Stochastic Calculus for Finance

by Marek Capinski, Ekkehard Kopp, Janusz Traple

Overview

This book focuses specifically on the key results in stochastic processes that have become essential for finance practitioners to understand. The authors study the Wiener process and Itô integrals in some detail, with a focus on results needed for the Black–Scholes option pricing model. After developing the required martingale properties of this process, the construction of the integral and the Itô formula (proved in detail) become the centrepiece, both for theory and applications, and to provide concrete examples of stochastic differential equations used in finance. Finally, proofs of the existence, uniqueness and the Markov property of solutions of (general) stochastic equations complete the book. Using careful exposition and detailed proofs, this book is a far more accessible introduction to Itô calculus than most texts. Students, practitioners and researchers will benefit from its rigorous, but unfussy, approach to technical issues. Solutions to the exercises are available online.

Product Details

ISBN-13:	9780521175739
Publisher:	Cambridge University Press
Publication date:	08/23/2012
Series:	Mastering Mathematical Finance
Edition description:	New Edition
Pages:	186
Product dimensions:	5.90(w) x 8.90(h) x 0.50(d)

About the Author

Marek Capiński has published over fifty research papers and nine books. His diverse interests include mathematical finance, corporate finance and stochastic hydrodynamics. For over thirty-five years he has been teaching these topics, mainly in Poland and in the UK, where he has held visiting fellowships. He is currently Professor of Applied Mathematics at AGH University of Science and Technology in Krakow, where he established a Master's programme in mathematical finance.

Ekkehard Kopp is Emeritus Professor of Mathematics at the University of Hull, where he taught courses at all levels in analysis, measure and probability, stochastic processes and mathematical finance between 1970 and 2007. His editorial experience includes service as founding member of the Springer Finance series (1998–2008) and the Cambridge University Press AIMS Library series. He has authored more than fifty research publications and five books.

Janusz Traple is Professor of Mathematics in the Faculty of Applied Mathematics at AGH University of Science and Technology in Krakow, Poland. His former positions and visiting fellowships include the Jagiellonian University in Krakow, Scuola Normale in Pisa, University of Siena and University of Florence. He has taught courses in differential equations, measure and probability and the theory of Markov processes, and he is the author of more than twenty research publications.

Table of Contents

Preface; 1. Discrete time processes; 2. Wiener process; 3. Stochastic integrals; 4. Itô formula; 5. Stochastic differential equations; Index.

Editorial Reviews

'… a very accessible and comprehensive introduction.'
Robert Stelzer, Mathematical Reviews

From the Publisher