Intro; Preface; Acknowledgements; Contents; 1 Motivation and Model; 1.1 Model Setup: Notation and Assumptions; 1.2 Arrival Times and Simulation; 1.3 Literature Review; 2 Properties of the Model; 2.1 Process Distribution; 2.2 Lévy and Compound Poisson Characterization; 2.3 Large Portfolio Approximation; 3 Estimation of the Parameters; 3.1 Estimation Procedures; 3.1.1 Discrete Monitoring; 3.1.2 Continuous Monitoring; 3.2 Simulation Study; 3.2.1 Setting: Inverse Gaussian Subordinator (No Drift); 3.2.2 Setting: Inverse Gaussian Subordinator with Drift; 3.2.3 Summary; 3.3 Real-World Data Example

4 Applications and Extensions4.1 Premium Calculation and Dependence Ordering; 4.1.1 Compound Model and Direct Insurer; 4.1.2 Stop-Loss Order and Reinsurer; 4.2 Model Extensions; 4.2.1 Compound Model; 4.2.2 Deterministic Time-Change; 4.2.3 Multivariate Subordination; 5 Appendix: Technical Background; 5.1 The Poisson Process and its Generalizations; 5.2 Lévy Subordinators; References; Index