Malliavin Calculus for Lévy Processes with Applications to Finance

Malliavin Calculus for Lévy Processes with Applications to Finance by Giulia Di Nunno, Bernt Øksendal, Frank Proske.

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 incom...

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Bibliographic Details
Main Authors: Di Nunno, Giulia (Author), Øksendal, Bernt (Author), Proske, Frank (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2009.
Edition:1st ed. 2009.
Series:Universitext,
Springer eBook Collection.
Subjects:
Probabilities.
Economics, Mathematical .
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • The Continuous Case: Brownian Motion
  • The Wiener—Itô Chaos Expansion
  • The Skorohod Integral
  • Malliavin Derivative via Chaos Expansion
  • Integral Representations and the Clark—Ocone formula
  • White Noise, the Wick Product, and Stochastic Integration
  • The Hida—Malliavin Derivative on the Space ? = S?(?)
  • The Donsker Delta Function and Applications
  • The Forward Integral and Applications
  • The Discontinuous Case: Pure Jump Lévy Processes
  • A Short Introduction to Lévy Processes
  • The Wiener—Itô Chaos Expansion
  • Skorohod Integrals
  • The Malliavin Derivative
  • Lévy White Noise and Stochastic Distributions
  • The Donsker Delta Function of a Lévy Process and Applications
  • The Forward Integral
  • Applications to Stochastic Control: Partial and Inside Information
  • Regularity of Solutions of SDEs Driven by Lévy Processes
  • Absolute Continuity of Probability Laws.

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