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＜電子ブック＞
Stochastic Calculus of Variations in Mathematical Finance / by Paul Malliavin, Anton Thalmaier
(Springer Finance. ISSN:21950687)

版	1st ed. 2006.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2006
本文言語	英語
大きさ	XII, 142 p : online resource
著者標目	*Malliavin, Paul author Thalmaier, Anton author SpringerLink (Online service)
件　名	LCSH:Finance, Public LCSH:Social sciences -- Mathematics  全ての件名で検索 LCSH:Mathematical analysis FREE:Public Economics FREE:Mathematics in Business, Economics and Finance FREE:Analysis
一般注記	Gaussian Stochastic Calculus of Variations -- Computation of Greeks and Integration by Parts Formulae -- Market Equilibrium and Price-Volatility Feedback Rate -- Multivariate Conditioning and Regularity of Law -- Non-Elliptic Markets and Instability in HJM Models -- Insider Trading -- Asymptotic Expansion and Weak Convergence -- Stochastic Calculus of Variations for Markets with Jumps Malliavin calculus provides an infinite-dimensional differential calculus in the context of continuous paths stochastic processes. The calculus includes formulae of integration by parts and Sobolev spaces of differentiable functions defined on a probability space. This new book, demonstrating the relevance of Malliavin calculus for Mathematical Finance, starts with an exposition from scratch of this theory. Greeks (price sensitivities) are reinterpreted in terms of Malliavin calculus. Integration by parts formulae provide stable Monte Carlo schemes for numerical valuation of digital options. Finite-dimensional projections of infinite-dimensional Sobolev spaces lead to Monte Carlo computations of conditional expectations useful for computing American options. The discretization error of the Euler scheme for a stochastic differential equation is expressed as a generalized Watanabe distribution on the Wiener space. Insider information is expressed as an infinite-dimensional drift. The last chapter gives an introduction to the same objects in the context of jump processes where incomplete markets appear HTTP:URL=https://doi.org/10.1007/3-540-30799-0

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