanuel Haven
Download or read book Quantum Social Science written by Emmanuel Haven and published by Cambridge University Press. This book was released on 2013-01-17 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by world experts in the foundations of quantum mechanics and its applications to social science, this book shows how elementary quantum mechanical principles can be applied to decision-making paradoxes in psychology and used in modelling information in finance and economics. The book starts with a thorough overview of some of the salient differences between classical, statistical and quantum mechanics. It presents arguments on why quantum mechanics can be applied outside of physics and defines quantum social science. The issue of the existence of quantum probabilistic effects in psychology, economics and finance is addressed and basic questions and answers are provided. Aimed at researchers in economics and psychology, as well as physics, basic mathematical preliminaries and elementary concepts from quantum mechanics are defined in a self-contained way.
