Introduction to Malliavin Calculus, David Nualart, Eulalia Nualart

Автор: Nourdin
Название: Normal Approximations with Malliavin Calculus
ISBN: 1107017777 ISBN-13(EAN): 9781107017771
Издательство: Cambridge Academ
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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: David Nualart
Название: The Malliavin Calculus and Related Topics
ISBN: 3642066518 ISBN-13(EAN): 9783642066511
Издательство: Springer
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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: Paul Malliavin; Anton Thalmaier
Название: Stochastic Calculus of Variations in Mathematical Finance
ISBN: 3642077838 ISBN-13(EAN): 9783642077838
Издательство: Springer
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Описание: Highly esteemed author Topics covered are relevant and timely

Автор: Lamberton, Damien
Название: Introduction to stochastic calculus applied to finance
ISBN: 1584886269 ISBN-13(EAN): 9781584886266
Издательство: Taylor&Francis
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Описание: Maintaining the lucid style of its popular predecessor, this concise and accessible introduction covers the probabilistic techniques required to understand the most widely used financial models. Along with additional exercises, this edition presents fully updated material on stochastic volatility models and option pricing.

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