Predictive Modeling Applications in Actuarial Science Volume 1, Predictive Modeling Techniques 1st Edition by Edward Frees ISBN 1139989995 9781139989992

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ISBN 10: 1139989995 
ISBN 13: 9781139989992
Author: Edward W. Frees 

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.

Predictive Modeling Applications in Actuarial Science Volume 1, Predictive Modeling Techniques 1st Table of contents:

1 Predictive Modeling in Actuarial Science

1.1 Introduction

1.2 Predictive Modeling and Insurance Company Operations

1.3 A Short History of Predictive Modeling in Actuarial Science

1.4 Goals of the Series

References

I Predictive Modeling Foundations

2 Overview of Linear Models

2.1 Introduction

2.2 Linear Model Theory with Examples

2.3 Case Study

2.4 Conclusion

2.5 Exercises

References

3 Regression with Categorical Dependent Variables

3.1 Coding Categorical Variables

3.2 Modeling a Binary Response

3.3 Logistic Regression Model

3.4 Probit and Other Binary Regression Models

3.5 Models for Ordinal Categorical Dependent Variables

3.6 Models for Nominal Categorical Dependent Variables

3.7 Further Reading

References

4 Regression with Count-Dependent Variables

4.1 Introduction

4.2 Poisson Distribution

4.3 Poisson Regression

4.4 Heterogeneity in the Distribution

4.5 Zero-Inflated Distribution

4.6 Conclusion

4.7 Further Reading

References

5 Generalized Linear Models

5.1 Introduction to Generalized Linear Models

5.2 Exponential Family of Distributions

5.3 Link Functions

5.4 Maximum Likelihood Estimation

5.5 Generalized Linear Model Review

5.6 Applications

5.7 Comparing Models

5.8 Conclusion

5.9 Appendix A. Binomial and Gamma Distributions in Exponential Family Form

5.10 Appendix B. Calculating Mean and Variance from Exponential Family Form

References

6 Frequency and Severity Models

6.1 How Frequency Augments Severity Information

6.2 Sampling and the Generalized Linear Model

6.3 Frequency-Severity Models

6.4 Application: Massachusetts Automobile Claims

6.5 Further Reading

6.6 Appendix A. Sample Average Distribution in Linear Exponential Families

6.7 Appendix B. Over-Sampling Claims

References

II Predictive Modeling Methods

7 Longitudinal and Panel Data Models

7.1 Introduction

7.2 Linear Models

7.3 Nonlinear Models

7.4 Additional Considerations

7.5 Further Reading

References

8 Linear Mixed Models

8.1 Mixed Models in Actuarial Science

8.2 Linear Mixed Models

8.3 Examples

8.4 Further Reading and Illustrations

References

9 Credibility and Regression Modeling

9.1 Introduction

9.2 Credibility and the LMM Framework

9.3 Numerical Examples

9.4 Theory versus Practice

9.5 Further Reading

9.6 Appendix

References

10 Fat-Tailed Regression Models

10.1 Introduction

10.2 Transformation

10.3 GLM

10.4 Regression with Generalized Distributions

10.5 Median Regression

10.6 Appendix A. Tail Measure

10.7 Appendix B. Information Matrix for GB2 Regression

References

11 Spatial Modeling

11.1 Introduction

11.2 Exploratory Analysis of Spatial Data

11.3 Spatial Autoregression

11.4 Average Claim Size Modeling

11.5 Hierarchical Model for Total Loss

11.6 Discussion and Conclusion

References

12 Unsupervised Learning

12.1 Introduction

12.2 Datasets

12.3 Factor and Principal Components Analysis

12.4 Cluster Analysis

12.5 Exercises

References

III Bayesian and Mixed Modeling

13 Bayesian Computational Methods

13.1 Why Bayesian?

13.2 Personal Automobile Claims Modeling

13.3 Basics of Bayesian Statistics

13.4 Computational Methods

13.5 Prior Distributions

13.6 Conclusion

13.7 Further Reading

References

14 Bayesian Regression Models

14.1 Introduction

14.2 The Bayesian Paradigm

14.3 Generalized Linear Models

14.4 Mixed and Hierarchical Models

14.5 Nonparametric Regression

14.6 Appendix. Formal Definition of a Polya Tree

References

15 Generalized Additive Models and Nonparametric Regression

15.1 Motivation for Generalized Additive Models and Nonparametric Regression

15.2 Additive Models for Nonparametric Regression

15.3 The Generalized Additive Model

15.4 Conclusion

References

16 Nonlinear Mixed Models

16.1 Introduction

16.2 Model Families for Multilevel Non-Gaussian Data

16.3 Generalized Linear Mixed Models

16.4 Nonlinear Mixed Models

16.5 Bayesian Approach to (L,GL,NL)MMs

16.6 Example: Poisson Regression for Workers’ Compensation Insurance Frequencies

References

IV Longitudinal Modeling

17 Time Series Analysis

17.1 Exploring Time Series Data

17.2 Modeling Foundations

17.3 Autoregressive, Moving Average (ARMA) Models

17.4 Additional Time Series Models

17.5 Further Reading

References

18 Claims Triangles/Loss Reserves

18.1 Introduction to Loss Reserving

18.2 The Chain Ladder

18.3 Models of Aggregate Claims Triangles

18.4 Models of Individual Claims

References

19 Survival Models

19.1 Survival Distribution Notation

19.2 Survival Data Censoring and Truncation

19.3 National Nursing Home Survey

19.4 Nonparametric Estimation of the Survival Function

19.5 Proportional Hazards Model

19.6 Parametric Survival Modeling

19.7 Further Reading

19.8 Exercises

19.9 Appendix. National Nursing Home Survey Data

References

20 Transition Modeling

20.1 Multistate Models and Their Actuarial Applications

20.2 Describing a Multistate Model

20.3 Estimating the Transition Intensity Functions

20.4 Estimating the Transition Intensities with Outcomes Observed at Distinct Time Points

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