The Cramér–Lundberg Model and Its Variants: A Queueing Perspective (Springer Actuarial)

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