Malliavin Calculus for Lvy Processes with Applications to Finance [Paperback]

This book is an introduction to Malliavin calculus as a generalization of the classical non-anticipating Ito calculus to an anticipating setting. It presents the development of the theory and its use in new fields of application.

The Continuous Case: Brownian Motion.- The WienerIt? 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 L?vy Processes.- A Short Introduction to L?vy Processes.- The WienerIt? Chaos Expansion.- Skorohod Integrals.- The Malliavin Derivative.- L?vy White Noise and Stochastic Distributions.- The Donsker Delta Function of a L?vy Process and Applications.- The Forward Integral.- Applications to Stochastic Control: Partial and Inside Information.- Regularity of Solutions of SDEs Driven by L?vy Processes.- Absolute Continuity of Probability Laws.From the reviews:The book under review gives a quite complete description of the Malliavin and white noise approaches to stochastic analysis on both the Wiener and Poisson spaces with applications to mathematical finance. & In addition each chapter is accompanied with exercises and their solutions. & The technical requirements of the book are kept at a reasonable level and its organisation into short chapters not only facilitates the reading but also provides several alternative study plans making it a valuable learning and reference tool. (Nicolas Privault, Mathematical Reviews, Issue 2010 f)

Giulia Di Nunno, Bernt ?ksendal 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.

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