Loss Models, 5th Edition

Loss Models, 5th Edition

by Stuart A. Klugman, Harry H. Panjer, Gordon E. Willmot
Released May 2019
Publisher(s): Wiley
ISBN: 9781119523789

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Book description

A guide that provides in-depth coverage of modeling techniques used throughout many branches of actuarial science, revised and updated

Now in its fifth edition, Loss Models: From Data to Decisions puts the focus on material tested in the Society of Actuaries (SOA) newly revised Exams STAM (Short-Term Actuarial Mathematics) and LTAM (Long-Term Actuarial Mathematics). Updated to reflect these exam changes, this vital resource offers actuaries, and those aspiring to the profession, a practical approach to the concepts and techniques needed to succeed in the profession. The techniques are also valuable for anyone who uses loss data to build models for assessing risks of any kind.

Loss Models contains a wealth of examples that highlight the real-world applications of the concepts presented, and puts the emphasis on calculations and spreadsheet implementation. With a focus on the loss process, the book reviews the essential quantitative techniques such as random variables, basic distributional quantities, and the recursive method, and discusses techniques for classifying and creating distributions. Parametric, non-parametric, and Bayesian estimation methods are thoroughly covered. In addition, the authors offer practical advice for choosing an appropriate model. This important text:

•    Presents a revised and updated edition of the classic guide for actuaries that aligns with newly introduced Exams STAM and LTAM

•    Contains a wealth of exercises taken from previous exams

•    Includes fresh and additional content related to the material required by the Society of Actuaries (SOA) and the Canadian Institute of Actuaries (CIA)

•    Offers a solutions manual available for further insight, and all the data sets and supplemental material are posted on a companion site

Written for students and aspiring actuaries who are preparing to take the SOA examinations, Loss Models offers an essential guide to the concepts and techniques of actuarial science. 

Table of contents

  1. Cover
  2. Series Page
  3. Title Page
  4. Copyright
  5. Preface
  6. About the Companion Website
  7. Part I: Introduction
    1. Chapter 1: Modeling
      1. 1.1 The Model-Based Approach
      2. 1.2 The Organization of This Book
    2. Chapter 2: Random Variables
      1. 2.1 Introduction
      2. 2.2 Key Functions and Four Models
    3. Chapter 3: Basic Distributional Quantities
      1. 3.1 Moments
      2. 3.2 Percentiles
      3. 3.3 Generating Functions and Sums of Random Variables
      4. 3.4 Tails of Distributions
      5. 3.5 Measures of Risk
  8. Part II: Actuarial Models
    1. Chapter 4: Characteristics of Actuarial Models
      1. 4.1 Introduction
      2. 4.2 The Role of Parameters
    2. Chapter 5: Continuous Models
      1. 5.1 Introduction
      2. 5.2 Creating New Distributions
      3. 5.3 Selected Distributions and Their Relationships
      4. 5.4 The Linear Exponential Family
    3. Chapter 6: Discrete Distributions
      1. 6.1 Introduction
      2. 6.2 The Poisson Distribution
      3. 6.3 The Negative Binomial Distribution
      4. 6.4 The Binomial Distribution
      5. 6.5 The (a,b,0) Class
      6. 6.6 Truncation and Modification at Zero
    4. Chapter 7: Advanced Discrete Distributions
      1. 7.1 Compound Frequency Distributions
      2. 7.2 Further Properties of the Compound Poisson Class
      3. 7.3 Mixed-Frequency Distributions
      4. 7.4 The Effect of Exposure on Frequency
      5. 7.5 An Inventory of Discrete Distributions
    5. Chapter 8: Frequency and Severity with Coverage Modifications
      1. 8.1 Introduction
      2. 8.2 Deductibles
      3. 8.3 The Loss Elimination Ratio and the Effect of Inflation for Ordinary Deductibles
      4. 8.4 Policy Limits
      5. 8.5 Coinsurance, Deductibles, and Limits
      6. 8.6 The Impact of Deductibles on Claim Frequency
    6. Chapter 9: Aggregate Loss Models
      1. 9.1 Introduction
      2. 9.2 Model Choices
      3. 9.3 The Compound Model for Aggregate Claims
      4. 9.4 Analytic Results
      5. 9.5 Computing the Aggregate Claims Distribution
      6. 9.6 The Recursive Method
      7. 9.7 The Impact of Individual Policy Modifications on Aggregate Payments
      8. 9.8 The Individual Risk Model
  9. Part III: Mathematical Statistics
    1. Chapter 10: Introduction to Mathematical Statistics
      1. 10.1 Introduction and Four Data Sets
      2. 10.2 Point Estimation
      3. 10.3 Interval Estimation
      4. 10.4 The Construction of Parametric Estimators
      5. 10.5 Tests of Hypotheses
    2. Chapter 11: Maximum Likelihood Estimation
      1. 11.1 Introduction
      2. 11.2 Individual Data
      3. 11.3 Grouped Data
      4. 11.4 Truncated or Censored Data
      5. 11.5 Variance and Interval Estimation for Maximum Likelihood Estimators
      6. 11.6 Functions of Asymptotically Normal Estimators
      7. 11.7 Nonnormal Confidence Intervals
    3. Chapter 12: Frequentist Estimation for Discrete Distributions
      1. 12.1 The Poisson Distribution
      2. 12.2 The Negative Binomial Distribution
      3. 12.3 The Binomial Distribution
      4. 12.4 The (a,b,1) Class
      5. 12.5 Compound Models
      6. 12.6 The Effect of Exposure on Maximum Likelihood Estimation
      7. 12.7 Exercises
    4. Chapter 13: Bayesian Estimation
      1. 13.1 Definitions and Bayes' Theorem
      2. 13.2 Inference and Prediction
      3. 13.3 Conjugate Prior Distributions and the Linear Exponential Family
      4. 13.4 Computational Issues
  10. Part IV: Construction of Models
    1. Chapter 14: Construction of Empirical Models
      1. 14.1 The Empirical Distribution
      2. 14.2 Empirical Distributions for Grouped Data
      3. 14.3 Empirical Estimation with Right Censored Data
      4. 14.4 Empirical Estimation of Moments
      5. 14.5 Empirical Estimation with Left Truncated Data
      6. 14.6 Kernel Density Models
      7. 14.7 Approximations for Large Data Sets
      8. 14.8 Maximum Likelihood Estimation of Decrement Probabilities
      9. 14.9 Estimation of Transition Intensities
    2. Chapter 15: Model Selection
      1. 15.1 Introduction
      2. 15.2 Representations of the Data and Model
      3. 15.3 Graphical Comparison of the Density and Distribution Functions
      4. 15.4 Hypothesis Tests
      5. 15.5 Selecting a Model
  11. Part V: Credibility
    1. Chapter 16: Introduction To Limited Fluctuation Credibility
      1. 16.1 Introduction
      2. 16.2 Limited Fluctuation Credibility Theory
      3. 16.3 Full Credibility
      4. 16.4 Partial Credibility
      5. 16.5 Problems with the Approach
      6. 16.6 Notes and References
      7. 16.7 Exercises
    2. Chapter 17: Greatest Accuracy Credibility
      1. 17.1 Introduction
      2. 17.2 Conditional Distributions and Expectation
      3. 17.3 The Bayesian Methodology
      4. 17.4 The Credibility Premium
      5. 17.5 The Bühlmann Model
      6. 17.6 The Bühlmann–Straub Model
      7. 17.7 Exact Credibility
      8. 17.8 Notes and References
      9. 17.9 Exercises
    3. Chapter 18: Empirical Bayes Parameter Estimation
      1. 18.1 Introduction
      2. 18.2 Nonparametric Estimation
      3. 18.3 Semiparametric Estimation
      4. 18.4 Notes and References
      5. 18.5 Exercises
  12. Part VI: Simulation
    1. Chapter 19: Simulation
      1. 19.1 Basics of Simulation
      2. 19.2 Simulation for Specific Distributions
      3. 19.3 Determining the Sample Size
      4. 19.4 Examples of Simulation in Actuarial Modeling
  13. Appendix A: An Inventory of Continuous Distributions
    1. A.1 Introduction
    2. A.2 The Transformed Beta Family
    3. A.3 The Transformed Gamma Family
    4. A.4 Distributions for Large Losses
    5. A.5 Other Distributions
    6. A.6 Distributions with Finite Support
  14. Appendix B: An Inventory of Discrete Distributions
    1. B.1 Introduction
    2. B.2 The (a,b,0) Class
    3. B.3 The (a,b,1) Class
    4. B.4 The Compound Class
    5. B.5 A Hierarchy of Discrete Distributions
  15. Appendix C: Frequency and Severity Relationships
  16. Appendix D: The Recursive Formula
  17. Appendix E: Discretization of the Severity Distribution
    1. E.1 The Method of Rounding
    2. E.2 Mean Preserving
    3. E.3 Undiscretization of a Discretized Distribution
  18. References
  19. Index
  20. End User License Agreement

Product information

  • Title: Loss Models, 5th Edition
  • Author(s): Stuart A. Klugman, Harry H. Panjer, Gordon E. Willmot
  • Release date: May 2019
  • Publisher(s): Wiley
  • ISBN: 9781119523789