Problems and Solutions in Mathematical Finance: Volume I - Stochastic Calculus, Chin Eric, Olafsson Sverrir, Nel Dian

Автор: Karatzas Название: Brownian Motion and Stochastic Calculus ISBN: 0387976558 ISBN-13(EAN): 9780387976556 Издательство: Springer Рейтинг: Цена: 5220 р. Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large number of problems and exercises.

Описание: Provides an introduction to probability theory and its applications.

Автор: Malliavin Название: Stochastic Calculus of Variations in Mathematical Finance ISBN: 3540434313 ISBN-13(EAN): 9783540434313 Издательство: Springer Рейтинг: Цена: 9404 р. 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.

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.

Описание: A collection of problems with detailed solutions which should be useful to students and research workers in mathematics, physics, engineering and other
sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained.

All relevant
definitions are given. Students can learn important principles and strategies required for problem solving. Teachers should find this text useful as a supplement, since important concepts
and techniques are developed through the problems.

The material has been tested in the author's lectures given around the world. The work is divided into two volumes. This
volume, Volume I, presents the introductory problems for undergraduate and advanced undergraduate students.

In Volume II, the more advanced problems, together with
detailed solutions, are collected, to meet the needs of graduate students and researchers. The problems included cover most of the new fields in theoretical and mathematical physics,
such as Lax representation, Backlund transformation, soliton equations, Lie-algebra-valued differential forms, the Hirota technique, the Painleve test, the Bethe ansatz, the Yang-Baxter
relation, chaos, fractals, complexity, and so on.

Описание: A collection of problems with detailed solutions which should be useful to students and research workers in mathematics, physics, engineering and other
sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained.

All relevant
definitions are given. Students can learn important principles and strategies required for problem solving. Teachers should find this text useful as a supplement, since important concepts
and techniques are developed through the problems.

The material has been tested in the author's lectures given around the world. The work is divided into two volumes.
Volume I presents the introductory problems for undergraduate and advanced undergraduate students.

In this volume, Volume II, the more advanced problems, together with
detailed solutions, are collected, to meet the needs of graduate students and researchers. The problems included cover most of the new fields in theoretical and mathematical physics,
such as Lax representation, Backlund transformation, soliton equations, Lie-algebra-valued differential forms, the Hirota technique, the Painleve test, the Bethe ansatz, the Yang-Baxter
relation, chaos, fractals, complexity, and so on.

Описание: This manuscript describes some mathematical problems arising in image analysis and computer vision. The authors consider both variational and pde approaches. The description focuses on theoretical- mathematical aspects of the problems, as well as on their applications and numerical descretiziations. This book is intended to be a reference and a basis for advanced courses in the fields of applied mathematics and computer vision.

Описание: The large number of already available textbooks on stochastic calculus with specific applications to finance requires a justification for another contribution to this subject. The justifcation is mainly pedagogical. These lecture notes start with an elementary approach to stochastic calculus due to FГ¶llmer, who showed that one can develop Ito's calculus "pathwise" as an exercise in real analysis. The text opens to students interested in finance a quick (but by no means "dirty") road to the tools required for advanced finance in continuous time, including option pricing by martingale methods, term structure models in a HJM-framework and the Libor market model. The reader is supposed only to be familiar with elementary real analysis (e.g. Taylor's Theorem) and basic probability theory. The text is also useful for mathematicians interested in the methods of modern mathematical finance without prior knowledge of advanced stochastic analysis.

Описание: Detailed guidance on the mathematics behind equity derivatives Problems and Solutions in Mathematical Finance Volume II is an innovative reference for quantitative practitioners and students, providing guidance through a range of mathematical problems encountered in the finance industry.

Описание: A collection of problems with detailed solutions which should be useful to students and research workers in mathematics, physics, engineering and other
sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained.

All relevant
definitions are given. Students can learn important principles and strategies required for problem solving. Teachers should find this text useful as a supplement, since important concepts
and techniques are developed through the problems.

The material has been tested in the author's lectures given around the world. The work is divided into two volumes. This
volume, Volume I, presents the introductory problems for undergraduate and advanced undergraduate students.

In Volume II, the more advanced problems, together with
detailed solutions, are collected, to meet the needs of graduate students and researchers. The problems included cover most of the new fields in theoretical and mathematical physics,
such as Lax representation, Backlund transformation, soliton equations, Lie-algebra-valued differential forms, the Hirota technique, the Painleve test, the Bethe ansatz, the Yang-Baxter
relation, chaos, fractals, complexity, and so on.

Описание: A collection of problems with detailed solutions which should be useful to students and research workers in mathematics, physics, engineering and other
sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained.

All relevant
definitions are given. Students can learn important principles and strategies required for problem solving. Teachers should find this text useful as a supplement, since important concepts
and techniques are developed through the problems.

The material has been tested in the author's lectures given around the world. The work is divided into two volumes.
Volume I presents the introductory problems for undergraduate and advanced undergraduate students.

In this volume, Volume II, the more advanced problems, together with
detailed solutions, are collected, to meet the needs of graduate students and researchers. The problems included cover most of the new fields in theoretical and mathematical physics,
such as Lax representation, Backlund transformation, soliton equations, Lie-algebra-valued differential forms, the Hirota technique, the Painleve test, the Bethe ansatz, the Yang-Baxter
relation, chaos, fractals, complexity, and so on.

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