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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.
Stock options --- Interest rates --- Options d'achat d'actions --- Taux d'intérêt --- Mathematical models --- Modèles mathématiques --- AA / International- internationaal --- 305.91 --- 305.7 --- 333.831.0 --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles. --- Econometrie van het gedrag van de financiële tussenpersonen. Monetaire econometrische modellen. Monetaire agregaten. vraag voor geld. Krediet. Rente. --- Evolutie van de rentetarieven naar de duur van de bedragen. Verband tussen de diverse rentetarieven: algemeenheden. --- Mathematical models. --- Taux d'intérêt --- Modèles mathématiques --- Options, Stock --- Options (Finance) --- Econometrie van het gedrag van de financiële tussenpersonen. Monetaire econometrische modellen. Monetaire agregaten. vraag voor geld. Krediet. Rente --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Evolutie van de rentetarieven naar de duur van de bedragen. Verband tussen de diverse rentetarieven: algemeenheden --- Physics --- General and Others
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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, and the topics covered focus on analyzing Black-Scholes option theory and Merton’s theory of corporate debt.
Economic theory. --- Economics, Mathematical . --- Statistics . --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Quantitative Finance. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Economics --- Mathematical economics --- Economic theory --- Political economy --- Social sciences --- Economic man --- Methodology --- Economics. --- Economics, Mathematical. --- Statistics.
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"The economic crisis of 2008 has shown that the capital markets need new theoretical and mathematical concepts to describe and price financial instruments. Focusing almost exclusively on interest rates and coupon bonds, this book does not employ stochastic calculus - the bedrock of the present day mathematical finance - for any of the derivations. Instead, it analyzes interest rates and coupon bonds using quantum finance. The Heath-Jarrow-Morton and the Libor Market Model are generalized by realizing the forward and Libor interest rates as an imperfectly correlated quantum field. Theoretical models have been calibrated and tested using bond and interest rates market data. Building on the principles formulated in the author's previous book (Quantum Finance, Cambridge University Press, 2004) this ground-breaking book brings together a diverse collection of theoretical and mathematical interest rate models. It will interest physicists and mathematicians researching in finance, and professionals working in the finance industry"--Provided by publisher.
Finance --- Interest rates --- Zero coupon securities --- 305.91 --- 333.605 --- 333.642 --- AA / International- internationaal --- Bonds, Zero coupon --- Liquid yield option notes --- Zero coupon bonds --- Zeros (Securities) --- Securities --- Money market rates --- Rate of interest --- Rates, Interest --- Interest --- Funding --- Funds --- Economics --- Currency question --- Econometrie van de financiële activa. Portfolio allocation en management. CAPM. Bubbles --- Nieuwe financiële instrumenten --- Termijn. Financial futures --- Interest rates. --- Zero coupon securities. --- Finance.
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An introduction to how the mathematical tools from quantum field theory can be applied to economics and finance, providing a wide range of quantum mathematical techniques for designing financial instruments. The ideas of Lagrangians, Hamiltonians, state spaces, operators and Feynman path integrals are demonstrated to be the mathematical underpinning of quantum field theory, and which are employed to formulate a comprehensive mathematical theory of asset pricing as well as of interest rates, which are validated by empirical evidence. Numerical algorithms and simulations are applied to the study of asset pricing models as well as of nonlinear interest rates. A range of economic and financial topics are shown to have quantum mechanical formulations, including options, coupon bonds, nonlinear interest rates, risky bonds and the microeconomic action functional. This is an invaluable resource for experts in quantitative finance and in mathematics who have no specialist knowledge of quantum field theory.
Economics --- Finance --- Quantum field theory. --- Relativistic quantum field theory --- Field theory (Physics) --- Quantum theory --- Relativity (Physics) --- Economics, Mathematical --- Mathematical models.
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""Why"? Why is the world, the Universe the way it is? Is space infinitely large? How small is small? What happens when one continues to divide matter into ever smaller pieces? Indeed, what is matter? Is there anything else besides what can be seen? Pursuing the questions employing the leading notions of physics, one soon finds that the tangible and visible world dissolves — rather unexpectedly — into invisible things and domains that are beyond direct perception. A remarkable feature of our Universe is that most of its constituents turn out to be invisible, and this fact is brought out with great force by this book. Exploring the Invisible Universe covers the gamut of topics in advanced modern physics and provides extensive and well substantiated answers to these questions and many more. Discussed in a non-technical, yet also non-trivial manner, are topics dominated by invisible things — such as Black Holes and Superstrings as well as Fields, Gravitation, the Standard Model, Cosmology, Relativity, the Origin of Elements, Stars and Planetary Evolution, and more. Just giving the answer, as so many books do, is really not telling anything at all. To truly answer the "why" questions of nature, one needs to follow the chain of reasoning that scientists have used to come to the conclusions they have. This book does not shy away from difficult-to-explain topics by reducing them to one-line answers and power phrases suitable for a popular talk show. The explanations are rigorous and straight to the point. This book is rarely mathematical without being afraid, however, to use elementary mathematics when called for. In order to achieve this, a large number of detailed figures, specially developed for this book and found nowhere else, convey insights that otherwise might either be inaccessible or need lengthy and difficult-to-follow explanations. After Exploring the Invisible Universe, a reader will have a deeper insight into our current understanding of the foundations of Nature and be able to answer all the questions above and then some. To understand Nature and the cutting edge ideas of contemporary physics, this is the book to have."--
Physics --- Physique --- Ouvrages de vulgarisation
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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.
Quantum computers. --- Computer science. --- Informatics --- Science --- Computers
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The Conference on Quantum Mechanics, Elementary Particles, Quantum Cosmology and Complexity was held in honour of Professor Murray Gell-Mann's 80th birthday in Singapore on 24-26 February 2010. The conference paid tribute to Professor Gell-Mann's great achievements in the elementary particle physics. This notable birthday volume contains the presentations made at the conference by many eminent scientists, including Nobel laureates C N Yang, G 't Hooft and K Wilson. Other invited speakers include G Zweig, N Samios, M Karliner, G Karl, M Shifman, J Ellis, S Adler and A Zichichi.
Quantum theory --- Particles (Nuclear physics) --- Quantum cosmology
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