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Quantum finance : path integrals and Hamiltonians for options and interest rates
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ISBN: 0521840457 0521714788 1107162777 0511265409 051126612X 0511331630 0511617577 1280750138 0511263864 0511264690 9780511266126 9780511263866 9780511264696 0511262264 9780511262265 9780511265402 9780511617577 9786610750139 6610750130 9780521840453 9780521714785 9781280750137 Year: 2004 Publisher: Cambridge, U.K. ; New York : Cambridge University Press,

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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.


Book
Mathematical methods and quantum mathematics for economics and finance
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ISBN: 9811566119 9811566100 Year: 2020 Publisher: Singapore : Springer,

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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.


Book
Interest rates and coupon bonds in quantum finance
Author:
ISBN: 9780511808715 9780521889285 9780511652028 051165202X 9780511634345 051163434X 0511808712 9780511633133 0511633130 0521889286 0511631928 9780511631924 1107211891 9781107211896 Year: 2010 Publisher: Cambridge, UK ; New York : Cambridge University Press,

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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.


Book
Quantum field theory for economics and finance
Author:
ISBN: 1108502423 1108399681 1108503748 Year: 2018 Publisher: Cambridge : Cambridge University Press,

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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.


Book
Exploring the invisible universe
Authors: ---
ISBN: 9814618683 9789814618687 9789814618670 9814618675 Year: 2015 Publisher: Hackensack, New Jersey

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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."--


Book
Quantum computers : theory and algorithms
Authors: ---
ISBN: 9811975175 9811975167 Year: 2023 Publisher: Singapore : Springer,

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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.


Book
Proceedings of the Conference in Honour of Murray Gell-Mann's 80th Birthday
Authors: --- --- ---
ISBN: 1283145286 9786613145284 9814335614 9789814335614 9789814335607 9814338621 9814335606 9789814338622 9781283145282 6613145289 Year: 2011 Publisher: Hackensack, N.J. World Scientific

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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.

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