Introductory lectures on fluctuations of Levy processes with applications 1st Edition by Andreas E Kyprianou ISBN 9783540313427 by Kyprianou A. 9783540313427, 3540313427 instant download after payment.

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ISBN 13: 9783540313427
Author: Andreas E Kyprianou

Introductory lectures on fluctuations of Levy processes with applications 1st Table of contents:

Chapter 1: Preliminaries and Background

• Introduction to Stochastic Processes
• Basic Concepts of Probability Theory (as needed)
• Review of Brownian Motion and Poisson Processes
• Martingales and Stopping Times
• Infinitely Divisible Distributions
• The Lévy–Khintchine Formula (Characterization of Lévy Processes)

Chapter 2: Introduction to Lévy Processes

• Definition and Basic Properties
• Examples of Lévy Processes (e.g., Compound Poisson, Gamma, Inverse Gaussian, Stable Processes)
• Path Properties (càdlàg paths, variation of paths)
• The Lévy–Itô Decomposition
• Generators of Lévy Processes

Chapter 3: Fluctuation Theory of Lévy Processes

• Running Maximum and Minimum
• Ladder Processes
• The Wiener–Hopf Factorization
• The Scale Function
• First Passage Times and Overshoots/Undershoots
• Local Times

Chapter 4: Exit Problems for Lévy Processes

• Exit from Intervals
• Probabilities of Reaching a Barrier
• Distribution of the Excess over a Barrier

Chapter 5: Applications in Risk Theory

• The Classical Cramér–Lundberg Model
• Ruin Probabilities in Different Settings
• Optimal Dividend Strategies
• Capital Injections

Chapter 6: Applications in Queueing Theory and Storage Models

• M/G/1 Queue
• Storage Processes
• Dams with Lévy Input

Chapter 7: Applications in Mathematical Finance

• Lévy Models for Asset Prices
• Option Pricing with Jumps (e.g., Merton, Kou models)
• Market Incompleteness
• Stochastic Volatility Models driven by Lévy Processes

Chapter 8: Other Selected Applications and Advanced Topics

• Branching Processes
• Optimal Stopping Problems
• Positive Self-Similar Markov Processes
• Connections to Partial Differential Equations

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