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Look Inside Stochastic Calculus for Finance

Stochastic Calculus for Finance

Part of Mastering Mathematical Finance

Authors:
Marek Capiński, AGH University of Science and Technology, Krakow
Ekkehard Kopp, University of Hull
Janusz Traple, AGH University of Science and Technology, Krakow

Date Published: August 2012
availability: Temporarily unavailable - available from TBC
format: Paperback
isbn: 9780521175739

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About the Authors

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.
- Written specifically at the Master's level by experienced lecturers, so readers can dive in directly
- Gives students confidence in Itô calculus
- Solutions to exercises are available online
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Reviews & endorsements
'… a very accessible and comprehensive introduction.' Robert Stelzer, Mathematical Reviews

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Product details
- Date Published: August 2012
- format: Paperback
- isbn: 9780521175739
- length: 186 pages
- dimensions: 228 x 152 x 13 mm
- weight: 0.32kg
- contains: 6 b/w illus. 85 exercises
- availability: Temporarily unavailable - available from TBC
Table of Contents
Preface
1. Discrete time processes
2. Wiener process
3. Stochastic integrals
4. Itô formula
5. Stochastic differential equations
Index.
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Instructors have used or reviewed this title for the following courses
- Actuarial Science
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Authors
Marek Capiński, AGH University of Science and Technology, Krakow
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, University of Hull
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, AGH University of Science and Technology, Krakow
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.