Malliavin Calculus for Lévy Processes with Applications to Finance

  • Giulia Di Nunno
  • Bernt Øksendal
  • Frank Proske

Part of the Universitext book series (UTX)

About this book


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 Lévy type of noise are treated.

Besides, forward integration is included and indeed extended to general Lévy 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.


Brownian motion Levy processes Lévy process Malliavin calculus Stochastic Differential Equations Stochastic calculus asymmetric information calculus optimization stochastic control white noise

Editors and affiliations

  • Giulia Di Nunno
    • 1
  • Bernt Øksendal
    • 1
  • Frank Proske
    • 1
  1. 1.Department of MathematicsUniversity of OsloOsloNorway

Bibliographic information

Industry Sectors
Finance, Business & Banking
IT & Software
Energy, Utilities & Environment
Oil, Gas & Geosciences