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Malliavin Calculus for Lévy Processes with Applications to Finance
Taschenbuch von Giulia Di Nunno (u. a.)
Sprache: Englisch

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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.

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.

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.

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2008
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 418
Inhalt: xiv
418 S.
ISBN-13: 9783540785712
ISBN-10: 354078571X
Sprache: Englisch
Herstellernummer: 978-3-540-78571-2
Autor: Di Nunno, Giulia
Øksendal, Bernt
Proske, Frank
Auflage: 2009
Hersteller: Springer
Springer, Berlin
Springer Berlin Heidelberg
Abbildungen: XIV, 418 p.
Maße: 18 x 156 x 236 mm
Von/Mit: Giulia Di Nunno (u. a.)
Erscheinungsdatum: 06.11.2008
Gewicht: 0,656 kg
preigu-id: 101849492
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2008
Fachbereich: Wahrscheinlichkeitstheorie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 418
Inhalt: xiv
418 S.
ISBN-13: 9783540785712
ISBN-10: 354078571X
Sprache: Englisch
Herstellernummer: 978-3-540-78571-2
Autor: Di Nunno, Giulia
Øksendal, Bernt
Proske, Frank
Auflage: 2009
Hersteller: Springer
Springer, Berlin
Springer Berlin Heidelberg
Abbildungen: XIV, 418 p.
Maße: 18 x 156 x 236 mm
Von/Mit: Giulia Di Nunno (u. a.)
Erscheinungsdatum: 06.11.2008
Gewicht: 0,656 kg
preigu-id: 101849492
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