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

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.

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, suchlCt