Loss Models Further Topics.

Detalles Bibliográficos
Autor principal: Klugman, Stuart A.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2013.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title Page
  • Copyright Page
  • CONTENTS
  • Preface
  • 1 Introduction
  • 2 Coxian and related distributions
  • 2.1 Introduction
  • 2.2 Combinations of exponentials
  • 2.3 Coxian-2 distributions
  • 3 Mixed Erlang distributions
  • 3.1 Introduction
  • 3.2 Members of the mixed Erlang class
  • 3.3 Distributional properties
  • 3.4 Mixed Erlang claim severity models
  • 4 Extreme value distributions
  • 4.1 Introduction
  • 4.2 Distribution of the maximum
  • 4.2.1 From a fixed number of losses
  • 4.2.2 From a random number of losses
  • 4.3 Stability of the maximum of the extreme value distribution
  • 4.4 The Fisher-Tippett theorem
  • 4.5 Maximum domain of attraction
  • 4.6 Generalized Pareto distributions
  • 4.7 Stability of excesses of the generalized Pareto
  • 4.8 Limiting distributions of excesses
  • 4.9 Parameter estimation
  • 4.9.1 Maximum likelihood estimation from the extreme value distribution
  • 4.9.2 Maximum likelihood estimation for the generalized Pareto distribution
  • 4.9.3 Estimating the Pareto shape parameter
  • 4.9.4 Estimating extreme probabilities
  • 4.9.5 Mean excess plots
  • 4.9.6 Further reading
  • 4.9.7 Exercises
  • 5 Analytic and related methods for aggregate claim models
  • 5.1 Introduction
  • 5.2 Elementary approaches
  • 5.3 Discrete analogues
  • 5.4 Right-tail asymptotics for aggregate losses
  • 5.4.1 Exercises
  • 6 Computational methods for aggregate models
  • 6.1 Recursive techniques for compound distributions
  • 6.2 Inversion methods
  • 6.2.1 Fast Fourier transform
  • 6.2.2 Direct numerical inversion
  • 6.3 Calculations with approximate distributions
  • 6.3.1 Arithmetic distributions
  • 6.3.2 Empirical distributions
  • 6.3.3 Piecewise linear cdf
  • 6.3.4 Exercises
  • 6.4 Comparison of methods
  • 6.5 The individual risk model
  • 6.5.1 De.nition and notation
  • 6.5.2 Direct calculation
  • 6.5.3 Recursive calculation
  • 7 Counting Processes
  • 7.1 Nonhomogeneous birth processes
  • 7.1.1 Exercises
  • 7.2 Mixed Poisson processes
  • 7.2.1 Exercises
  • 8 Discrete Claim Count Models
  • 8.1 Unification of the (a, b, 1) and mixed Poisson classes
  • 8.2 A class of discrete generalized tail-based distributions
  • 8.3 Higher order generalized tail-based distributions
  • 8.4 Mixed Poisson properties of generalized tail-based distributions
  • 8.5 Compound geometric properties of generalized tail-based distributions
  • 8.5.1 Exercises
  • 9 Compound distributions with time dependent claim amounts
  • 9.1 Introduction
  • 9.2 A model for infiation
  • 9.3 A model for claim payment delays
  • 10 Copula models
  • 10.1 Introduction
  • 10.2 Sklar's theorem and copulas
  • 10.3 Measures of dependency
  • 10.3.1 Spearman's rho
  • 10.3.2 Kendall's tau
  • 10.4 Tail dependence
  • 10.5 Archimedean copulas
  • 10.5.1 Exercise
  • 10.6 Elliptical copulas
  • 10.6.1 Exercise
  • 10.7 Extreme value copulas
  • 10.7.1 Exercises
  • 10.8 Archimax copulas

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