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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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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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