Fluctuations of Lévy Processes with Applications Introductory Lectures /

• Main Author: Kyprianou, Andreas E. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2014.
• Edition: 2nd ed. 2014.
• Series: Universitext,
• Subjects: Mathematics.; Economics, Mathematical.; Probabilities.; Probability Theory and Stochastic Processes.; Quantitative Finance.

Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal...

Table of Contents:

• Lévy Processes and Applications
• The Lévy–Itô Decomposition and Path Structure
• More Distributional and Path-Related Properties
• General Storage Models and Paths of Bounded Variation
• Subordinators at First Passage and Renewal Measures
• The Wiener–Hopf Factorisation
• Lévy Processes at First Passage
• Exit Problems for Spectrally Negative Processes
• More on Scale Functions
• Ruin Problems and Gerber-Shiu Theory
• Applications to Optimal Stopping Problems
• Continuous-State Branching Processes
• Positive Self-similar Markov Processes
• Epilogue
• Hints for Exercises
• References
• Index.