Derivatives of Links: Milnor's Concordance Invariants and Massey's Products

Derivatives of Links: Milnor's Concordance Invariants and Massey's Products PDF

Author: Tim D. Cochran

Publisher: American Mathematical Soc.

Published: 1990

Total Pages: 102

ISBN-13: 9780821824894

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We investigate higher-order cohomology operations (Massey products) on complements of links of circles in [italic]S3. These are known to be essentially equivalent to the [lowercase Greek]Mu [with macron]-invariants of John Milnor, which detect whether or not the longitudes of the link lie in the [italic]n[superscript]th term of the lower central series of the fundamental group of the link compliment. We define a geometric "derivative" on the set of all links and use this to define higher-order linking numbers which are shown to be "pieces" of Massey products.

Derivatives

Derivatives PDF

Author: Keith Cuthbertson

Publisher: John Wiley & Sons

Published: 2019-12-16

Total Pages: 116

ISBN-13: 1119595592

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Three experts provide an authoritative guide to the theory and practice of derivatives Derivatives: Theory and Practice and its companion website explore the practical uses of derivatives and offer a guide to the key results on pricing, hedging and speculation using derivative securities. The book links the theoretical and practical aspects of derivatives in one volume whilst keeping mathematics and statistics to a minimum. Throughout the book, the authors put the focus on explanations and applications. Designed as an engaging resource, the book contains commentaries that make serious points in a lighthearted manner. The authors examine the real world of derivatives finance and include discussions on a wide range of topics such as the use of derivatives by hedge funds and the application of strip and stack hedges by corporates, while providing an analysis of how risky the stock market can be for long-term investors, and more. To enhance learning, each chapter contains learning objectives, worked examples, details of relevant finance blogs technical appendices and exercises.

Fundamentals and Advanced Techniques in Derivatives Hedging

Fundamentals and Advanced Techniques in Derivatives Hedging PDF

Author: Bruno Bouchard

Publisher: Springer

Published: 2016-06-23

Total Pages: 286

ISBN-13: 3319389904

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This book covers the theory of derivatives pricing and hedging as well as techniques used in mathematical finance. The authors use a top-down approach, starting with fundamentals before moving to applications, and present theoretical developments alongside various exercises, providing many examples of practical interest.A large spectrum of concepts and mathematical tools that are usually found in separate monographs are presented here. In addition to the no-arbitrage theory in full generality, this book also explores models and practical hedging and pricing issues. Fundamentals and Advanced Techniques in Derivatives Hedging further introduces advanced methods in probability and analysis, including Malliavin calculus and the theory of viscosity solutions, as well as the recent theory of stochastic targets and its use in risk management, making it the first textbook covering this topic. Graduate students in applied mathematics with an understanding of probability theory and stochastic calculus will find this book useful to gain a deeper understanding of fundamental concepts and methods in mathematical finance.

Mathematical Models of Financial Derivatives

Mathematical Models of Financial Derivatives PDF

Author: Yue-Kuen Kwok

Publisher: Springer Science & Business Media

Published: 2008-07-10

Total Pages: 541

ISBN-13: 3540686886

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This second edition, now featuring new material, focuses on the valuation principles that are common to most derivative securities. A wide range of financial derivatives commonly traded in the equity and fixed income markets are analysed, emphasising aspects of pricing, hedging and practical usage. This second edition features additional emphasis on the discussion of Ito calculus and Girsanovs Theorem, and the risk-neutral measure and equivalent martingale pricing approach. A new chapter on credit risk models and pricing of credit derivatives has been added. Up-to-date research results are provided by many useful exercises.

Evaluating Derivatives

Evaluating Derivatives PDF

Author: Andreas Griewank

Publisher: SIAM

Published: 2008-11-06

Total Pages: 448

ISBN-13: 0898716594

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This title is a comprehensive treatment of algorithmic, or automatic, differentiation. The second edition covers recent developments in applications and theory, including an elegant NP completeness argument and an introduction to scarcity.

Derivatives

Derivatives PDF

Author: T. V. Somanathan

Publisher: Cambridge University Press

Published: 2017-11-24

Total Pages: 350

ISBN-13: 1108596843

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This book provides a comprehensive but concise treatment of the subject of derivatives. It focuses on making essential concepts accessible to a wider audience. The book eschews complicated mathematics and high school level mathematics is sufficient to understand it. It describes and explains various derivative instruments, their use and pricing, and the functioning of derivative markets. It uses a large number of examples to elucidate concepts and illustrate their real-life application. A distinguishing feature of the book is that it goes beyond the narrow perspective of derivative traders and investors and takes a broader approach which enhances its appeal to a range of readers. This book will be useful for students in the fields of economics, econometrics, derivatives, and finance and financial professionals, bankers and investors.

Numerical Derivatives and Nonlinear Analysis

Numerical Derivatives and Nonlinear Analysis PDF

Author: Harriet Kagiwada

Publisher: Springer Science & Business Media

Published: 2013-03-08

Total Pages: 206

ISBN-13: 1468450565

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For many years it has been an article of faith of numerical analysts that the evaluation of derivatives of complicated functions should be avoided. Derivatives were evaluated using finite differences or, more recently, using symbolic manipulation packages. The first has the disadvantage of limited accuracy. The second has disadvantages of being expensive and requiring considerable computer memory. The recent developments described in this text allow the evaluation of derivatives using simple automatic derivative evaluation subroutines pro grammed in FORTRAN or BASIC. These subroutines can even be programmed on a personal computer. The concept for the evaluation of the derivatives was originally developed by Wengert over 20 years ago. Significant im provements have been made in Wengert's method and are utilized in this text. The purpose of this text is to familiarize computer users with a simple and practical method for obtaining the partial derivatives of complicated mathematical expressions. The text illustrates the use of automatic deriva tive evaluation subroutines to solve a wide range of nonlinear least-squares, optimal control, system identification, two-point boundary value problems, and integral equations. The numerical values of the derivatives are evalu~ ated exactly, except for roundoff, using simple FORTRAN or BASIC sub routines. These derivatives are derived automatically behind the scenes, from the equivalent of analytical expressions, without any effort from the user. The use of costly software packages is not required.

Latin Suffixal Derivatives in English

Latin Suffixal Derivatives in English PDF

Author: D. Gary Miller

Publisher: Oxford University Press

Published: 2006-07-20

Total Pages: 423

ISBN-13: 0199285055

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This is the fullest account ever published of Latin suffixes in English. It explores the rich variety of English words formed by the addition of one or more Latin suffixes, such as ial, -able, -ability, -ible, and -id. It traces the histories of over 3,000 words and reveals the range of derivational patterns in Indo-European, Latin, and English. It makes an important contribution to the history of English and Latin morphology and etymology, as well as to the history of suffixal derivation in Indo-European.

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