The Cramér-Lundberg Model and Its Variants : A Queueing Perspective / / Michel Mandjes and Onno Boxma

• Autore: Mandjes Michel <1970->
• Pubblicazione: Cham, Switzerland : , : Springer, , [2023]; ©2023
• Edizione: First edition.
• Descrizione fisica: 1 online resource (XI, 246 p. 31 illus.)
• Disciplina: 354.81150006
• Soggetto topico: Insurance - Mathematical models
• Persona (resp. second.): BoxmaOnno
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Cramér-Lundberg Model -- 1.1 Introduction -- 1.2 Ruin Model, and Dual Queueing Model -- 1.3 Method 1: Conditioning on the First Event -- 1.4 Method 2: Ladder Heights, Busy Periods -- 1.5 Method 3: Kella-Whitt Martingale -- 1.6 Method 4: Kolmogorov Forward Equations -- 1.7 Discussion and Bibliographical Notes -- 1.8 Biographical Sketches -- Exercises -- References -- 2 Asymptotics -- 2.1 Introduction -- 2.2 Light-Tailed Case -- 2.3 Subexponential Case -- 2.4 Time-Dependent Ruin Probability -- 2.5 Heavy Traffic -- 2.6 Discussion and Bibliographical Notes -- Exercises -- References -- 3 Regime Switching -- 3.1 Introduction -- 3.2 System of Linear Equations for Transforms -- 3.3 Identification of the Unknown Constants -- 3.4 Cramér-Lundberg Model Over a Phase-Type Horizon -- 3.5 Resampling -- 3.6 Discussion and Bibliographical Notes -- Exercises -- References -- 4 Interest and Two-Sided Jumps -- 4.1 Introduction -- 4.2 Model and Notation -- 4.3 Exponential Upward Jumps -- 4.4 Relaxation of the Exponentiality Assumptions -- 4.5 Discussion and Bibliographical Notes -- Exercises -- References -- 5 Threshold-Based Net Cumulative Claim Process -- 5.1 Introduction -- 5.2 Scale Functions -- 5.3 Decomposition -- 5.4 Computation of Auxiliary Objects -- 5.5 Discussion and Bibliographical Notes -- Exercises -- References -- 6 Level-Dependent Dynamics -- 6.1 Introduction -- 6.2 Level-Dependent Premium Rate -- 6.3 Level-Dependent Premium Rate and Claim Arrival Rate -- 6.4 A Specific Level-Dependent Model -- 6.5 A Tax Identity -- 6.6 Discussion and Bibliographical Notes -- Exercises -- References -- 7 Multivariate Ruin -- 7.1 Introduction -- 7.2 Two-Dimensional Case -- 7.3 Higher-Dimensional Case -- 7.4 Tandem Queueing Networks -- 7.5 Multivariate Gerber-Shiu Metrics -- 7.6 Discussion and Bibliographical Notes -- Exercises. ; References -- 8 Arrival Processes with Clustering -- 8.1 Introduction -- 8.2 M/G/Infinity Driven Arrivals -- 8.3 Shot-Noise Driven Arrivals -- 8.4 Hawkes Driven Arrivals -- 8.5 Discussion and Bibliographical Notes -- Exercises -- References -- 9 Dependence Between Claim Sizes and Interarrival Times -- 9.1 Introduction -- 9.2 Claim Size Being Correlated with Previous Interarrival Time -- 9.3 Interarrival Time Being Correlated with Previous Claim Size -- 9.4 A More General Markov-Dependent Risk Model -- 9.5 Discussion and Bibliographical Notes -- Exercises -- References -- 10 Advanced Bankruptcy Concepts -- 10.1 Introduction -- 10.2 Poisson Inspection Times -- 10.3 Length of First Excursion -- 10.4 Total Time with Negative Surplus -- 10.5 Discussion and Bibliographical Notes -- Exercises -- References -- A Laplace Transforms -- A.1 Definitions -- A.2 Some Convenient Properties -- A.3 Some Useful Concepts and Results -- A.4 Discussion and Bibliographical Notes -- Exercises -- B Some Queueing Theory -- B.1 Single-Server Queue M/G/1 -- B.2 Infinite-Server Queue M/G/Infinity -- B.3 Discussion and Bibliographical Notes -- Exercises -- References.
• Sommario/riassunto: 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.
• Titolo autorizzato: The Cramér-Lundberg Model and Its Variants
• ISBN: 3-031-39105-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910766880203321
• Lo trovi qui: Univ. Federico II
• Serie: Springer advanced texts in chemistry.