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＜電子ブック＞
Malliavin Calculus for Lévy Processes with Applications to Finance / by Giulia Di Nunno, Bernt Øksendal, Frank Proske
(Universitext. ISSN:21916675)

版	1st ed. 2009.
出版者	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer
出版年	2009
本文言語	英語
大きさ	XIV, 418 p : online resource
著者標目	*Di Nunno, Giulia author Øksendal, Bernt author Proske, Frank author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Social sciences -- Mathematics  全ての件名で検索 FREE:Probability Theory FREE:Mathematics in Business, Economics and Finance
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-540-78572-9

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