A Course on Malliavin-Skorohod Calculus for Additive Processes with Applications to Finance
1st Edition
Will be published approx. on 31. August 2031
Book
Hardback
400 pages
978-1-4987-6855-9 (ISBN)
Description
The purpose of the book is to present the Malliavin-Skorohod calculus for additive processes, that is, processes with independent increments; in other words, Levy processes without the hypothesis of stationarity of increments. This will be the addition of Malliavin calculus for Gaussian processes and Malliavin calculus for Poisson random measures. The second is the application of the previous theory to finance, concretely, to stochastic volatility jump diffusion models, in order to solve problems related with pricing and hedging via Clark-Ocone formula, computation of sensitivities, obtaining useful price decompositions (Hull and White type formulas) and local risk minimizing strategies.
More details
Series
Language
English
Place of publication
Oxford
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Dimensions
Height: 234 mm
Width: 156 mm
ISBN-13
978-1-4987-6855-9 (9781498768559)
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Schweitzer Classification
Person
Professor Josep Vives received his PhD in Mathematics in 1994 at Universitat de Barcelona under the supervision of Professor David Nualart. From 1995-2005 he was Professor Titular (Associate Professor) in the Department of Mathematics of the UAB. Since September 2005 he has been Professor Titular (Associate Professor) in the Faculty of Mathematics of the Universitat de Barcelona. He has also been vice-dean of postgraduate studies and research since 2009. He has given more than 60 talks in conferences since 1992, is a regular referee for more than 15 journals and has published over 30 papers in international journals.
Content
Introduction: Levy and Additive Processes, Levy Processes in Finance. Malliavin-Skorohod Type Calculus without Probabilities: The Fock Space Setting. Additive Processes: The Chaotic Representation Propert. Malliavin-Skorohod Calculus for Gaussian Processes: A Review. Malliavin-Skorohod Calculus for Poisson Random Measures in the Canonical Space. Examples: The Cases of Standard Poisson Process and Simple Levy Process. Clark-Hausmann-Ocone Formula. Pricing and Hedging Financial Derivatives. Sensitivity Analysis for Stochastic Volatility Additive Models. Price Decomposition for Stochastic Volatility Jump Diffusion Models and Applications. Local Risk Minimizing Hedging Strategies.