Introductory Lectures on Fluctuations of Lévy Processes with Applications

• Main Author: Kyprianou, Andreas E. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Economics, Mathematical.; Probabilities.; Analysis.; 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 mathematical significance is justified by their application in many areas of classical and modern stochastic models including...

Table of Contents:

• Lévy Processes and Applications
• TheLévy–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 and Insurance Risk
• Exit Problems for Spectrally Negative Processes
• Applications to Optimal Stopping Problems
• Continuous-State Branching Processes.