A Course on Malliavin-Skorohod Calculus for Additive Processes with Applications to Finance
Chapman & Hall/CRC Monographs and Research Notes in Mathematics Series

The purpose of the book is to present the Malliavin-Skorohod calculus for additive processes, that is, processes with independent increments; in other words, Lévy 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.

Introduction: Lévy and Additive Processes, Lévy 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 Lévy 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.

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.