Actuarial Notes

An Example of Credibility and Shifting Risk Parameters

By Howard C. Mahler · Casualty Actuarial Society · 1990

Study guide: Exam 8

A paper that uses the won-lost record of baseball teams to examine and illustrate credibility concepts, an example analogous to the use of experience rating in insurance. It illustrates a situation where the phenomenon of shifting parameters over time has a very significant impact, and examines three criteria for selecting the optimal credibility: least squares, limited fluctuation and Meyers/Dorweiler.

On the syllabus

  • Exam 8 — objectives A2, A4; PCAS LXXVII, 1990, pp. 225–282; candidates will not be tested on the appendices.

1 Introduction

2 Credibility and Experience Rating

  • 2.1 Shifting Parameters Over Time

3 The Data Sets

  • 3.1 Advantages of this Data

4 Analysis of the General Structure of Data

  • 4.1 Is There an Inherent Difference Between Teams?
  • 4.2 Shifting Parameters Over Time

5 Statement of the Problem

6 Simple Solutions to the Problem

  • 6.1 Every Risk is Average
  • 6.2 The Most Recent Year Repeats
  • 6.3 Credibility Weight the Most Recent Year and the Grand Mean
  • 6.4 Determining the Credibility
  • 6.5 Equal Weight to the N Most Recent Years of Data

7 Criteria to Decide Between Solutions

  • 7.1 Least Squared Error
  • 7.2 Small Chance of Large Errors
  • 7.3 Meyers/Dorweiler

8 The Criteria Applied to the Simple Solutions

  • 8.1 The Two Base Cases
  • 8.2 Applying Credibility to the Latest Year of Data
  • 8.3 Applying Credibility to the Latest N Years of Data
  • 8.4 Comparison of the Results of the Three Criteria
  • 8.5 Putting the Reduction in Squared Error in Context
  • 8.6 Effect of Delay in Receiving Data

9 More General Solutions

  • 9.1 Combine Previous Estimate and Most Recent Data
  • 9.2 More General Varying Weights

10 The Criteria Applied to the More General Solutions

  • 10.1 Geometrically Decreasing Weights
  • 10.2 More General Varying Weights

11 Equations for Least Squares Credibilities

  • 11.1 The Covariance Structure
  • 11.2 Matrix Equations for Least Squares Credibilities
  • 11.3 Placing No Weight on the Grand Mean
  • 11.4 Mean Squared Error
  • 11.5 Validity of Results

12 Miscellaneous

  • 12.1 Contrasting the Meyers/Dorweiler Criterion vs. the Other Criteria
  • 12.2 A Ratemaking Example
  • 12.3 Baseball Example vs. Typical Insurance Applications
  • 12.4 Estimates in Balance
  • 12.5 Choice of a Prediction Method

13 Conclusions

References

Appendix A Some Relevant Features of Baseball

Appendix B Meyers/Dorweiler Criterion and Kendall's Tau

Appendix C Matrix Equations for Least Squares Credibility

Appendix D Covariance Structure

Appendix E Putting the Reduction in Squared Error in Context

Appendix F Squared Errors

Appendix G The Second Criterion and Limited Fluctuation Credibility

Sources