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INTRODUCTION TO STOCHASTIC CALCULUS WITH APPLICATIONS
(Second Edition)
by Fima C Klebaner (Monash University, Australia)
Thisbook presents a concise treatment of stochastic calculus and itsapplications. It gives a simple but rigorous treatment of the subjectincluding a range of advanced topics, it is useful for practitionerswho use advanced theoretical results. It covers advanced applications,such as models in mathematical finance, biology and engineering.
Self-containedand unified in presentation, the book contains many solved examples andexercises. It may be used as a textbook by advanced undergraduates andgraduate students in stochastic calculus and financial mathematics. Itis also suitable for practitioners who wish to gain an understanding orworking knowledge of the subject. For mathematicians, this book couldbe a first text on stochastic calculus; it is good companion to moreadvanced texts by a way of examples and exercises. For people fromother fields, it provides a way to gain a working knowledge ofstochastic calculus. It shows all readers the applications ofstochastic calculus methods and takes readers to the technical levelrequired in research and sophisticated modelling.
This secondedition contains a new chapter on bonds, interest rates and theiroptions. New materials include more worked out examples in allchapters, best estimators, more results on change of time, change ofmeasure, random measures, new results on exotic options, FX options,stochastic and implied volatility, models of the age-dependentbranching 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.
Contents:
- Preliminaries from Calculus
- Concepts of Probability Theory
- Basic Stochastic Processes
- Brownian Motion Calculus
- Stochastic Differential Equations
- Diffusion Processes
- Martingales
- Calculus for Semimartingales
- Pure Jump Processes
- Change of Probability Measure
- Applications in Finance: Stock and FX Options
- Applications in Finance: Bonds, Rates and Options
- Applications in Biology
- Applications in Engineering and Physics
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