Malliavin Calculus for LȨvy Processes with Applications to Finance [electronic resource] / edited by Giulia Di Nunno, Bernt ksendal, Frank Proske.

The Continuous Case: Brownian Motion -- The WienerItȳ Chaos Expansion -- The Skorohod Integral -- Malliavin Derivative via Chaos Expansion -- Integral Representations and the ClarkOcone formula -- White Noise, the Wick Product, and Stochastic Integration -- The HidaMalliavin Derivative on the Space ? = S?(?) -- The Donsker Delta Function and Applications -- The Forward Integral and Applications -- The Discontinuous Case: Pure Jump LȨvy Processes -- A Short Introduction to LȨvy Processes -- The WienerItȳ Chaos Expansion -- Skorohod Integrals -- The Malliavin Derivative -- LȨvy White Noise and Stochastic Distributions -- The Donsker Delta Function of a LȨvy Process and Applications -- The Forward Integral -- Applications to Stochastic Control: Partial and Inside Information -- Regularity of Solutions of SDEs Driven by LȨvy Processes -- Absolute Continuity of Probability Laws.

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 LȨvy type of noise are treated. Besides, forward integration is included and indeed extended to general LȨvy 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.

ZDB-2-SMA