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Malliavin Calculus for Lévy Processes with Applications to Finance
ISBN-13:
9783540785729
Veröffentl:
2008
Seiten:
418
Autor:
Giulia Di Nunno
Serie:
Universitext
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
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.
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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