Malliavin Calculus and Stochastic Analysis, Frederi Viens; Jin Feng; Yaozhong Hu; Eulalia Nual

Автор: Malliavin
Название: Stochastic Calculus of Variations in Mathematical Finance
ISBN: 3540434313 ISBN-13(EAN): 9783540434313
Издательство: Springer
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Цена: 83850.00 T
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Описание: 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.

Автор: Tijana Levajkovi?; Hermann Mena
Название: Equations Involving Malliavin Calculus Operators
ISBN: 3319656775 ISBN-13(EAN): 9783319656779
Издательство: Springer
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Цена: 51230.00 T
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Описание: A major contribution of the book is the development of generalized Malliavin calculus in the framework of white noise analysis, based on chaos expansion representation of stochastic processes and its application for solving several classes of stochastic differential equations with singular data involving the main operators of Malliavin calculus.

Автор: Nourdin
Название: Normal Approximations with Malliavin Calculus
ISBN: 1107017777 ISBN-13(EAN): 9781107017771
Издательство: Cambridge Academ
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Цена: 79200.00 T
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Описание: This book studies normal approximations by means of two powerful probabilistic techniques: the Malliavin calculus and Stein`s method. Largely self-contained it is perfect for self-study and will appeal both to researchers and to graduate students in probability and statistics.

Автор: Paul Malliavin; Anton Thalmaier
Название: Stochastic Calculus of Variations in Mathematical Finance
ISBN: 3642077838 ISBN-13(EAN): 9783642077838
Издательство: Springer
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Цена: 65210.00 T
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Описание: Highly esteemed author Topics covered are relevant and timely

Автор: Paul Malliavin; L. Kay; H. Airault; L. Kay; G. Let
Название: Integration and Probability
ISBN: 1461286948 ISBN-13(EAN): 9781461286943
Издательство: Springer
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Цена: 60550.00 T
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Описание: It is a distinct pleasure to have the opportunity to introduce Professor Malliavin's book to the English-speaking mathematical world. In recent years there has been a noticeable retreat from the level of ab- straction at which graduate-level courses in analysis were previously taught in the United States and elsewhere. In contrast to the practices used in the 1950s and 1960s, when great emphasis was placed on the most general context for integration and operator theory, we have recently witnessed an increased emphasis on detailed discussion of integration over Euclidean space and related problems in probability theory, harmonic analysis, and partial differential equations. Professor Malliavin is uniquely qualified to introduce the student to anal- ysis with the proper mix of abstract theories and concrete problems. His mathematical career includes many notable contributions to harmonic anal- ysis, complex analysis, and related problems in probability theory and par- tial differential equations. Rather than developed as a thing-in-itself, the abstract approach serves as a context into which special models can be couched. For example, the general theory of integration is developed at an abstract level, and only then specialized to discuss the Lebesgue measure and integral on the real line. Another important area is the entire theory of probability, where we prefer to have the abstract model in mind, with no other specialization than total unit mass. Generally, we learn to work at an abstract level so that we can specialize when appropriate.

Автор: M.-P. Malliavin
Название: S?minaire d`Alg?bre Paul Dubreil et Marie-Paule Malliavin
ISBN: 3540126996 ISBN-13(EAN): 9783540126997
Издательство: Springer
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Цена: 32560.00 T
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Автор: Marie-Paule Malliavin
Название: S?minaire d`Alg?bre Paul Dubreil et Marie-Paule Malliavin
ISBN: 3540518126 ISBN-13(EAN): 9783540518129
Издательство: Springer
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Цена: 46540.00 T
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Автор: David Nualart
Название: The Malliavin Calculus and Related Topics
ISBN: 3642066518 ISBN-13(EAN): 9783642066511
Издательство: Springer
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Цена: 79190.00 T
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Описание: There have been ten years since the publication of the ?rst edition of this book. Since then, new applications and developments of the Malliavin c- culus have appeared. In preparing this second edition we have taken into account some of these new applications, and in this spirit, the book has two additional chapters that deal with the following two topics: Fractional Brownian motion and Mathematical Finance. The presentation of the Malliavin calculus has been slightly modi?ed at some points, where we have taken advantage of the material from the lecturesgiveninSaintFlourin1995(seereference 248]).Themainchanges and additional material are the following: In Chapter 1, the derivative and divergence operators are introduced in the framework of an isonormal Gaussian process associated with a general 2 Hilbert space H. The case where H is an L -space is trated in detail aft- s, p wards (white noise case). The Sobolev spaces D, with s is an arbitrary real number, are introduced following Watanabe's work. Chapter2includesageneralestimateforthedensityofaone-dimensional random variable, with application to stochastic integrals. Also, the c- position of tempered distributions with nondegenerate random vectors is discussed following Watanabe's ideas. This provides an alternative proof of the smoothness of densities for nondegenerate random vectors. Some properties of the support of the law are also presented.

Автор: Marie-Paule Malliavin
Название: S?minaire d`Alg?bre Paul Dubreil et Marie-Paul Malliavin
ISBN: 3540171851 ISBN-13(EAN): 9783540171850
Издательство: Springer
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Цена: 41920.00 T
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