Introduction to Stochastic Calculus with Applications
Introduction to Stochastic Calculus with Applications

Author: Fima C. Klebaner

Publisher: Imperial College Press

Published: 2005

Total Pages: 431

ISBN-13: 1860945554

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This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

Introduction to Stochastic Calculus for Finance
Introduction to Stochastic Calculus for Finance

Author: Dieter Sondermann

Publisher: Springer Science & Business Media

Published: 2006-12-02

Total Pages: 144

ISBN-13: 3540348379

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Although there are many textbooks on stochastic calculus applied to finance, this volume earns its place with a pedagogical approach. The text presents a quick (but by no means "dirty") road to the tools required for advanced finance in continuous time, including option pricing by martingale methods, term structure models in a HJM-framework and the Libor market model. The reader should be familiar with elementary real analysis and basic probability theory.

Elementary Stochastic Calculus with Finance in View
Elementary Stochastic Calculus with Finance in View

Author: Thomas Mikosch

Publisher: World Scientific

Published: 1998

Total Pages: 230

ISBN-13: 9789810235437

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Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black -- Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Ito calculus and/or stochastic finance.

Stochastic Calculus and Financial Applications
Stochastic Calculus and Financial Applications

Author: J. Michael Steele

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 303

ISBN-13: 1468493051

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Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas. From the reviews: "As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract’. This is also reflected in the style of writing which is unusually lively for a mathematics book." --ZENTRALBLATT MATH

Stochastic Calculus for Finance I
Stochastic Calculus for Finance I

Author: Steven Shreve

Publisher: Springer Science & Business Media

Published: 2005-06-28

Total Pages: 212

ISBN-13: 9780387249681

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Developed for the professional Master's program in Computational Finance at Carnegie Mellon, the leading financial engineering program in the U.S. Has been tested in the classroom and revised over a period of several years Exercises conclude every chapter; some of these extend the theory while others are drawn from practical problems in quantitative finance

Financial Calculus
Financial Calculus

Author: Martin Baxter

Publisher: Cambridge University Press

Published: 1996-09-19

Total Pages: 252

ISBN-13: 9780521552899

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A rigorous introduction to the mathematics of pricing, construction and hedging of derivative securities.

Introduction to Stochastic Finance
Introduction to Stochastic Finance

Author: Jia-An Yan

Publisher: Springer

Published: 2018-10-10

Total Pages: 406

ISBN-13: 9811316570

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This book gives a systematic introduction to the basic theory of financial mathematics, with an emphasis on applications of martingale methods in pricing and hedging of contingent claims, interest rate term structure models, and expected utility maximization problems. The general theory of static risk measures, basic concepts and results on markets of semimartingale model, and a numeraire-free and original probability based framework for financial markets are also included. The basic theory of probability and Ito's theory of stochastic analysis, as preliminary knowledge, are presented.

Introduction to Stochastic Calculus
Introduction to Stochastic Calculus

Author: Rajeeva L. Karandikar

Publisher: Springer

Published: 2018-06-01

Total Pages: 446

ISBN-13: 9811083185

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This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly addresses continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellaumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level students in the engineering and mathematics disciplines, the book is also an excellent reference resource for applied mathematicians and statisticians looking for a review of the topic.

Brownian Motion and Stochastic Calculus
Brownian Motion and Stochastic Calculus

Author: Ioannis Karatzas

Publisher: Springer

Published: 2014-03-27

Total Pages: 490

ISBN-13: 1461209498

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A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.

Stochastic Calculus
Stochastic Calculus

Author: Paolo Baldi

Publisher: Springer

Published: 2017-11-09

Total Pages: 632

ISBN-13: 3319622269

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This book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. It is the only textbook on the subject to include more than two hundred exercises with complete solutions. After explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used. Stochastic Calculus will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. Including full mathematical statements and rigorous proofs, this book is completely self-contained and suitable for lecture courses as well as self-study.