Overview
- Malliavin Calculus is presented for both Brownian noise and Lévy type of noise
- Presents applications to mathematical finance
- New development of anticipating calculus
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (18 chapters)
-
The Continuous Case: Brownian Motion
-
The Discontinuous Case: Pure Jump Lévy Processes
Keywords
About this book
While the original works on Malliavin calculus aimed to study the smoothness of densities of solutions to stochastic differential equations, this book has another goal. It portrays the most important and innovative applications in stochastic control and finance, such as hedging in complete and incomplete markets, optimisation in the presence of asymmetric information and also pricing and sensitivity analysis. In a self-contained fashion, both the Malliavin calculus with respect to Brownian motion and general Lévy type of noise are treated.
Besides, forward integration is included and indeed extended to general Lévy processes. The forward integration is a recent development within anticipative stochastic calculus that, together with the Malliavin calculus, provides new methods for the study of insider trading problems.
To allow more flexibility in the treatment of the mathematical tools, the generalization of Malliavin calculus to the white noise framework is also discussed.
This book is a valuable resource for graduate students, lecturers in stochastic analysis and applied researchers.
Reviews
Editors and Affiliations
About the editors
Giulia Di Nunno, Bernt Øksendal and Frank Proske are professors at the Department of Mathematics, University of Oslo, Norway. The three scholars are active in the fields of stochastic analysis, mathematical and quantitative finance.
Bibliographic Information
Book Title: Malliavin Calculus for Lévy Processes with Applications to Finance
Editors: Giulia Di Nunno, Bernt Øksendal, Frank Proske
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-540-78572-9
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2009
Softcover ISBN: 978-3-540-78571-2Published: 06 November 2008
eBook ISBN: 978-3-540-78572-9Published: 08 October 2008
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XIV, 418
Topics: Probability Theory and Stochastic Processes, Quantitative Finance