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Predictive Modeling Applications in Actuarial Science

Book Description

Predictive modeling involves the use of data to forecast future events. It relies on capturing relationships between explanatory variables and the predicted variables from past occurrences and exploiting this to predict future outcomes. Forecasting future financial events is a core actuarial skill - actuaries routinely apply predictive-modeling techniques in insurance and other risk-management applications. This book is for actuaries and other financial analysts who are developing their expertise in statistics and wish to become familiar with concrete examples of predictive modeling. The book also addresses the needs of more seasoned practising analysts who would like an overview of advanced statistical topics that are particularly relevant in actuarial practice. Predictive Modeling Applications in Actuarial Science emphasizes lifelong learning by developing tools in an insurance context, providing the relevant actuarial applications, and introducing advanced statistical techniques that can be used by analysts to gain a competitive advantage in situations with complex data.

Table of Contents

  1. Cover
  2. Half title
  3. Series
  4. Title page
  5. Copyright
  6. Table of Contents
  7. Contributor List
  8. Acknowledgments
  9. 1 Predictive Modeling in Actuarial Science
    1. 1.1 Introduction
    2. 1.2 Predictive Modeling and Insurance Company Operations
    3. 1.3 A Short History of Predictive Modeling in Actuarial Science
    4. 1.4 Goals of the Series
    5. References
  10. I Predictive Modeling Foundations
    1. 2 Overview of Linear Models
      1. 2.1 Introduction
      2. 2.2 Linear Model Theory with Examples
      3. 2.3 Case Study
      4. 2.4 Conclusion
      5. 2.5 Exercises
      6. References
    2. 3 Regression with Categorical Dependent Variables
      1. 3.1 Coding Categorical Variables
      2. 3.2 Modeling a Binary Response
      3. 3.3 Logistic Regression Model
      4. 3.4 Probit and Other Binary Regression Models
      5. 3.5 Models for Ordinal Categorical Dependent Variables
      6. 3.6 Models for Nominal Categorical Dependent Variables
      7. 3.7 Further Reading
      8. References
    3. 4 Regression with Count-Dependent Variables
      1. 4.1 Introduction
      2. 4.2 Poisson Distribution
      3. 4.3 Poisson Regression
      4. 4.4 Heterogeneity in the Distribution
      5. 4.5 Zero-Inflated Distribution
      6. 4.6 Conclusion
      7. 4.7 Further Reading
      8. References
    4. 5 Generalized Linear Models
      1. 5.1 Introduction to Generalized Linear Models
      2. 5.2 Exponential Family of Distributions
      3. 5.3 Link Functions
      4. 5.4 Maximum Likelihood Estimation
      5. 5.5 Generalized Linear Model Review
      6. 5.6 Applications
      7. 5.7 Comparing Models
      8. 5.8 Conclusion
      9. 5.9 Appendix A. Binomial and Gamma Distributions in Exponential Family Form
      10. 5.10 Appendix B. Calculating Mean and Variance from Exponential Family Form
      11. References
    5. 6 Frequency and Severity Models
      1. 6.1 How Frequency Augments Severity Information
      2. 6.2 Sampling and the Generalized Linear Model
      3. 6.3 Frequency-Severity Models
      4. 6.4 Application: Massachusetts Automobile Claims
      5. 6.5 Further Reading
      6. 6.6 Appendix A. Sample Average Distribution in Linear Exponential Families
      7. 6.7 Appendix B. Over-Sampling Claims
      8. References
  11. II Predictive Modeling Methods
    1. 7 Longitudinal and Panel Data Models
      1. 7.1 Introduction
      2. 7.2 Linear Models
      3. 7.3 Nonlinear Models
      4. 7.4 Additional Considerations
      5. 7.5 Further Reading
      6. References
    2. 8 Linear Mixed Models
      1. 8.1 Mixed Models in Actuarial Science
      2. 8.2 Linear Mixed Models
      3. 8.3 Examples
      4. 8.4 Further Reading and Illustrations
      5. References
    3. 9 Credibility and Regression Modeling
      1. 9.1 Introduction
      2. 9.2 Credibility and the LMM Framework
      3. 9.3 Numerical Examples
      4. 9.4 Theory versus Practice
      5. 9.5 Further Reading
      6. 9.6 Appendix
      7. References
    4. 10 Fat-Tailed Regression Models
      1. 10.1 Introduction
      2. 10.2 Transformation
      3. 10.3 GLM
      4. 10.4 Regression with Generalized Distributions
      5. 10.5 Median Regression
      6. 10.6 Appendix A. Tail Measure
      7. 10.7 Appendix B. Information Matrix for GB2 Regression
      8. References
    5. 11 Spatial Modeling
      1. 11.1 Introduction
      2. 11.2 Exploratory Analysis of Spatial Data
      3. 11.3 Spatial Autoregression
      4. 11.4 Average Claim Size Modeling
      5. 11.5 Hierarchical Model for Total Loss
      6. 11.6 Discussion and Conclusion
      7. References
    6. 12 Unsupervised Learning
      1. 12.1 Introduction
      2. 12.2 Datasets
      3. 12.3 Factor and Principal Components Analysis
      4. 12.4 Cluster Analysis
      5. 12.5 Exercises
      6. References
  12. III Bayesian and Mixed Modeling
    1. 13 Bayesian Computational Methods
      1. 13.1 Why Bayesian?
      2. 13.2 Personal Automobile Claims Modeling
      3. 13.3 Basics of Bayesian Statistics
      4. 13.4 Computational Methods
      5. 13.5 Prior Distributions
      6. 13.6 Conclusion
      7. 13.7 Further Reading
      8. References
    2. 14 Bayesian Regression Models
      1. 14.1 Introduction
      2. 14.2 The Bayesian Paradigm
      3. 14.3 Generalized Linear Models
      4. 14.4 Mixed and Hierarchical Models
      5. 14.5 Nonparametric Regression
      6. 14.6 Appendix. Formal Definition of a Polya Tree
      7. References
    3. 15 Generalized Additive Models and Nonparametric Regression
      1. 15.1 Motivation for Generalized Additive Models and Nonparametric Regression
      2. 15.2 Additive Models for Nonparametric Regression
      3. 15.3 The Generalized Additive Model
      4. 15.4 Conclusion
      5. References
    4. 16 Nonlinear Mixed Models
      1. 16.1 Introduction
      2. 16.2 Model Families for Multilevel Non-Gaussian Data
      3. 16.3 Generalized Linear Mixed Models
      4. 16.4 Nonlinear Mixed Models
      5. 16.5 Bayesian Approach to (L,GL,NL)MMs
      6. 16.6 Example: Poisson Regression for Workers’ Compensation Insurance Frequencies
      7. References
  13. IV Longitudinal Modeling
    1. 17 Time Series Analysis
      1. 17.1 Exploring Time Series Data
      2. 17.2 Modeling Foundations
      3. 17.3 Autoregressive, Moving Average (ARMA) Models
      4. 17.4 Additional Time Series Models
      5. 17.5 Further Reading
      6. References
    2. 18 Claims Triangles/Loss Reserves
      1. 18.1 Introduction to Loss Reserving
      2. 18.2 The Chain Ladder
      3. 18.3 Models of Aggregate Claims Triangles
      4. 18.4 Models of Individual Claims
      5. References
    3. 19 Survival Models
      1. 19.1 Survival Distribution Notation
      2. 19.2 Survival Data Censoring and Truncation
      3. 19.3 National Nursing Home Survey
      4. 19.4 Nonparametric Estimation of the Survival Function
      5. 19.5 Proportional Hazards Model
      6. 19.6 Parametric Survival Modeling
      7. 19.7 Further Reading
      8. 19.8 Exercises
      9. 19.9 Appendix. National Nursing Home Survey Data
      10. References
    4. 20 Transition Modeling
      1. 20.1 Multistate Models and Their Actuarial Applications
      2. 20.2 Describing a Multistate Model
      3. 20.3 Estimating the Transition Intensity Functions
      4. 20.4 Estimating the Transition Intensities with Outcomes Observed at Distinct Time Points
      5. References
  14. Index