Normal Approximations with Malliavin Calculus, Nourdin

Автор: Malliavin
Название: Stochastic Calculus of Variations in Mathematical Finance
ISBN: 3540434313 ISBN-13(EAN): 9783540434313
Издательство: Springer
Рейтинг:
Цена: 83850.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
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: Holger Wendland
Название: Scattered Data Approximation
ISBN: 0521843359 ISBN-13(EAN): 9780521843355
Издательство: Cambridge Academ
Рейтинг:
Цена: 116160.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A complete self-contained introduction to the theory of scattered data approximation. Written with graduates and researchers in mind, the text brings together much of the necessary background material into a single treatment and provides students with complete proofs to the theory developed within.

Автор: Govindan
Название: Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications
ISBN: 3319456822 ISBN-13(EAN): 9783319456829
Издательство: Springer
Рейтинг:
Цена: 102480.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This research monograph brings together, for the first time, the varied literature on Yosida approximations of stochastic differential equations (SDEs) in infinite dimensions and their applications into a single cohesive work. The author provides a clear and systematic introduction to the Yosida approximation method and justifies its power by presenting its applications in some practical topics such as stochastic stability and stochastic optimal control. The theory assimilated spans more than 35 years of mathematics, but is developed slowly and methodically in digestible pieces.The book begins with a motivational chapter that introduces the reader to several different models that play recurring roles throughout the book as the theory is unfolded, and invites readers from different disciplines to see immediately that the effort required to work through the theory that follows is worthwhile. From there, the author presents the necessary prerequisite material, and then launches the reader into the main discussion of the monograph, namely, Yosida approximations of SDEs, Yosida approximations of SDEs with Poisson jumps, and their applications. Most of the results considered in the main chapters appear for the first time in a book form, and contain illustrative examples on stochastic partial differential equations. The key steps are included in all proofs, especially the various estimates, which help the reader to get a true feel for the theory of Yosida approximations and their use.This work is intended for researchers and graduate students in mathematics specializing in probability theory and will appeal to numerical analysts, engineers, physicists and practitioners in finance who want to apply the theory of stochastic evolution equations. Since the approach is based mainly in semigroup theory, it is amenable to a wide audience including non-specialists in stochastic processes.