Lévy Processes and Stochastic Calculus
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- Author: David Applebaum, University of Sheffield
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Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. David Applebaum connects the two subjects together in this monograph. After an introduction to the general theory of Lévy processes, he accessibly develops the stochastic calculus for Lévy processes. All the tools needed for the stochastic approach to option pricing, including Itô's formula, Girsanov's theorem and the martingale representation theorem, are described.Read more
- For first time in book form, develops stochastic integrals and stochastic differential equations driven by Levy processes, including introduction to the theory of Dirichlet forms
- Discussion of all the tools which are needed for the stochastic approach to option pricing, including Itô's formula, Girsanov's theorem and the martingale representation theorem
- An introduction to option pricing with particular reference to incomplete markets
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"I would recommend this book as a reference textbook for advanced courses like stochastic modeling or stochastic calculus in finance."
Alexander Novikov, University of Technology
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- Date Published: July 2006
- format: Adobe eBook Reader
- isbn: 9780511207617
- contains: 133 exercises
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
2. Lévy processes
3. Martingales, stopping times and random measures
4. Markov processes, semigroups and generators
5. Stochastic integration
6. Exponential martingales, change of measure and financial applications
7. Stochastic differential equations
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