Stochastic Analysis

Author: Hiroyuki Matsumoto
Publisher: Cambridge University Press
ISBN: 1108107885
Format: PDF, ePub, Mobi
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Thanks to the driving forces of the Itô calculus and the Malliavin calculus, stochastic analysis has expanded into numerous fields including partial differential equations, physics, and mathematical finance. This book is a compact, graduate-level text that develops the two calculi in tandem, laying out a balanced toolbox for researchers and students in mathematics and mathematical finance. The book explores foundations and applications of the two calculi, including stochastic integrals and differential equations, and the distribution theory on Wiener space developed by the Japanese school of probability. Uniquely, the book then delves into the possibilities that arise by using the two flavors of calculus together. Taking a distinctive, path-space-oriented approach, this book crystallizes modern day stochastic analysis into a single volume.

L vy Processes and Stochastic Calculus

Author: David Applebaum
Publisher: Cambridge University Press
ISBN: 0521738652
Format: PDF, ePub, Docs
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A fully revised and appended edition of this unique volume, which develops together these two important subjects.

The Three Dimensional Navier Stokes Equations

Author: James C. Robinson
Publisher: Cambridge University Press
ISBN: 1107019664
Format: PDF, Mobi
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An accessible treatment of the main results in the mathematical theory of the Navier-Stokes equations, primarily aimed at graduate students.

The Mathematics of Derivatives Securities with Applications in MATLAB

Author: Mario Cerrato
Publisher: John Wiley & Sons
ISBN: 1119973414
Format: PDF, Docs
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Quantitative Finance is expanding rapidly. One of the aspects of the recent financial crisis is that, given the complexity of financial products, the demand for people with high numeracy skills is likely to grow and this means more recognition will be given to Quantitative Finance in existing and new course structures worldwide. Evidence has suggested that many holders of complex financial securities before the financial crisis did not have in-house experts or rely on a third-party in order to assess the risk exposure of their investments. Therefore, this experience shows the need for better understanding of risk associate with complex financial securities in the future. The Mathematics of Derivative Securities with Applications in MATLAB provides readers with an introduction to probability theory, stochastic calculus and stochastic processes, followed by discussion on the application of that knowledge to solve complex financial problems such as pricing and hedging exotic options, pricing American derivatives, pricing and hedging under stochastic volatility and an introduction to interest rates modelling. The book begins with an overview of MATLAB and the various components that will be used alongside it throughout the textbook. Following this, the first part of the book is an in depth introduction to Probability theory, Stochastic Processes and Ito Calculus and Ito Integral. This is essential to fully understand some of the mathematical concepts used in the following part of the book. The second part focuses on financial engineering and guides the reader through the fundamental theorem of asset pricing using the Black and Scholes Economy and Formula, Options Pricing through European and American style options, summaries of Exotic Options, Stochastic Volatility Models and Interest rate Modelling. Topics covered in this part are explained using MATLAB codes showing how the theoretical models are used practically. Authored from an academic’s perspective, the book discusses complex analytical issues and intricate financial instruments in a way that it is accessible to postgraduate students with or without a previous background in probability theory and finance. It is written to be the ideal primary reference book or a perfect companion to other related works. The book uses clear and detailed mathematical explanation accompanied by examples involving real case scenarios throughout and provides MATLAB codes for a variety of topics.

Brownian Motion

Author: Peter Mörters
Publisher: Cambridge University Press
ISBN: 1139486578
Format: PDF, ePub, Docs
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This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.

Strength from Weakness Structural Consequences of Weak Interactions in Molecules Supermolecules and Crystals

Author: Aldo Domenicano
Publisher: Springer Science & Business Media
ISBN: 940100546X
Format: PDF, Mobi
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The accurate determination of the structure of molecular systems provides information about the consequences of weak interactions both within and between molecules. These consequences impact the properties of the materials and the behaviour in interactions with other substances. The book presents modern experimental and computational techniques for the determination of molecular structure. It also highlights applications ranging from the simplest molecules to DNA and industrially significant materials. Readership: Graduate students and researchers in structural chemistry, computational chemistry, molecular spectroscopy, crystallography, supramolecular chemistry, solid state chemistry and physics, and materials science.

Tools for Computational Finance

Author: Rüdiger U. Seydel
Publisher: Springer
ISBN: 1447173384
Format: PDF, ePub, Mobi
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Computational and numerical methods are used in a number of ways across the field of finance. It is the aim of this book to explain how such methods work in financial engineering. By concentrating on the field of option pricing, a core task of financial engineering and risk analysis, this book explores a wide range of computational tools in a coherent and focused manner and will be of use to anyone working in computational finance. Starting with an introductory chapter that presents the financial and stochastic background, the book goes on to detail computational methods using both stochastic and deterministic approaches. Now in its sixth edition, Tools for Computational Finance has been significantly revised and contains: Several new parts such as a section on extended applications of tree methods, including multidimensional trees, trinomial trees, and the handling of dividends; Additional material in the field of generating normal variates with acceptance-rejection methods, and on Monte Carlo methods; 115 exercises, and more than 100 figures, many in color. Written from the perspective of an applied mathematician, all methods are introduced for immediate and straightforward application. A ‘learning by calculating’ approach is adopted throughout this book, enabling readers to explore several areas of the financial world. Interdisciplinary in nature, this book will appeal to advanced undergraduate and graduate students in mathematics, engineering, and other scientific disciplines as well as professionals in financial engineering.