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Banach, Fréchet, Hilbert and Neumann Spaces

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Discrete-time Asset Pricing Models in Applied Stochastic Finance

P. C.G. Vassiliou, University College London, UK

ISBN: 9781848211582

Publication Date: January 2010   Hardback   416 pp.

165.00 USD

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Stochastic finance and financial engineering are fields of science that have expanded rapidly over the past four decades, due mainly to the success of sophisticated quantitative methodologies in helping professionals manage financial risks. In recent years, we have witnessed a tremendous acceleration in research efforts aimed at better comprehending, modeling and hedging these types of risk, and of course real-world economic developments have only served to emphasize the importance of this understanding and its limitations.
This book aims to provide a foundation course on applied stochastic finance. It assumes only an introductory course in probability theory and basic mathematical analysis. It is designed for three groups of readers: students of various backgrounds seeking a core knowledge on the subject of stochastic finance; financial analysts and practitioners in the investment, banking and insurance industries; and finally, professionals in other fields who are interested in learning advanced mathematical and stochastic methods (basic knowledge in many areas) through finance.
First, an introduction to basic financial instruments and the fundamental principles of financial modeling and arbitrage valuation of derivatives is given. Next, we use the discrete-time binomial model to introduce all the relevant concepts that will follow. The mathematical simplicity of the binomial model also provides us with the opportunity to introduce and discuss in depth concepts such as conditional expectations and martingales in discrete time. Importantly, the level of mathematical complexity is not expanded beyond the needs of the stochastic finance framework. Numerous examples, each highlighted and isolated within the text for easy reference and identification, are included. Finally, the binomial model is used to introduce interest rate models and the Markov chain model is used to introduce credit risk. The book is designed in such a way that, in addition to other uses, it is extremely suitable for use as part of an undergraduate course.


1. Probability and Random Variables.
2. An introduction to the Financial Instruments and Derivatives.
3. Conditional Expectation and Markov Chains.
4. The No-arbitrage Binomial Pricing Model.
5. Martingales
6. Equivalent Martingale Mesures.
7. American Derivative Securities.
8. Fixed-income Markets and Interest Rates.
9. Credit Risk.
10. The Heath-Jarrow-Morton Model.

About the Authors

P.C.G. Vassiliou is Professor at the Mathematics Department of Aristotle University of Thessaloniki, Greece. For the last two years he has been a Visiting Professor at University College London, Department of Statistical Sciences, where the current book was written. He is well known in the area of Stochastic Mathematics and Applied Probability in which he has published more than 50 papers in well known journals.


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