Loss models : further topics / Stuart A. Klugman, Society of Actuaries, Schaumburg, IL, Harry H. Panjer, Department of Statistics and Actuarial Science, University of Waterloo, Ontario, Canada, Gordon E. Willmot, Department of Statistics and Actuarial Science, University of Waterloo, Ontario, Canada.

Includes bibliographical references and index.

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 attraction4.6 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 analogues5.4 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 processes7.1.1 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 delays10 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.

An essential resource for constructing and analyzing advanced actuarial models Loss Models: Further Topics presents extended coverage of modeling through the use of tools related to risk theory, loss distributions, and survival models. The book uses these methods to construct and evaluate actuarial models in the fields of insurance and business. Providing an advanced study of actuarial methods, the book features extended discussions of risk modeling and risk measures, including Tail-Value-at-Risk. Loss Models: Further Topics contains additional material to accompany the Fourth Edition of Loss.

Print version record and CIP data provided by publisher.