Lévy Processes and Stochastic Calculus

David Applebaum - Collection Cambridge Studies in Advanced Mathematics

384 pages, parution le 21/06/2004

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Résumé

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.

Sommaire

Lévy Processes
Martingales, stopping times and random measures
Markov processes, semigroups and generators
Stochastic integration
Exponential martingales, change of measure and financial applications
Stochastic differential equations

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	David Applebaum
Collection	Cambridge Studies in Advanced Mathematics
Parution	21/06/2004
Nb. de pages	384
Format	15,5 x 23,5
Couverture	Relié
Poids	670g
Intérieur	Noir et Blanc
EAN13	9780521832632
ISBN13	978-0-521-83263-2