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: Gallager Название: Stochastic Processes ISBN: 1107039754 ISBN-13(EAN): 9781107039759 Издательство: Cambridge Academ Рейтинг: Цена: 4831 р. 6901.00-30% Наличие на складе: Есть (1 шт.) Описание: This definitive textbook provides a solid introduction to discrete and continuous stochastic processes, tackling a complex field in a way that instils a deep understanding of the relevant mathematical principles, and develops an intuitive grasp of the way these principles can be applied to modelling real-world systems. It includes a careful review of elementary probability and detailed coverage of Poisson, Gaussian and Markov processes with richly varied queuing applications. The theory and applications of inference, hypothesis testing, estimation, random walks, large deviations, martingales and investments are developed. Written by one of the world's leading information theorists, evolving over twenty years of graduate classroom teaching and enriched by over 300 exercises, this is an exceptional resource for anyone looking to develop their understanding of stochastic processes.
Описание: This book demonstrates the structural characteristics of the optimal control policies in various stochastic supply chains and to shows how to make use of these characteristics to construct easy-to-operate sub-optimal policies.
Описание: Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.
Автор: Milstein G.N., Tretyakov M.V. Название: Stochastic Numerics for Mathematical Physics ISBN: 3540211101 ISBN-13(EAN): 9783540211105 Издательство: Springer Рейтинг: Цена: 14649 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Stochastic differential equations have many applications in the natural sciences. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce solution of multi-dimensional problems for partial differential equations to integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. The authors propose many new special schemes, some published here for the first time. In the second part of the book they construct numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.
Описание: Dedicated to the eminent Russian mathematician Albert Shiryaev on the occasion of his 70th birthday, the Festschrift is a collection of papers, including several surveys, written by his former students, co-authors and colleagues. These reflect the wide range of scientific interests of the teacher and his Moscow school. The topics range from the disorder problems to stochastic calculus and their applications to mathematical economics and finance. A full biobibliography of ShiryaevвЂ™s works is included.The book represents the modern state of art of many aspects of a quickly maturing theory and will be an essential source and reading for researchers in this area. The diversity of the topics and the comprehensive style of the papers make the book amenable and attractive for PhD students and young researchers.
Описание: This book contains 17 articles on stochastic processes (stochastic calculus and Malliavin calculus, functionals of Brownian motions and Levy processes,
stochastic control and optimization problems, stochastic numerics, and so on) and their applications to problems in mathematical finance.
Описание: The book collects a series of papers centered on two main streams: Feynman path integral approach to Quantum Mechanics and statistical mechanics of
quantum open systems. Key authors discuss the state-of-the-art within their fields of expertise. In addition, the volume includes a number of contributed papers with new results, which
have been thoroughly refereed.
The contributions in this volume highlight emergent research in the area of stochastic analysis and mathematical physics, focusing, in
particular on Feynman functional integral approach and, on the other hand, in quantum probability. The book is addressed to an audience of mathematical physicists, as well as
specialists in probability theory, stochastic analysis and operator algebras.
Описание: The ideas and principles of stochastic analysis have managed to penetrate into various fields of pure and applied mathematics in the last 15 years; it is
particularly true for mathematical physics. This volume provides a wide range of applications of stochastic analysis in fields as varied as statistical mechanics, hydrodynamics, Yang-Mills
theory and spin-glass theory. The proper concept of stochastic dynamics relevant to each type of application is described in detail here.
Altogether, these approaches
illustrate the reasons why their dissemination in other fields is likely to accelerate in the years to come.
Описание: This volume contains the contributions to a conference that is among the most important meetings in financial mathematics. Serving as a bridge between
probabilists in Japan (called the Ito School and known for its highly sophisticated mathematics) and mathematical finance and financial engineering, the conference elicits the very
highest quality papers in the field of financial mathematics.
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