Fluctuations of Lévy Processes with Applications

Andreas Kyprianou has a degree in Mathematics from the University of Oxford and a Ph.D. in Probability Theory from The University of Sheffield. He is currently a Professor of Probability at the University of Bath, having held academic positions in Mathematics and Statistics Departments at the London School of Economics, Edinburgh University, Utrecht University and Heriot-Watt University, besides working for nearly two years as a research mathematician in the oil industry. His research is focused on pure and applied probability.

"The book grew out of lectures pitched at an advanced undergraduate or beginning graduate audience, the prerequisite being a course on abstract Lebesgue integration and a good foundation in probability theory ... . Fluctuations of Levy processes is an interesting book and it is currently the best introduction for the novice to this important topic." (Rene L. Schilling, Mathematical Reviews, April, 2015)

• 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.