Introduction To Stochastic Calculus With Applications - Hardcover

Klebaner, Fima C

Hardcover

ISBN 10: 186094129X ISBN 13: 9781860941290

Publisher: Imperial College Press, 1998

Synopsis

This book provides a concise introduction to stochastic calculus with some of its applications in mathematical finance, engineering and the sciences. Applications in finance include pricing of financial derivatives, such as options on stocks, exotic options and interest rate options. The filtering problem and its solution is presented as an application in engineering. Population models and randomly perturbed equations of physics are given as examples of applications in biology and physics.Only a basic knowledge of calculus and probability is required for reading the book. The text takes the reader from a fairly low technical level to a sophisticated one gradually. Heuristic arguments are often given before precise results are stated, and many ideas are illustrated by worked-out examples. Exercises are provided at the end of chapters to help to test readers' understanding. This book is suitable for advanced undergraduate students, graduate students as well as research workers and practitioners.

About this title

Review

"It provides a good introduction to stochastic analysis, leaving out several of the more technical proofs. The variety of examples and exercises suggests to use the book for self-studies" Zentralblatt MATH "This book is an excellent introduction to a subject which often presents difficulties to the student of probability ... The numerous exercises are both challenging and illuminating. I greatly enjoyed the book, and can recommend it unreservedly to all probabilists and statisticians wishing to acquire a working knowledge of the stochastic calculus. For libraries, it is an absolute 'must'." Australian & New Zealand Journal of Statistics, 1999 "... the author does a good job at achieving a difficult objective ... the text is best suited for the mathematically inclined graduate student in engineering ... It fills a niche in the literature, as it is hard to find books on stochastic analysis which present such a wide spectrum of results with relatively modest prerequisites." Mathematical Reviews, 2002

From the Inside Flap

This book presents a concise and rigorous treatment of stochastic calculus. It also gives its main applications in finance, biology and engineering. In finance, the stochastic calculus is applied to pricing options by no arbitrage. In biology, it is applied to populations' models, and in engineering it is applied to filter signal from noise. Not everything is proved, but enough proofs are given to make it a mathematically rigorous exposition.

This book aims to present the theory of stochastic calculus and its applications to an audience which possesses only a basic knowledge of calculus and probability. It may be used as a textbook by graduate and advanced undergraduate students in stochastic processes, financial mathematics and engineering. It is also suitable for researchers to gain working knowledge of the subject. It contains many solved examples and exercises making it suitable for self study.

In the book many of the concepts are introduced through worked-out examples, eventually leading to a complete, rigorous statement of the general result, and either a complete proof, a partial proof or a reference. Using such structure, the text will provide a mathematically literate reader with rapid introduction to the subject and its advanced applications. The book covers models in mathematical finance, biology and engineering. For mathematicians, this book can be used as a first text on stochastic calculus or as a companion to more rigorous texts by a way of examples and exercises.

Edition details

• Publisher: Imperial College Press
• Publication date: 1998
• ISBN 10: 186094129X
• ISBN 13: 9781860941290
• Binding: Hardcover
• Language: English
• Number of pages: 336