Brownian Motion Calculus - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Brownian Motion Calculus write by Ubbo F. Wiersema. This book was released on 2008-12-08. Brownian Motion Calculus available in PDF, EPUB and Kindle. BROWNIAN MOTION CALCULUS Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. The sequence of chapters starts with a description of Brownian motion, the random process which serves as the basic driver of the irregular behaviour of financial quantities. That exposition is based on the easily understood discrete random walk. Thereafter the gains from trading in a random environment are formulated in a discrete-time setting. The continuous-time equivalent requires a new concept, the Itō stochastic integral. Its construction is explained step by step, using the so-called norm of a random process (its magnitude), of which a motivated exposition is given in an Annex. The next topic is Itō’s formula for evaluating stochastic integrals; it is the random process counter part of the well known Taylor formula for functions in ordinary calculus. Many examples are given. These ingredients are then used to formulate some well established models for the evolution of stock prices and interest rates, so-called stochastic differential equations, together with their solution methods. Once all that is in place, two methodologies for option valuation are presented. One uses the concept of a change of probability and the Girsanov transformation, which is at the core of financial mathematics. As this technique is often perceived as a magic trick, particular care has been taken to make the explanation elementary and to show numerous applications. The final chapter discusses how computations can be made more convenient by a suitable choice of the so-called numeraire. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website www.wiley.com/go/brownianmotioncalculus.
Brownian Motion and Stochastic Calculus
Brownian Motion and Stochastic Calculus - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Brownian Motion and Stochastic Calculus write by Ioannis Karatzas. This book was released on 2014-03-27. Brownian Motion and Stochastic Calculus available in PDF, EPUB and Kindle. A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing 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, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The 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 whole is backed by a large number of problems and exercises.
Brownian Motion, Martingales, and Stochastic Calculus
Brownian Motion, Martingales, and Stochastic Calculus - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Brownian Motion, Martingales, and Stochastic Calculus write by Jean-François Le Gall. This book was released on 2016-04-28. Brownian Motion, Martingales, and Stochastic Calculus available in PDF, EPUB and Kindle. This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.
Stochastic Calculus for Fractional Brownian Motion and Applications
Stochastic Calculus for Fractional Brownian Motion and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Calculus for Fractional Brownian Motion and Applications write by Francesca Biagini. This book was released on 2008-02-17. Stochastic Calculus for Fractional Brownian Motion and Applications available in PDF, EPUB and Kindle. The purpose of this book is to present a comprehensive account of the different definitions of stochastic integration for fBm, and to give applications of the resulting theory. Particular emphasis is placed on studying the relations between the different approaches. Readers are assumed to be familiar with probability theory and stochastic analysis, although the mathematical techniques used in the book are thoroughly exposed and some of the necessary prerequisites, such as classical white noise theory and fractional calculus, are recalled in the appendices. This book will be a valuable reference for graduate students and researchers in mathematics, biology, meteorology, physics, engineering and finance.
Stochastic Calculus for Fractional Brownian Motion and Related Processes
Stochastic Calculus for Fractional Brownian Motion and Related Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Calculus for Fractional Brownian Motion and Related Processes write by Yuliya Mishura. This book was released on 2008-01-02. Stochastic Calculus for Fractional Brownian Motion and Related Processes available in PDF, EPUB and Kindle. This volume examines the theory of fractional Brownian motion and other long-memory processes. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. It proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional market.
