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.
Описание: This is an introductory level text on stochastic modeling. It is suited for undergraduate or graduate students in actuarial science, business management, computer science, engineering, operations research, public policy, statistics, and mathematics. It employs a large number of examples to teach how to build stochastic models of physical systems, analyze these models to predict their performance, and use the analysis to design and control them. The book provides a self-contained review of the relevant topics in probability theory. The rest of the book is devoted to important classes of stochastic models. In discrete and continuous time Markov models it covers the transient and long term behavior, cost models, and first passage times. Under generalized Markov models, it covers renewal processes, cumulative processes and semi-Markov processes. All the material is illustrated with many examples. There is a separate chapter on queueing models. In the chapter on design the author shows how the techniques developed in the text can be used to optimize the performance of a system. Finally, in the last chapter, linear programming is used to compute optimal control policies for stochastic systems. The book emphasizes numerical answers to the problems. A software package called MAXIM, which runs on MATLAB, is made available for downloading. Vidyadhar G. Kulkarni is Professor of Operations Research at the University of North Craolina at Chapel Hill. He has authored a graduate level text 'Modeling and Analysis of Stochastic Systems' and research articles on stochastic models of queues, computer systems and telecommunication systems. He holds a patent on traffic management in telecommunication networks, and he has served as an editor and associate editor of Stochastic Models and Operations Research Letters.
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: 13107 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: Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, and with the reflecting SDE technique to enable study of optimal stochastic population control problems. These two techniques are powerful and efficient, and can also be applied to research in many other problems in nature, science and elsewhere.
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: Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. This book introduces the electromagnetics of complex media through a systematic account of their mathematical theory.
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