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Loss Models: From Data to Decisions (One Year Online: Preparation for Actuarial Exam C/4), 3rd Edition

ISBN: 978-0-470-30027-5
October 2011, ©2011
Loss Models: From Data to Decisions (One Year Online: Preparation for Actuarial Exam C/4), 3rd Edition (0470300272) cover image


This online, multi-color, self-looping electronic product has full text with searchable links; more than 75 plugged-in data sets (in EXCEL); thousands of uniquely-designed and randomly-selected sample SOA/CAS/CIA test exercises, complete with hints and worked-out solutions; and multiple forms of simulated exams; and a built-in record-keeping system.

There are three modules in this application:

  • The Prologue Module describes the book, its authors, and how to best use the product.
  • The Chapter Modules represent the text proper, complete with examples and exercise/solution sets (some static, some with spreadsheet functionality, and some with regeneration functionality).
  • The Exam Modules present simulations of the actuarial Exam C/4. Each exam features multiple choice questions similar in content and difficulty to those on C/4. Detailed solutions are provided.

Upon ordering, customers will receive an email that contains a registration code, which is needed to access the application.

To explore our additional offerings in actuarial exam preparation visit www.wiley.com/go/c4actuarial

Online3e is the perfect electronic substitute for a traditional linear book. Price includes one-year access/subscription. Once purchased, the product is nonreturnable.

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Table of Contents



1. Modeling.

1.1 The model-based approach.

1.2 Organization of this book.

2. Random variables.

2.1 Introduction.

2.2 Key functions and four models.

3. Basic distributional quantities.

3.1 Moments.

3.2 Quantiles.

3.3 Generating functions and sums of random variables.

3.4 Tails of distributions.

3.5 Measures of Risk.


4. Characteristics of actuarial models.

4.1 Introduction.

4.2 The role of parameters.

5. Continuous models.

5.1 Introduction.

5.2 Creating new distributions.

5.3 Selected distributions and their relationships.

5.4 The linear exponential family.

5.5 TVaR for continuous distributions.

5.6 Extreme value distributions.

6. Discrete distributions and processes.

6.1 Introduction.

6.2 The Poisson distribution.

6.3 The negative binomial distribution.

6.4 The binomial distribution.

6.5 The (a, b, 0) class.

6.6 Counting processes.

6.7 Truncation and modification at zero.

6.8 Compound frequency models.

6.9 Further properties of the compound Poisson class.

6.10 Mixed Poisson distributions.

6.11 Mixed Poisson processes.

6.12 Effect of exposure on frequency.

6.13 An inventory of discrete distributions.

6.14 TVaR for discrete distributions.

7. Multivariate models.

7.1 Introduction.

7.2 Sklara??s theorem and copulas.

7.3 Measures of dependency.

7.4 Tail dependence.

7.5 Archimedean copulas.

7.6 Elliptical copulas.

7.7 Extreme value copulas.

7.8 Archimax copulas.

8. Frequency and severity with coverage modifications.

8.1 Introduction.

8.2 Deductibles.

8.3 The loss elimination ratio and the effect of inflation for ordinary deductibles.

8.4 Policy limits.

8.5 Coinsurance, deductibles, and limits.

8.6 The impact of deductibles on claim frequency.

9. Aggregate loss models.

9.1 Introduction.

9.2 Model choices.

9.3 The compound model for aggregate claims.

9.4 Analytic results.

9.5 Computing the aggregate claims distribution.

9.6 The recursive method.

9.7 The impact of individual policy modifications on aggregate payments.

9.8 Inversion methods.

9.9 Calculations with approximate distributions.

9.10 Comparison of methods.

9.11 The individual risk model.

9.12 TVaR for aggregate losses.

10. Discrete-time ruin models.

10.1 Introduction.

10.2 Process models for insurance.

10.3 Discrete, finite-time ruin probabilities.

11. Continuous-time ruin models.

11.1 Introduction.

11.2 The adjustment coefficient and Lundberga??s inequality.

11.3 An integrodifferential equation.

11.4 The maximum aggregate loss.

11.5 Cramera??s asymptotic ruin formula and Tijms' approximation.

11.6 The Brownian motion risk process.

11.7 Brownian motion and the probability of ruin.


12. Review of mathematical statistics.

12.1 Introduction.

12.2 Point estimation.

12.3 Interval estimation.

12.4 Tests of hypotheses.

13. Estimation for complete data.

13.1 Introduction.

13.2 The empirical distribution for complete, individual data.

13.3 Empirical distributions for grouped data.

14. Estimation for modified data.

14.1 Point estimation.

14.2 Means, variances, and interval estimation.

14.3 Kernel density models.

14.4 Approximations for large data sets.


15. Parameter estimation.

15.1 Method of moments and percentile matching.

15.2 Maximum likelihood estimation.

15.3 Variance and interval estimation.

15.4 Non-normal confidence intervals.

15.5 Bayesian estimation.

15.6 Estimation for discrete distributions.

15.6.7 Exercises.

16. Model selection.

16.1 Introduction.

16.2 Representations of the data and model.

16.3 Graphical comparison of the density and distribution functions.

16.4 Hypothesis tests.

16.5 Selecting a model.

17. Estimation and model selection for more complex models.

17.1 Extreme value models.

17.2 Copula models.

17.3 Models with covariates.

18. Five examples.

18.1 Introduction.

18.2 Time to death.

18.3 Time from incidence to report.

18.4 Payment amount.

18.5 An aggregate loss example.

18.6 Another aggregate loss example.

18.7 Comprehensive exercises.


19. Interpolation and smoothing.

19.1 Introduction.

19.2 Polynomial interpolation and smoothing.

19.3 Cubic spline interpolation.

19.4 Approximating functions with splines.

19.5 Extrapolating with splines.

19.6 Smoothing splines.

20. Credibility.

20.1 Introduction.

20.2 Limited fluctuation credibility theory.

20.3 Greatest accuracy credibility theory.

20.4 Empirical Bayes parameter estimation.


21. Simulation.

21.1 Basics of simulation.

21.2 Examples of simulation in actuarial modeling.

21.3 Examples of simulation in finance.

Appendix A: An inventory of continuous distributions.

Appendix B: An inventory of discrete distributions.

Appendix C: Frequency and severity relationships.

Appendix D: The recursive formula.

Appendix E: Discretization of the severity distribution.

Appendix F: Numerical optimization and solution of systems of equations.



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Author Information

STUART A. KLUGMAN, PhD, is Principal Financial Group Distinguished Professor of Actuarial Science at Drake University. A Fellow of the Society of Actuaries, Dr. Klugman was vice president of the SOA from 2001–2003.

HARRY H. PANJER, PhD, is Professor Emeritus in the Department of Statistics and Actuarial Science at the University of Waterloo, Canada. Past president of both the Canadian Institute of Actuaries and the Society of Actuaries, Dr. Panjer has published numerous articles on risk modeling in the fields of finance and actuarial science.

GORDON E. WILLMOT, PhD, is Munich Re Chair in Insurance and Professor in the Department of Statistics and Actuarial Science at the University of Waterloo, Canada. Dr. Willmot has authored or coauthored over sixty published articles in the areas of risk theory, queueing theory, distribution theory, and stochastic modeling in insurance.

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