The Mathematics Of Arbitrage
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The Mathematics Of Arbitrage
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Author : Freddy Delbaen
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-14
The Mathematics Of Arbitrage written by Freddy Delbaen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-14 with Mathematics categories.
Proof of the "Fundamental Theorem of Asset Pricing" in its general form by Delbaen and Schachermayer was a milestone in the history of modern mathematical finance and now forms the cornerstone of this book. Puts into book format a series of major results due mostly to the authors of this book. Embeds highest-level research results into a treatment amenable to graduate students, with introductory, explanatory background. Awaited in the quantitative finance community.
Market Consistent Prices
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Author : Pablo Koch-Medina
language : en
Publisher: Springer Nature
Release Date : 2020-07-16
Market Consistent Prices written by Pablo Koch-Medina and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-16 with Mathematics categories.
Arbitrage Theory provides the foundation for the pricing of financial derivatives and has become indispensable in both financial theory and financial practice. This textbook offers a rigorous and comprehensive introduction to the mathematics of arbitrage pricing in a discrete-time, finite-state economy in which a finite number of securities are traded. In a first step, various versions of the Fundamental Theorem of Asset Pricing, i.e., characterizations of when a market does not admit arbitrage opportunities, are proved. The book then focuses on incomplete markets where the main concern is to obtain a precise description of the set of “market-consistent” prices for nontraded financial contracts, i.e. the set of prices at which such contracts could be transacted between rational agents. Both European-type and American-type contracts are considered. A distinguishing feature of this book is its emphasis on market-consistent prices and a systematic description of pricing rules, also at intermediate dates. The benefits of this approach are most evident in the treatment of American options, which is novel in terms of both the presentation and the scope, while also presenting new results. The focus on discrete-time, finite-state models makes it possible to cover all relevant topics while requiring only a moderate mathematical background on the part of the reader. The book will appeal to mathematical finance and financial economics students seeking an elementary but rigorous introduction to the subject; mathematics and physics students looking for an opportunity to get acquainted with a modern applied topic; and mathematicians, physicists and quantitatively inclined economists working or planning to work in the financial industry.
Arbitrage Theory In Continuous Time
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Author : Tomas Björk
language : en
Publisher: OUP Oxford
Release Date : 2009-08-06
Arbitrage Theory In Continuous Time written by Tomas Björk and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-06 with Business & Economics categories.
The third edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory and Merton's fund separation theory, the book is designed for graduate students and combines necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. In this substantially extended new edition Bjork has added separate and complete chapters on the martingale approach to optimal investment problems, optimal stopping theory with applications to American options, and positive interest models and their connection to potential theory and stochastic discount factors. More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.
Introduction To The Mathematics Of Finance
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Author : Steven Roman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-24
Introduction To The Mathematics Of Finance written by Steven Roman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-24 with Mathematics categories.
The Mathematics of Finance has been a hot topic ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for advanced undergraduate or beginning graduate students in mathematics, finance or economics. This book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model. This second edition is a complete rewrite of the first edition with significant changes to the topic organization, thus making the book flow much more smoothly. Several topics have been expanded such as the discussions of options, including the history of options, and pricing nonattainable alternatives. In this edition the material on probability has been condensed into fewer chapters, and the material on the capital asset pricing model has been removed. The mathematics is not watered down, but it is appropriate for the intended audience. Previous knowledge of measure theory is not needed and only a small amount of linear algebra is required. All necessary probability theory is developed throughout the book on a "need-to-know" basis. No background in finance is required, since the book contains a chapter on options.
Portfolio Theory And Arbitrage A Course In Mathematical Finance
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Author : Ioannis Karatzas
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-08-12
Portfolio Theory And Arbitrage A Course In Mathematical Finance written by Ioannis Karatzas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-12 with Education categories.
This book develops a mathematical theory for finance, based on a simple and intuitive absence-of-arbitrage principle. This posits that it should not be possible to fund a non-trivial liability, starting with initial capital arbitrarily near zero. The principle is easy-to-test in specific models, as it is described in terms of the underlying market characteristics; it is shown to be equivalent to the existence of the so-called “Kelly” or growth-optimal portfolio, of the log-optimal portfolio, and of appropriate local martingale deflators. The resulting theory is powerful enough to treat in great generality the fundamental questions of hedging, valuation, and portfolio optimization. The book contains a considerable amount of new research and results, as well as a significant number of exercises. It can be used as a basic text for graduate courses in Probability and Stochastic Analysis, and in Mathematical Finance. No prior familiarity with finance is required, but it is assumed that readers have a good working knowledge of real analysis, measure theory, and of basic probability theory. Familiarity with stochastic analysis is also assumed, as is integration with respect to continuous semimartingales.
Arbitrage Theory
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Author : Jochen E.M. Wilhelm
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Arbitrage Theory written by Jochen E.M. Wilhelm and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
The present 'Introductory Lectures on Arbitrage-based Financial Asset Pricing' are a first attempt to give a comprehensive presentation of Arbitrage Theory in a discrete time framework (by the way: all the re sults given in these lectures apply to a continuous time framework but, probably, in continuous time we could achieve stronger results - of course at the price of stronger assumptions). It has been turned out in the last few years that capital market theory as derived and evolved from the capital asset pricing model (CAPM) in the middle sixties, can, to an astonishing extent, be based on arbitrage arguments only, rather than on mean-variance preferences of investors. On the other hand, ar bitrage arguments provided access to a wider range of results which could not be obtained by standard CAPM-methods, e. g. the valuation of contingent claims (derivative assets) Dr the_ investigation of futures prices. To some extent the presentation will loosely follow historical lines. A selected set of capital asset pricing models will be derived according to their historical progress and their increasing complexity as well. It will be seen that they all share common structural properties. After having made this observation the presentation will become an axiomatical one: it will be stated in precise terms what arbitrage is about and what the consequences are if markets do not allow for risk-free arbitrage opportunities. The presentation will partly be accompanied by an illus trating example: two-state option pricing.
Introduction To The Mathematics Of Finance
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Author : Steven Roman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Introduction To The Mathematics Of Finance written by Steven Roman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
An elementary introduction to probability and mathematical finance including a chapter on the Capital Asset Pricing Model (CAPM), a topic that is very popular among practitioners and economists. Dr. Roman has authored 32 books, including a number of books on mathematics, such as Coding and Information Theory, Advanced Linear Algebra, and Field Theory, published by Springer-Verlag.
Mathematics Of Financial Markets
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Author : Robert J Elliott
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Mathematics Of Financial Markets written by Robert J Elliott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
This book explores the mathematics that underpins pricing models for derivative securities such as options, futures and swaps in modern markets. Models built upon the famous Black-Scholes theory require sophisticated mathematical tools drawn from modern stochastic calculus. However, many of the underlying ideas can be explained more simply within a discrete-time framework. This is developed extensively in this substantially revised second edition to motivate the technically more demanding continuous-time theory.
Arbitrage Credit And Informational Risks
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Author : Ying Jiao
language : en
Publisher: World Scientific
Release Date : 2014-03-27
Arbitrage Credit And Informational Risks written by Ying Jiao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-27 with Mathematics categories.
This book contains a collection of research papers in mathematical finance covering recent advances in arbitrage, credit and asymmetric information risks. These subjects have attracted academic and practical attention, in particular after the international financial crisis. The volume is split into three parts which treat each of these topics.
Arbitrage Theory In Continuous Time
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Author : TOMAS. BJOERK
language : en
Publisher:
Release Date : 2019
Arbitrage Theory In Continuous Time written by TOMAS. BJOERK and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Arbitrage categories.