Graduate text decsribing two of the main tools for modern mathematical finance.
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 develops the stochastic calculus for Lévy processes in a direct and accessible way. En route, the reader is introduced to important concepts in modern probability theory, such as martingales, semimartingales, Markov and Feller processes, semigroups and generators, and the theory of Dirichlet forms. There is a careful development of stochastic integrals and stochastic differential equations driven by Lévy processes. The book introduces all the tools that are needed for the stochastic approach to option pricing, including Itô's formula, Girsanov's theorem and the martingale representation theorem.
1. Introduction; 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; Notation; Bibliography; Index.
For the first time in a book, Applebaum ties Lévy processes and stochastic calculus together. 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.
Collana: Cambridge Studies in Advanced Mathematics
Dimensioni: 236 x 26 x 160 mm
Illustration Notes:133 exercises
Pagine Arabe: 408