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.
Lévy Processes and Stochastic Calculus
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Editorial Reviews
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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
Alexander Novikov, University of Technology
Book Description
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. For the first time in a book, Applebaum ties the two subjects together. He begins with an introduction to the general theory of Lévy processes. The second part 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.
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This review is from: Lévy Processes and Stochastic Calculus (Cambridge Studies in Advanced Mathematics) (Hardcover)
but there are better books out there on stochastic calculus
and Levy processes. The material covered is essentially a rewriting of existing mathematics. There are also minor math mistakes throughout. For example on page 197, the definition of stochastic integration and the definition of random measures on page 89 are consistent for defining stochastic integration with respect to Brownian motion only if we we assume Brownian motion is a function of finite variation which is not.
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Inside This Book
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First Sentence:
The aim of this section is to give a brief resume of key notions of measure theory and probability that will be used extensively throughout the book and to fix some notation and terminology once and for all. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof First, Proof Fix, Proof Suppose, Proof Define, The Doob-Meyer New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The aim of this section is to give a brief resume of key notions of measure theory and probability that will be used extensively throughout the book and to fix some notation and terminology once and for all. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, Proof First, Proof Fix, Proof Suppose, Proof Define, The Doob-Meyer New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 68
books:
See all 68 books this book cites
- Probability Theory (Courant Lecture Notes) by S. R. S. Varadhan in Back Matter (1), and Back Matter (2)
- Perturbation Theory for Linear Operators (Classics in Mathematics) by Tosio Kato in Back Matter
- A Modern Approach to Probability Theory (Probability and its Applications) by Bert E. Fristedt in Back Matter
- Non-Gaussian Merton-Black-Scholes Theory by Svetlana I. Boyarchenko in Back Matter
- Introduction to Stochastic Calculus Applied to Finance (Chapman & Hall/CRC Financial Mathematics Series) by Damien Lamberton in Back Matter
See all 68 books this book cites
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