Loss Models Further Topics 1st Edition by Stuart A Klugman, Harry H Panjer, Gordon E Willmot ISBN 1118343565 9781118343562

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ISBN 10: 1118343565 
ISBN 13: 9781118343562
Author: Stuart A Klugman, Harry H Panjer, Gordon E Willmot

Loss Models Further Topics 1st Table of contents:

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 Definition 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 inflation
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
  10.9 Estimation of parameters

• 10.9.1 Introduction

• 10.9.2 Maximum likelihood estimation

• 10.9.3 Semiparametric estimation

• 10.9.4 The role of deductibles

• 10.9.5 Goodness-of-fit testing

• 10.9.6 An example

• 10.9.7 Exercise
  10.10 Simulation from Copula Models

• 10.10.1 Simulating from the Gaussian copula

• 10.10.2 Simulating from the t copula

11. Continuous-Time Ruin Models
11.1 Introduction

• 11.1.1 The Poisson process

• 11.1.2 The continuous-time problem
  11.2 The adjustment coefficient and Lundberg’s inequality

• 11.2.1 The adjustment coefficient

• 11.2.2 Lundberg’s inequality

• 11.2.3 Exercises
  11.3 An integrodifferential equation

• 11.3.1 Exercises
  11.4 The maximum aggregate loss

• 11.4.1 Exercises
  11.5 Cramer’s asymptotic ruin formula and Tijms’ approximation

• 11.5.1 Exercises
  11.6 The Brownian motion risk process
  11.7 Brownian motion and the probability of ruin

12. Interpolation and Smoothing
12.1 Introduction
12.2 Interpolation with Splines

• 12.2.1 Exercises
  12.3 Extrapolating with splines

• 12.3.1 Exercise
  12.4 Smoothing with Splines

• 12.4.1 Exercise

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