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Full Description
This book offers a comprehensive examination of the Cramér-Lundberg model, which is the most extensively researched model in ruin theory. It covers the fundamental dynamics of an insurance company's surplus level in great detail, presenting a thorough analysis of the ruin probability and related measures for both the standard model and its variants.
Providing a systematic and self-contained approach to evaluate the crucial quantities found in the Cramér-Lundberg model, the book makes use of connections with related queueing models when appropriate, and its emphasis on clean transform-based techniques sets it apart from other works. In addition to consolidating a wealth of existing results, the book also derives several new outcomes using the same methodology.
This material is complemented by a thoughtfully chosen collection of exercises. The book's primary target audience is master's and starting PhD students in applied mathematics, operations research, and actuarial science, although it also serves as a useful methodological resource for more advanced researchers. The material is self-contained, requiring only a basic grounding in probability theory and some knowledge of transform techniques.
Contents
- 1. Cramér-Lundberg Model. - 2. Asymptotics. - 3. Regime Switching. - 4. Interest and Two-Sided Jumps. - 5. Threshold-Based Net Cumulative Claim Process. - 6. Level-Dependent Dynamics. - 7. Multivariate Ruin. - 8. Arrival Processes with Clustering. - 9. Dependence Between Claim Sizes and Interarrival Times. - 10. Advanced Bankruptcy Concepts.
