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001484595 001__ 1484595
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001484595 019__ $$a1410861576$$a1411308502
001484595 020__ $$a9783031391057$$q(electronic bk.)
001484595 020__ $$a3031391055$$q(electronic bk.)
001484595 020__ $$z9783031391040
001484595 020__ $$z3031391047
001484595 0247_ $$a10.1007/978-3-031-39105-7$$2doi
001484595 035__ $$aSP(OCoLC)1412155200
001484595 040__ $$aGW5XE$$beng$$erda$$epn$$cGW5XE$$dEBLCP$$dYDX$$dOCLCO
001484595 049__ $$aISEA
001484595 050_4 $$aHG8781
001484595 08204 $$a368/.01$$223/eng/20231207
001484595 1001_ $$aMandjes, Michel$$q(Michael Robertus Hendrikus),$$d1970-$$eauthor.
001484595 24514 $$aThe Cramér–Lundberg model and its variants :$$ba queueing perspective /$$cMichel Mandjes, Onno Boxma.
001484595 264_1 $$aCham :$$bSpringer,$$c[2023]
001484595 264_4 $$c©2023
001484595 300__ $$a1 online resource (xi, 246 pages) :$$billustrations.
001484595 336__ $$atext$$btxt$$2rdacontent
001484595 337__ $$acomputer$$bc$$2rdamedia
001484595 338__ $$aonline resource$$bcr$$2rdacarrier
001484595 4901_ $$aSpringer actuarial. Springer actuarial textbooks,$$x2523-3319
001484595 504__ $$aIncludes bibliographical references.
001484595 5050_ $$aIntro -- Preface -- Contents -- 1 Cramér-Lundberg Model -- 1.1 Introduction -- 1.2 Ruin Model, and Dual Queueing Model -- 1.3 Method 1: Conditioning on the First Event -- 1.4 Method 2: Ladder Heights, Busy Periods -- 1.5 Method 3: Kella-Whitt Martingale -- 1.6 Method 4: Kolmogorov Forward Equations -- 1.7 Discussion and Bibliographical Notes -- 1.8 Biographical Sketches -- Exercises -- References -- 2 Asymptotics -- 2.1 Introduction -- 2.2 Light-Tailed Case -- 2.3 Subexponential Case -- 2.4 Time-Dependent Ruin Probability -- 2.5 Heavy Traffic -- 2.6 Discussion and Bibliographical Notes
001484595 5058_ $$aExercises -- 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
001484595 5058_ $$a5.1 Introduction -- 5.2 Scale Functions -- 5.3 Decomposition -- 5.4 Computation of Auxiliary Objects -- 5.5 Discussion and Bibliographical Notes -- Exercises -- References -- 6 Level-Dependent Dynamics -- 6.1 Introduction -- 6.2 Level-Dependent Premium Rate -- 6.3 Level-Dependent Premium Rate and Claim Arrival Rate -- 6.4 A Specific Level-Dependent Model -- 6.5 A Tax Identity -- 6.6 Discussion and Bibliographical Notes -- Exercises -- References -- 7 Multivariate Ruin -- 7.1 Introduction -- 7.2 Two-Dimensional Case -- 7.3 Higher-Dimensional Case -- 7.4 Tandem Queueing Networks
001484595 5058_ $$a7.5 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
001484595 5058_ $$a9.5 Discussion and Bibliographical Notes -- Exercises -- References -- 10 Advanced Bankruptcy Concepts -- 10.1 Introduction -- 10.2 Poisson Inspection Times -- 10.3 Length of First Excursion -- 10.4 Total Time with Negative Surplus -- 10.5 Discussion and Bibliographical Notes -- Exercises -- References -- A Laplace Transforms -- A.1 Definitions -- A.2 Some Convenient Properties -- A.3 Some Useful Concepts and Results -- A.4 Discussion and Bibliographical Notes -- Exercises -- B Some Queueing Theory -- B.1 Single-Server Queue M/G/1 -- B.2 Infinite-Server Queue M/G/Infinity
001484595 506__ $$aAccess limited to authorized users.
001484595 520__ $$aThis book offers a comprehensive examination of the Cramér–Lundberg model, which is the most extensively researched model in ruin theory. It covers the fundamental dynamics of an insurance company's surplus level in great detail, presenting a thorough analysis of the ruin probability and related measures for both the standard model and its variants. Providing a systematic and self-contained approach to evaluate the crucial quantities found in the Cramér–Lundberg model, the book makes use of connections with related queueing models when appropriate, and its emphasis on clean transform-based techniques sets it apart from other works. In addition to consolidating a wealth of existing results, the book also derives several new outcomes using the same methodology. This material is complemented by a thoughtfully chosen collection of exercises. The book's primary target audience is master's and starting PhD students in applied mathematics, operations research, and actuarial science, although it also serves as a useful methodological resource for more advanced researchers. The material is self-contained, requiring only a basic grounding in probability theory and some knowledge of transform techniques.
001484595 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed December 7, 2023).
001484595 650_6 $$aAssurance$$xModèles mathématiques.
001484595 650_0 $$aInsurance$$xMathematical models.$$0(DLC)sh 85066827
001484595 655_0 $$aElectronic books.
001484595 7001_ $$aBoxma, O. J.,$$d1952-$$eauthor.
001484595 77608 $$iPrint version:$$aMandjes, Michel$$tThe Cramér-Lundberg Model and Its Variants$$dCham : Springer,c2024$$z9783031391040
001484595 830_0 $$aSpringer actuarial.$$pSpringer actuarial textbooks.$$x2523-3319
001484595 852__ $$bebk
001484595 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-39105-7$$zOnline Access$$91397441.1
001484595 909CO $$ooai:library.usi.edu:1484595$$pGLOBAL_SET
001484595 980__ $$aBIB
001484595 980__ $$aEBOOK
001484595 982__ $$aEbook
001484595 983__ $$aOnline
001484595 994__ $$a92$$bISE