Download or read book Quantum Duality in Mathematical Finance written by Paul McCloud and published by . This book was released on 2017 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical finance explores the consistency relationships between the prices of securities imposed by elementary economic principles. Commonplace among these are replicability and the absence of arbitrage, both essentially algebraic constraints on the valuation map from a security to its price.The discussion is framed in terms of observables, the securities, and states, the linear and positive maps from security to price. Founded on the principles of replicability and the absence of arbitrage, mathematical finance then equates to the theory of positive linear maps and their numeraire invariances. This acknowledges the algebraic nature of the defining principles which, crucially, may be applied in the context of quantum probability as well as the more familiar classical setting.Quantum groups are here defined to be dual pairs of ∗-Hopf algebras, and the central claim of this thesis is that the model for the dynamics of information relies solely on the quantum group properties of observables and states, as demonstrated by the application to finance. This naturally leads to the study of models based on restrictions of the ∗-Hopf algebras, such as the Quadratic Gauss model, that retain much of the phenomenology of their parent within a more tractable domain, and extensions of the ∗-Hopf algebras, such as the Linear Dirac model, with novel features unattainable in the classical case.
Download or read book Duality in Mathematical Finance written by Marco Frittelli and published by Springer. This book was released on 2007 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents an advanced and unified treatment of four important issues that have dominated the theoretical research in mathematical finance for the last ten years: (1) the fundamental theorem of asset pricing; (2) utility maximization in incomplete markets; (3) pricing in incomplete markets; (4) the risk measurement of a static payoff and of a cash-flow stream. The powerful tools of convex analysis and duality theory are systematically applied to investigate these topics, under very general assumptions on the financial markets. This duality approach reveals the prominent role of the investor’s preferences in all these fundamental issues and contributes to a deeper understanding of the economic aspects of the theory.
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.
Download or read book Quantum Finance written by Raymond S. T. Lee and published by Springer Nature. This book was released on 2019-11-15 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the exponential growth of program trading in the global financial industry, quantum finance and its underlying technologies have become one of the hottest topics in the fintech community. Numerous financial institutions and fund houses around the world require computer professionals with a basic understanding of quantum finance to develop intelligent financial systems. This book presents a selection of the author’s past 15 years’ R&D work and practical implementation of the Quantum Finance Forecast System – which integrates quantum field theory and related AI technologies to design and develop intelligent global financial forecast and quantum trading systems. The book consists of two parts: Part I discusses the basic concepts and theories of quantum finance and related AI technologies, including quantum field theory, quantum price fields, quantum price level modelling and quantum entanglement to predict major financial events. Part II then examines the current, ongoing R&D projects on the application of quantum finance technologies in intelligent real-time financial prediction and quantum trading systems. This book is both a textbook for undergraduate & masters level quantum finance, AI and fintech courses and a valuable resource for researchers and data scientists working in the field of quantum finance and intelligent financial systems. It is also of interest to professional traders/ quants & independent investors who would like to grasp the basic concepts and theory of quantum finance, and more importantly how to adopt this fascinating technology to implement intelligent financial forecast and quantum trading systems. For system implementation, the interactive quantum finance programming labs listed on the Quantum Finance Forecast Centre official site (QFFC.org) enable readers to learn how to use quantum finance technologies presented in the book.
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.
Download or read book MASTERING QUANTUM ANALYSIS FOR FINANCIAL GROWTH written by Marcel Souza and published by GAVEA LAB . This book was released on with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlock the untapped potential of quantum analysis and skyrocket your financial success with this groundbreaking book – "MASTERING QUANTUM ANALYSIS FOR FINANCIAL GROWTH" In this revolutionary guide, you'll dive deep into the world of quantum finance and discover how cutting-edge technologies can empower you to make smarter investment decisions. Whether you're a seasoned investor or a curious beginner, this comprehensive book will equip you with the knowledge and strategies to thrive in the dynamic world of quantum analysis. Embrace the power of quantum computing and gain a competitive edge by leveraging its processing capabilities to analyze complex financial data. Learn how to harness quantum algorithms to detect market patterns, forecast trends, and identify lucrative opportunities that traditional methods often overlook. Discover how to decode the language of quantum mechanics and apply its principles to interpret financial markets in a whole new light. This book will demystify the complexities of quantum analysis and present them in a digestible and actionable format, making it accessible to everyone. Learn how to use quantum computing to optimize portfolio management, risk assessment, and asset allocation. By harnessing the power of quantum analysis, you can achieve higher returns and safeguard your investments like never before. Explore the intersection of quantum physics and behavioral finance, gaining insights into human decision-making biases and using this knowledge to your advantage. With a deeper understanding of the psychological factors driving market movements, you'll be better equipped to navigate market volatility and capitalize on opportunities. Tap into the potential of quantum machine learning and uncover hidden patterns in financial data that can lead to breakthrough investment strategies. By combining quantum computing with machine learning, you'll be at the forefront of the financial revolution. From cryptocurrency trading to traditional stock markets, "MASTERING QUANTUM ANALYSIS FOR FINANCIAL GROWTH" covers a wide range of financial instruments, allowing you to apply quantum principles to any investment avenue. Unleash the power of quantum analysis and stay ahead of the curve in the fast-paced world of finance. This book will guide you through the intricate world of quantum finance, providing you with the tools to make informed and profitable decisions. Prepare to revolutionize your investment approach and embark on a journey of financial prosperity with "MASTERING QUANTUM ANALYSIS FOR FINANCIAL GROWTH" Embrace the future of finance, where quantum computing meets savvy investment strategies, and unlock the door to limitless opportunities. The potential for financial success is waiting – are you ready to seize it?
Download or read book Paris Princeton Lectures on Mathematical Finance 2002 written by Peter Bank and published by Springer. This book was released on 2003-12-10 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Paris-Princeton Lectures in Financial Mathematics, of which this is the first volume, will, on an annual basis, publish cutting-edge research in self-contained, expository articles from outstanding - established or upcoming! - specialists. The aim is to produce a series of articles that can serve as an introductory reference for research in the field. It arises as a result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with articles by P. Bank/H. Föllmer, F. Baudoin, L.C.G. Rogers, and M. Soner/N. Touzi.
Download or read book Mathematical Foundations of Quantum Theory written by A.R. Marlow and published by Elsevier. This book was released on 2012-12-02 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues. Organized into 20 chapters, this book's opening chapters establish a sound mathematical basis for quantum theory and a mode of observation in the double slit experiment. This book then describes the Lorentz particle system and other mathematical structures with which fundamental quantum theory must deal, and then some unsolved problems in the quantum logic approach to the foundations of quantum mechanics are considered. Considerable chapters cover topics on manuals and logics for quantum mechanics. This book also examines the problems in quantum logic, and then presents examples of their interpretation and relevance to nonclassical logic and statistics. The accommodation of conventional Fermi-Dirac and Bose-Einstein statistics in quantum mechanics or quantum field theory is illustrated. The final chapters of the book present a system of axioms for nonrelativistic quantum mechanics, with particular emphasis on the role of density operators as states. Specific connections of this theory with other formulations of quantum theory are also considered. These chapters also deal with the determination of the state of an elementary quantum mechanical system by the associated position and momentum distribution. This book is of value to physicists, mathematicians, and researchers who are interested in quantum theory.
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.
Download or read book Quantum Economics and Finance written by David Orrell and published by . This book was released on 2022-07-13 with total page 0 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 third edition contains many updates including new material on quantum logic and quantum agent-based models. David Orrell is an applied mathematician with extensive experience in mathematical modelling, and the author of a dozen books on science and economics.
Download or read book Mathematical Aspects of Conformal and Topological Field Theories and Quantum Groups written by Paul J. Sally (Jr.) and published by American Mathematical Soc.. This book was released on 1994 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers presented by speakers at the AMS-IMS-SIAM Joint Summer Research Conference on Conformal Field Theory, Topological Field Theory and Quantum Groups, held at Mount Holyoke College in June 1992. One group of papers deals with one aspect of conformal field theory, namely, vertex operator algebras or superalgebras and their representations. Another group deals with various aspects of quantum groups. Other topics covered include the theory of knots in three-manifolds, symplectic geometry, and tensor products. This book provides an excellent view of some of the latest developments in this growing field of research.
Download or read book From Quadratic Gaussian to Quantum Groups written by Paul McCloud and published by . This book was released on 2017 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical finance explores the consistency relationships between the prices of securities imposed by elementary economic principles. Commonplace among these are replicability and the absence of arbitrage, both essentially algebraic constraints on the valuation map from a security to its price.The discussion is framed in terms of observables, the securities, and states, the linear and positive maps from security to price. Founded on the principles of replicability and the absence of arbitrage, mathematical finance then equates to the theory of positive linear maps and their scale invariances. This recognises that the defining principles are in essence algebraic, and may be satisfied in circumstances more general than the classical probabilistic setting.These slides consider the dual Hopf algebraic structures of observables and states, and how they may be utilised to create efficient models for pricing. This naturally leads to the study of models based on restrictions of the dual Hopf algebras, such as the Quadratic Gauss model, that retain much of the phenomenology of their parents within a more tractable domain, and extensions of the dual Hopf algebras, such as the Linear Dirac model, with novel features unattainable in the classical case.
Download or read book Mathematical Control Theory and Finance written by Andrey Sarychev and published by Springer Science & Business Media. This book was released on 2009-03-31 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control theory provides a large set of theoretical and computational tools with applications in a wide range of ?elds, running from ”pure” branches of mathematics, like geometry, to more applied areas where the objective is to ?nd solutions to ”real life” problems, as is the case in robotics, control of industrial processes or ?nance. The ”high tech” character of modern business has increased the need for advanced methods. These rely heavily on mathematical techniques and seem indispensable for competitiveness of modern enterprises. It became essential for the ?nancial analyst to possess a high level of mathematical skills. C- versely, the complex challenges posed by the problems and models relevant to ?nance have, for a long time, been an important source of new research topics for mathematicians. The use of techniques from stochastic optimal control constitutes a well established and important branch of mathematical ?nance. Up to now, other branches of control theory have found comparatively less application in ?n- cial problems. To some extent, deterministic and stochastic control theories developed as di?erent branches of mathematics. However, there are many points of contact between them and in recent years the exchange of ideas between these ?elds has intensi?ed. Some concepts from stochastic calculus (e.g., rough paths) havedrawntheattentionofthedeterministiccontroltheorycommunity.Also, some ideas and tools usual in deterministic control (e.g., geometric, algebraic or functional-analytic methods) can be successfully applied to stochastic c- trol.
Download or read book Tales of the Quantum written by Art Hobson and published by Oxford University Press. This book was released on 2017 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a book about the quanta that make up our universe--the highly unified bundles of energy of which everything is made. It explains wave-particle duality, randomness, quantum states, non-locality, Schrodinger's cat, quantum jumps, and more, in everyday language for non-scientists and scientists who wish to fathom science's most fundamental theory.
Download or read book A Robust Approach to Pricing hedging Duality and Related Problems in Mathematical Finance written by Zhaoxu Hou and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cones and Duality written by Charalambos D. Aliprantis and published by American Mathematical Soc.. This book was released on 2007-06-12 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordered vector spaces and cones made their debut in mathematics at the beginning of the twentieth century. They were developed in parallel (but from a different perspective) with functional analysis and operator theory. Before the 1950s, ordered vector spaces appeared in the literature in a fragmented way. Their systematic study began around the world after 1950 mainly through the efforts of the Russian, Japanese, German, and Dutch schools. Since cones are being employed to solve optimization problems, the theory of ordered vector spaces is an indispensable tool for solving a variety of applied problems appearing in several diverse areas, such as engineering, econometrics, and the social sciences. For this reason this theory plays a prominent role not only in functional analysis but also in a wide range of applications. This is a book about a modern perspective on cones and ordered vector spaces. It includes material that has not been presented earlier in a monograph or a textbook. With many exercises of varying degrees of difficulty, the book is suitable for graduate courses. Most of the new topics currently discussed in the book have their origins in problems from economics and finance. Therefore, the book will be valuable to any researcher and graduate student who works in mathematics, engineering, economics, finance, and any other field that uses optimization techniques.
Download or read book Foundations of Grothendieck Duality for Diagrams of Schemes written by Joseph Lipman and published by Springer Science & Business Media. This book was released on 2009-02-05 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part written by Joseph Lipman, accessible to mid-level graduate students, is a full exposition of the abstract foundations of Grothendieck duality theory for schemes (twisted inverse image, tor-independent base change,...), in part without noetherian hypotheses, and with some refinements for maps of finite tor-dimension. The ground is prepared by a lengthy treatment of the rich formalism of relations among the derived functors, for unbounded complexes over ringed spaces, of the sheaf functors tensor, hom, direct and inverse image. Included are enhancements, for quasi-compact quasi-separated schemes, of classical results such as the projection and Künneth isomorphisms. In the second part, written independently by Mitsuyasu Hashimoto, the theory is extended to the context of diagrams of schemes. This includes, as a special case, an equivariant theory for schemes with group actions. In particular, after various basic operations on sheaves such as (derived) direct images and inverse images are set up, Grothendieck duality and flat base change for diagrams of schemes are proved. Also, dualizing complexes are studied in this context. As an application to group actions, we generalize Watanabe's theorem on the Gorenstein property of invariant subrings.
