Rare events in stochastic systems: Modeling, simulation design and algorithm analysis

This dissertation explores a few topics in the study of rare events in stochastic systems, with a particular emphasis on the simulation aspect. This line of research has been receiving a substantial amount of interest in recent years, mainly motivated by scientic and industrial applications in which system performance is frequently measured in terms of events with very small probabilities.;The topics mainly break down into the following themes: - Algorithm Analysis: Chapters 2, 3, 4 and 5. - Simulation Design: Chapters 3, 4 and 5. - Modeling: Chapter 5. The titles of the main chapters are detailed as follows: Chapter 2: Analysis of a Splitting Estimator for Rare Event Probabilities in Jackson Networks Chapter 3: Splitting for Heavy-tailed Systems: An Exploration with Two Algorithms Chapter 4: State Dependent Importance Sampling with Cross Entropy for Heavy-tailed Systems Chapter 5: Stochastic Insurance-Reinsurance Networks: Modeling, Analysis and Efficient Monte Carlo.