The Cramér-Lundberg model and its variants : a queueing perspective / Michel Mandjes, Onno Boxma.
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 relat...
Saved in:
| Online Access: |
Full Text (via Springer) |
|---|---|
| Main Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham :
Springer,
[2023]
|
| Series: | Springer actuarial. Springer actuarial textbooks.
|
| Subjects: |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | in00000116452 | ||
| 006 | m o d | ||
| 007 | cr ||||||||||| | ||
| 008 | 231207s2023 sz a ob 000 0 eng d | ||
| 005 | 20240423173752.5 | ||
| 019 | |a 1410861576 |a 1411308502 | ||
| 020 | |a 9783031391057 |q (electronic bk.) | ||
| 020 | |a 3031391055 |q (electronic bk.) | ||
| 020 | |z 9783031391040 | ||
| 020 | |z 3031391047 | ||
| 024 | 7 | |a 10.1007/978-3-031-39105-7 |2 doi | |
| 035 | |a (OCoLC)spr1412155200 | ||
| 035 | |a (OCoLC)1412155200 |z (OCoLC)1410861576 |z (OCoLC)1411308502 | ||
| 037 | |a spr978-3-031-39105-7 | ||
| 040 | |a GW5XE |b eng |e rda |e pn |c GW5XE |d EBLCP |d YDX |d OCLCO | ||
| 049 | |a GWRE | ||
| 050 | 4 | |a HG8781 | |
| 100 | 1 | |a Mandjes, Michel |q (Michael Robertus Hendrikus), |d 1970- |e author. |0 http://id.loc.gov/authorities/names/nb2007011360 |1 http://isni.org/isni/0000000114774136 | |
| 245 | 1 | 4 | |a The Cramér-Lundberg model and its variants : |b a queueing perspective / |c Michel Mandjes, Onno Boxma. |
| 264 | 1 | |a Cham : |b Springer, |c [2023] | |
| 264 | 4 | |c ©2023 | |
| 300 | |a 1 online resource (xi, 246 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Springer actuarial. Springer actuarial textbooks, |x 2523-3319 | |
| 504 | |a Includes bibliographical references. | ||
| 520 | |a 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. | ||
| 588 | 0 | |a Online resource; title from PDF title page (SpringerLink, viewed December 7, 2023). | |
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 650 | 0 | |a Insurance |x Mathematical models. |0 http://id.loc.gov/authorities/subjects/sh2008123875 | |
| 700 | 1 | |a Boxma, O. J., |d 1952- |e author. |0 http://id.loc.gov/authorities/names/n83065324 |1 http://isni.org/isni/000000010892998X | |
| 776 | 0 | 8 | |i Print version: |a Mandjes, Michel |t The Cramér-Lundberg Model and Its Variants |d Cham : Springer,c2024 |z 9783031391040 |
| 856 | 4 | 0 | |u https://colorado.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-39105-7 |z Full Text (via Springer) |
| 830 | 0 | |a Springer actuarial. |p Springer actuarial textbooks. | |
| 915 | |a - | ||
| 944 | |a MARS | ||
| 956 | |a Springer e-books | ||
| 956 | |b Springer Nature - Springer Mathematics and Statistics eBooks 2023 English International | ||
| 994 | |a 92 |b COD | ||
| 998 | |b OCLC control number change | ||
| 999 | f | f | |s ae065f7c-c97c-4d06-993e-81cf5f40defa |i 99d7a463-3f10-46e1-9528-244c546e53a8 |
| 952 | f | f | |p Can circulate |a University of Colorado Boulder |b Online |c Online |d Online |e HG8781 |h Library of Congress classification |i web |