LÚvy Processes and Stochastic Calculus

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Cambridge University Press, Jul 5, 2004 - Mathematics - 384 pages
LÚvy 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 LÚvy processes. The second part accessibly develops the stochastic calculus for LÚvy processes. All the tools needed for the stochastic approach to option pricing, including It˘'s formula, Girsanov's theorem and the martingale representation theorem are described.
 

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Contents

Martingales stopping times and random measures
70
Markov processes semigroups and generators
120
Stochastic integration
190
Exponential martingales change of measure and financial
246
Stochastic differential equations
292
References
360
Index of notation
375
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