This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

Since the publication of the first edition of this book, the area of mathematical finance has grown rapidly, with financial analysts using more sophisticated mathematical concepts, such as stochastic integration, to describe the behavior of markets and to derive computing methods. Maintaining the lucid style of its popular predecessor, this concise and accessible introduction covers the probabilistic techniques required to understand the most widely used financial models. Along with additional exercises, this edition presents fully updated material on stochastic volatility models and option pricing as well as a new chapter on credit risk modeling. It contains many numerical experiments and real-world examples taken from the authors' own experiences. The book also provides all of the necessary stochastic calculus theory and implements some of the algorithms using SciLab. Key topics covered include martingales, arbitrage, option pricing, and the Black-Scholes model.

Although there are many textbooks on stochastic calculus applied to finance, this volume earns its place with a pedagogical approach. The text presents 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 should be familiar with elementary real analysis and basic probability theory.

Stochastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas. From the reviews: "As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract’. This is also reflected in the style of writing which is unusually lively for a mathematics book." --ZENTRALBLATT MATH

This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly addresses continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellaumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level students in the engineering and mathematics disciplines, the book is also an excellent reference resource for applied mathematicians and statisticians looking for a review of the topic.

This book gives a systematic introduction to the basic theory of financial mathematics, with an emphasis on applications of martingale methods in pricing and hedging of contingent claims, interest rate term structure models, and expected utility maximization problems. The general theory of static risk measures, basic concepts and results on markets of semimartingale model, and a numeraire-free and original probability based framework for financial markets are also included. The basic theory of probability and Ito's theory of stochastic analysis, as preliminary knowledge, are presented.

Modelling with the Ito integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory. This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black -- Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Ito calculus and/or stochastic finance.