Lévy Processes and Stochastic Calculus (Cambridge Studies in Advanced Mathematics, Series Number 93) - Hardcover

Applebaum, David

Hardcover

ISBN 10: 0521832632 ISBN 13: 9780521832632

Publisher: Cambridge University Press, 2004

Synopsis

Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. For the first time in a book, Applebaum ties the two subjects together. He begins with an introduction to the general theory of Lévy processes. The second part develops the stochastic calculus for Lévy processes in a direct and accessible way. En route, the reader is introduced to important concepts in modern probability theory, such as martingales, semimartingales, Markov and Feller processes, semigroups and generators, and the theory of Dirichlet forms. There is a careful development of stochastic integrals and stochastic differential equations driven by Lévy processes. The book introduces all the tools that are needed for the stochastic approach to option pricing, including Itô's formula, Girsanov's theorem and the martingale representation theorem.

About this title

Review

'... the monograph closes the gap between classical textbooks on stochastic analysis where either Brownian motion or general semimartingales are considered. ... Besides standard results on existence and uniqueness of a solution and its Markov property, more advanced concepts are presented, such as representation of the solutions as Feller processes and as a stochastic flow.' Zentralblatt MATH

Book Description

For the first time in a book, Applebaum ties Lévy processes and stochastic calculus together. All the tools needed for the stochastic approach to option pricing, including Itô's formula, Girsanov's theorem and the martingale representation theorem are described.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2004
• ISBN 10: 0521832632
• ISBN 13: 9780521832632
• Binding: Hardcover
• Language: English
• Number of pages: 408