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Loss Models: From Data to Decisions, 4th Edition

Book Description

Praise for the Third Edition

"This book provides in-depth coverage of modelling techniques used throughout many branches of actuarial science. . . . The exceptional high standard of this book has made it a pleasure to read."Annals of Actuarial Science

Newly organized to focus exclusively on material tested in the Society of Actuaries' Exam C and the Casualty Actuarial Society's Exam 4, Loss Models: From Data to Decisions, Fourth Edition continues to supply actuaries with a practical approach to the key concepts and techniques needed on the job. With updated material and extensive examples, the book successfully provides the essential methods for using available data to construct models for the frequency and severity of future adverse outcomes.

The book continues to equip readers with the tools needed for the construction and analysis of mathematical models that describe the process by which funds flow into and out of an insurance system. Focusing on the loss process, the authors explore key quantitative techniques including random variables, basic distributional quantities, and the recursive method, and discuss techniques for classifying and creating distributions. Parametric, non-parametric, and Bayesian estimation methods are thoroughly covered along with advice for choosing an appropriate model.

New features of this Fourth Edition include:

  • Expanded discussion of working with large data sets, now including more practical elements of constructing decrement tables

  • Added coverage of methods for simulating several special situations

  • An updated presentation of Bayesian estimation, outlining conjugate prior distributions and the linear exponential family as well as related computational issues

  • Throughout the book, numerous examples showcase the real-world applications of the presented concepts, with an emphasis on calculations and spreadsheet implementation. A wealth of new exercises taken from previous Exam C/4 exams allows readers to test their comprehension of the material, and a related FTP site features the book's data sets.

    Loss Models, Fourth Edition is an indispensable resource for students and aspiring actuaries who are preparing to take the SOA and CAS examinations. The book is also a valuable reference for professional actuaries, actuarial students, and anyone who works with loss and risk models.

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

    Table of Contents

    1. Cover
    2. Half Title page
    3. Title page
    4. Copyright page
    5. Preface
    6. Part I: Introduction
      1. Chapter 1: Modeling
        1. 1.1 The model-based approach
        2. 1.2 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
    7. 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 Effect of exposure on frequency
        5. Appendix: 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
    8. Part III: Construction of Empirical Models
      1. Chapter 10: Review of Mathematical Statistics
        1. 10.1 Introduction
        2. 10.2 Point estimation
        3. 10.3 Interval estimation
        4. 10.4 Tests of hypotheses
      2. Chapter 11: Estimation for Complete Data
        1. 11.1 Introduction
        2. 11.2 The empirical distribution for complete, individual data
        3. 11.3 Empirical distributions for grouped data
      3. Chapter 12: Estimation for Modified Data
        1. 12.1 Point estimation
        2. 12.2 Means, variances, and interval estimation
        3. 12.3 Kernel density models
        4. 12.4 Approximations for large data sets
    9. Part IV: Parametric Statistical Methods
      1. Chapter 13: Frequentist Estimation
        1. 13.1 Method of moments and percentile matching
        2. 13.2 Maximum likelihood estimation
        3. 13.3 Variance and interval estimation
        4. 13.4 Nonnormal confidence intervals
        5. 13.5 Maximum likelihood estimation of decrement probabilities
      2. Chapter 14: Frequentist Estimation for Discrete Distributions
        1. 14.1 Poisson
        2. 14.2 Negative binomial
        3. 14.3 Binomial
        4. 14.4 The (a, b,1) class
        5. 14.5 Compound models
        6. 14.6 Effect of exposure on maximum likelihood estimation
        7. 14.7 Exercises
      3. Chapter 15: Bayesian Estimation
        1. 15.1 Definitions and Bayes’ Theorem
        2. 15.2 Inference and prediction
        3. 15.3 Conjugate prior distributions and the linear exponential family
        4. 15.4 Computational issues
      4. Chapter 16: Model Selection
        1. 16.1 Introduction
        2. 16.2 Representations of the data and model
        3. 16.3 Graphical comparison of the density and distribution functions
        4. 16.4 Hypothesis tests
        5. 16.5 Selecting a model
    10. Part V: Credibility
      1. Chapter 17: Introduction and Limited Fluctuation Credibility
        1. 17.1 Introduction
        2. 17.2 Limited fluctuation credibility theory
        3. 17.3 Full credibility
        4. 17.4 Partial credibility
        5. 17.5 Problems with the approach
        6. 17.6 Notes and References
        7. 17.7 Exercises
      2. Chapter 18: Greatest Accuracy Credibility
        1. 18.1 introduction
        2. 18.2 Conditional distributions and expectation
        3. 18.3 The Bayesian methodology
        4. 18.4 The credibility premium
        5. 18.5 The Bühlmann model
        6. 18.6 The Bühlmann–Straub model
        7. 18.7 Exact credibility
        8. 18.8 Notes and References
        9. 18.9 Exercises
      3. Chapter 19: Empirical Bayes Parameter Estimation
        1. 19.1 Introduction
        2. 19.2 Nonparametric estimation
        3. 19.3 Semi parametric estimation
        4. 19.4 Notes and References
        5. 19.5 Exercises
    11. Part VI: Simulation
      1. Chapter 20: Simulation
        1. 20.1 Basics of simulation
        2. 20.2 Simulation for specific distributions
        3. 20.3 Determining the sample size
        4. 20.4 Examples of simulation in actuarial modeling
    12. Appendix A: An Inventory of Continuous Distributions
      1. A.1 Introduction
      2. A.2 Transformed beta family
      3. A.3 Transformed gamma family
      4. A.4 Distributions for large losses
      5. A.5 Other distributions
      6. A.6 Distributions with finite support
    13. 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
    14. Appendix C: Frequency and Severity Relationships
    15. Appendix D: The Recursive Formula
    16. 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
    17. Appendix F: Numerical Optimization and Solution of Systems of Equations
      1. F.1 Maximization using Solver
      2. F.2 The simplex method
      3. F.3 Using Excel® to solve equations
    18. References
    19. Index